Bundle: Calculus: Early Transcendentals, Loose-Leaf Version, 8th + WebAssign Printed Access Card for Stewart's Calculus: Early Transcendentals, 8th Edition, Multi-Term
8th Edition
ISBN: 9781305616691
Author: James Stewart
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 1.4, Problem 2E
Use the Law of Exponents to rewrite and simplify the expression.
2. (a) 84/3
(b) x(3x2)3
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Evaluate the definite integral using the given integration limits and the limits obtained by trigonometric substitution.
14
x²
dx
249
(a) the given integration limits
(b) the limits obtained by trigonometric substitution
Assignment #1
Q1: Test the following series for convergence. Specify the test you use:
1
n+5
(-1)n
a) Σn=o
√n²+1
b) Σn=1 n√n+3
c) Σn=1 (2n+1)3
3n
1
d) Σn=1 3n-1
e) Σn=1
4+4n
answer problem 1a, 1b, 1c, 1d, and 1e and show work/ explain how you got the answer
Chapter 1 Solutions
Bundle: Calculus: Early Transcendentals, Loose-Leaf Version, 8th + WebAssign Printed Access Card for Stewart's Calculus: Early Transcendentals, 8th Edition, Multi-Term
Ch. 1.1 - If f(x)=x+2x and g(u)=u+2u, is it true that f = g?Ch. 1.1 - If f(x)=x2xx1andg(x)=x is it true that f = g?Ch. 1.1 - The graph of a function f is given. (a) State the...Ch. 1.1 - The graphs of f and g are given. (a) State the...Ch. 1.1 - Figure 1 was recorded by an instrument operated by...Ch. 1.1 - Determine whether the curve is the graph of a...Ch. 1.1 - Determine whether the curve is the graph of a...Ch. 1.1 - Determine whether the curve is the graph of a...Ch. 1.1 - Determine whether the curve is the graph of a...Ch. 1.1 - Shown is a graph of the global average temperature...
Ch. 1.1 - Trees grow faster and form wider rings in warm...Ch. 1.1 - You put some ice cubes in a glass, fill the glass...Ch. 1.1 - Three runners compete in a 100-meter race. The...Ch. 1.1 - The graph shows the power consumption for a day in...Ch. 1.1 - Sketch a rough graph of the number of hours of...Ch. 1.1 - Sketch a rough graph of the outdoor temperature as...Ch. 1.1 - Sketch a rough graph of the market value of a new...Ch. 1.1 - Sketch the graph of the amount of a particular...Ch. 1.1 - You place a frozen pie in an oven and bake it for...Ch. 1.1 - A homeowner mows the lawn every Wednesday...Ch. 1.1 - An airplane takes off from an airport and lands an...Ch. 1.1 - Temperature readings T (in F) were recorded every...Ch. 1.1 - Researchers measured the blood alcohol...Ch. 1.1 - If f(x) = 3x2 x + 2, find f(2), f(2), f(a), f(a),...Ch. 1.1 - A spherical balloon with radius r inches has...Ch. 1.1 - Evaluate the difference quotient for the given...Ch. 1.1 - Evaluate the difference quotient for the given...Ch. 1.1 - Evaluate the difference quotient for the given...Ch. 1.1 - Evaluate the difference quotient for the given...Ch. 1.1 - Find the domain of the function. 31. f(x)=x+4x29Ch. 1.1 - Find the domain of the function. 32....Ch. 1.1 - Find the domain of the function. 33. f(t)=2t13Ch. 1.1 - Find the domain of the function. 34. g(t)=3t2+tCh. 1.1 - Find the domain of the function. 35. h(x)=1x25x4Ch. 1.1 - Find the domain of the function. 36....Ch. 1.1 - Find the domain of the function. 37. F(p)=2pCh. 1.1 - Find the domain and range and sketch the graph of...Ch. 1.1 - Find the domain and sketch the graph of the...Ch. 1.1 - Find the domain and sketch the graph of the...Ch. 1.1 - Evaluate f(3), f(0), and f(2) for the piecewise...Ch. 1.1 - Evaluate f(3), f(0), and f(2) for the piecewise...Ch. 1.1 - Evaluate f(3), f(0), and f(2) for the piecewise...Ch. 1.1 - Evaluate f(3), f(0), and f(2) for the piecewise...Ch. 1.1 - Sketch the graph of the function. 45. f(x) = x +...Ch. 1.1 - Sketch the graph of the function. 46. f(x) = |x +...Ch. 1.1 - Sketch the graph of the function. 47. g(t) = |1 ...Ch. 1.1 - Sketch the graph of the function. 48. h(t) = |t| +...Ch. 1.1 - Sketch the graph of the function. 49....Ch. 1.1 - Sketch the graph of the function. 50. g(x) = ||x| ...Ch. 1.1 - Find an expression for the function whose graph is...Ch. 1.1 - Find an expression for the function whose graph is...Ch. 1.1 - Find an expression for the function whose graph is...Ch. 1.1 - Find an expression for the function whose graph is...Ch. 1.1 - Find an expression for the function whose graph is...Ch. 1.1 - Find an expression for the function whose graph is...Ch. 1.1 - Find a formula for the described function and...Ch. 1.1 - Find a formula for the described function and...Ch. 1.1 - Find a formula for the described function and...Ch. 1.1 - Find a formula for the described function and...Ch. 1.1 - Find a formula for the described function and...Ch. 1.1 - A Norman window has the shape of a rectangle...Ch. 1.1 - A box with an open top is to be constructed from a...Ch. 1.1 - A cell phone plan has a basic charge of 35 a...Ch. 1.1 - In a certain state the maximum speed permitted on...Ch. 1.1 - An electricity company charges its customers a...Ch. 1.1 - In a certain country, income tax is assessed as...Ch. 1.1 - The functions in Example 10 and Exercise 67 are...Ch. 1.1 - Graphs of f and g are shown. Decide whether each...Ch. 1.1 - Graphs of f and g are shown. Decide whether each...Ch. 1.1 - (a) If the point (5, 3) is on the graph of an even...Ch. 1.1 - A function f has domain [5, 5] and a portion of...Ch. 1.1 - Determine whether f is even, odd, or neither. If...Ch. 1.1 - Determine whether f is even, odd, or neither. If...Ch. 1.1 - Determine whether f is even, odd, or neither. If...Ch. 1.1 - Determine whether f is even, odd, or neither. If...Ch. 1.1 - Determine whether f is even, odd, or neither. If...Ch. 1.1 - Determine whether f is even, odd, or neither. If...Ch. 1.1 - If f and g are both even functions, is f + g even?...Ch. 1.1 - If f and g are both even functions, is the product...Ch. 1.2 - Classify each function as a power function, root...Ch. 1.2 - Classify each function as a power function, root...Ch. 1.2 - Match each equation with its graph. Explain your...Ch. 1.2 - Match each equation with its graph. Explain your...Ch. 1.2 - Find the domain of the function. 5. f(x)=cosx1sinxCh. 1.2 - Find the domain of the function. 6. g(x)=11tanxCh. 1.2 - (a) Find an equation for the family of linear...Ch. 1.2 - What do all members of the family of linear...Ch. 1.2 - What do all members of the family of linear...Ch. 1.2 - Find expressions for the quadratic functions whose...Ch. 1.2 - Find an expression for a cubic function f if...Ch. 1.2 - Recent studies indicate that the average surface...Ch. 1.2 - If the recommended adult dosage for a drug is D...Ch. 1.2 - The manager of a weekend flea market knows from...Ch. 1.2 - The relationship between the Fahrenheit (F) and...Ch. 1.2 - Jason leaves Detroit at 2:00 PM and drives at a...Ch. 1.2 - Biologists have noticed that the chirping rate of...Ch. 1.2 - The manager of a furniture factory finds that it...Ch. 1.2 - At the surface of the ocean, the water pressure is...Ch. 1.2 - The monthly cost of driving a car depends on the...Ch. 1.2 - For each scatter plot, decide what type of...Ch. 1.2 - For each scatter plot, decide what type of...Ch. 1.3 - Suppose the graph of f is given. Write equations...Ch. 1.3 - Explain how each graph is obtained from the graph...Ch. 1.3 - The graph of y=f(x) is given. Match each equation...Ch. 1.3 - The graph of f is given. Draw the graphs of the...Ch. 1.3 - The graph of f is given. Use it to graph the...Ch. 1.3 - The graph of y=3xx2 is given. Use transformations...Ch. 1.3 - The graph of y=3xx2 is given. Use transformations...Ch. 1.3 - (a) How is the graph of y = 2 sin x related to the...Ch. 1.3 - Graph the function by hand, not by plotting...Ch. 1.3 - Prob. 10ECh. 1.3 - Graph the function by hand, not by plotting...Ch. 1.3 - Graph the function by hand, not by plotting...Ch. 1.3 - Graph the function by hand, not by plotting...Ch. 1.3 - Graph the function by hand, not by plotting...Ch. 1.3 - Graph the function by hand, not by plotting...Ch. 1.3 - Graph the function by hand, not by plotting...Ch. 1.3 - Graph the function by hand, not by plotting...Ch. 1.3 - Prob. 18ECh. 1.3 - Graph the function by hand, not by plotting...Ch. 1.3 - Graph the function by hand, not by plotting...Ch. 1.3 - Prob. 21ECh. 1.3 - Prob. 22ECh. 1.3 - Prob. 23ECh. 1.3 - Prob. 24ECh. 1.3 - The city of New Orleans is located at latitude...Ch. 1.3 - A variable star is one whose brightness...Ch. 1.3 - Some of the highest tides in the world occur in...Ch. 1.3 - In a normal respiratory cycle the volume of air...Ch. 1.3 - (a) How is the graph of y=f(|x|)related to the...Ch. 1.3 - Use the given graph of f to sketch the graph of y...Ch. 1.3 - Prob. 31ECh. 1.3 - Find (a) f + g, (b) f g, (c) fg, and (d) f/g and...Ch. 1.3 - Find the functions (a) fg, (b) gf, (c) ff, and (d)...Ch. 1.3 - Find the functions (a) fg, (b) gf, (c) ff, and (d)...Ch. 1.3 - Find the functions (a) fg, (b) gf, (c) ff, and (d)...Ch. 1.3 - Prob. 36ECh. 1.3 - Find the functions (a) f g, (b) g f, (c) f f,...Ch. 1.3 - Find the functions (a) f g, (b) g f, (c) f f,...Ch. 1.3 - Find f g h. 39. f(x) = 3x 2, g (x) = sin x,...Ch. 1.3 - Prob. 40ECh. 1.3 - Find f g h. 41.f(x)=x3, g(x) = x2, h(x) = x3 + 2Ch. 1.3 - Find f g h. 42. f(x) = tan x, g(x)=xx1,h(x)=x3Ch. 1.3 - Express the function in the form f g. 43. F(x) =...Ch. 1.3 - Express the function in the form f g. 44. F(x) =...Ch. 1.3 - Prob. 45ECh. 1.3 - Prob. 46ECh. 1.3 - Express the function in the form f g. 47. v(t) =...Ch. 1.3 - Prob. 48ECh. 1.3 - Prob. 49ECh. 1.3 - Prob. 50ECh. 1.3 - Prob. 51ECh. 1.3 - Use the table to evaluate each expression. (a)...Ch. 1.3 - Use the given graphs of f and g to evaluate each...Ch. 1.3 - Use the given graphs of f and g to estimate the...Ch. 1.3 - A stone is dropped into a lake, creating a...Ch. 1.3 - A spherical balloon is being inflated and the...Ch. 1.3 - Prob. 57ECh. 1.3 - An airplane is flying at a speed of 350 mi/h at an...Ch. 1.3 - The Heaviside function H is defined by It is used...Ch. 1.3 - The Heaviside function defined in Exercise 59 can...Ch. 1.3 - Let f and g be linear functions with equations...Ch. 1.3 - Prob. 62ECh. 1.3 - (a) If g(x) = 2x + 1 and h(x) = 4x2 + 4x + 7, find...Ch. 1.3 - If f(x) = x + 4 and h(x) = 4x 1, find a function...Ch. 1.3 - Suppose g is an even function and let h =f g. Is...Ch. 1.3 - Suppose g is an odd function and let h = f g. Is...Ch. 1.4 - Use the Law of Exponents to rewrite and simplify...Ch. 1.4 - Use the Law of Exponents to rewrite and simplify...Ch. 1.4 - Use the Law of Exponents to rewrite and simplify...Ch. 1.4 - Use the Law of Exponents to rewrite and simplify...Ch. 1.4 - (a) Write an equation that defines the exponential...Ch. 1.4 - (a) How is the number e defined? (b) What is an...Ch. 1.4 - Graph the given functions on a common screen. How...Ch. 1.4 - Graph the given functions on a common screen. How...Ch. 1.4 - Graph the given functions on a common screen. How...Ch. 1.4 - Graph the given functions on a common screen. How...Ch. 1.4 - Make a rough sketch of the graph of the function....Ch. 1.4 - Make a rough sketch of the graph of the function....Ch. 1.4 - Make a rough sketch of the graph of the function....Ch. 1.4 - Make a rough sketch of the graph of the function....Ch. 1.4 - Make a rough sketch of the graph of the function....Ch. 1.4 - Make a rough sketch of the graph of the function....Ch. 1.4 - Starting with the graph of y = ex, write the...Ch. 1.4 - Starting with the graph of y = ex, find the...Ch. 1.4 - Find the domain of each function. 19. (a)...Ch. 1.4 - Find the domain of each function. 20. (a)...Ch. 1.4 - Find the exponential function f(x) = Cb2 whose...Ch. 1.4 - Find the exponential function f(x) = Cbx whose...Ch. 1.4 - If f(x) = 5x, show that f(x+h)f(x)h=5x(5h1h)Ch. 1.4 - Suppose you are offered a job that lasts one...Ch. 1.4 - Prob. 25ECh. 1.4 - Compare the functions f(x) = x5and g(x) = 5x by...Ch. 1.4 - Compare the functions f(x) = x10 and g(x) = ex by...Ch. 1.4 - Use a graph to estimate the values of x such that...Ch. 1.4 - A bacteria culture starts with 500 bacteria and...Ch. 1.4 - The half-life of bismuth-210, 210Bi, is 5 days....Ch. 1.4 - An isotope of sodium, 24Na, has a half-life of 15...Ch. 1.4 - Prob. 33ECh. 1.4 - After alcohol is fully absorbed into the body, it...Ch. 1.4 - Use a graphing calculator with exponential...Ch. 1.4 - The table gives the population of the United...Ch. 1.4 - If you graph the function f(x)=1e1/x1+e1/x you' ll...Ch. 1.4 - Graph several members of the family of functions...Ch. 1.5 - (a) What is a one-to-one function? (b) How can you...Ch. 1.5 - (a) Suppose f is a one-to-one function with domain...Ch. 1.5 - A function is given by a table of values, a graph,...Ch. 1.5 - A function is given by a table of values, a graph,...Ch. 1.5 - A function is given by a table of values, a graph,...Ch. 1.5 - A function is given by a table of values, a graph,...Ch. 1.5 - A function is given by a table of values, a graph,...Ch. 1.5 - A function is given by a table of values, a graph,...Ch. 1.5 - A function is given by a table of values, a graph,...Ch. 1.5 - A function is given by a table of values, a graph,...Ch. 1.5 - A function is given by a table of values, a graph,...Ch. 1.5 - A function is given by a table of values, a graph,...Ch. 1.5 - A function is given by a table of values, a graph,...Ch. 1.5 - A function is given by a table of values, a graph,...Ch. 1.5 - Assume that f is a one-to-one function. (a) If...Ch. 1.5 - If f(x) = x5 + x3 + x, find f1(3) and f(f 1(2)).Ch. 1.5 - If g(x) = 3 + x + ex, find g1(4).Ch. 1.5 - The graph of f is given. (a) Why is f one-to-one?...Ch. 1.5 - The formula C=59(F32), where F 459.67, expresses...Ch. 1.5 - In the theory of relativity, the mass of a...Ch. 1.5 - Find a formula for the inverse of the function....Ch. 1.5 - Find a formula for the inverse of the function....Ch. 1.5 - Find a formula for the inverse of the function....Ch. 1.5 - Find a formula for the inverse of the function....Ch. 1.5 - Find a formula for the inverse of the function....Ch. 1.5 - Find a formula for the inverse of the function....Ch. 1.5 - Find an explicit formula for f1 and use it to...Ch. 1.5 - Find an explicit formula for f1 and use it to...Ch. 1.5 - Prob. 29ECh. 1.5 - Use the given graph of f to sketch the graph of...Ch. 1.5 - Let f(x)=1x2,0x1. (a) Find f1. How is it related...Ch. 1.5 - Prob. 32ECh. 1.5 - Prob. 33ECh. 1.5 - (a) What is the natural logarithm? (b) What is the...Ch. 1.5 - Find the exact value of each expression. 35. (a)...Ch. 1.5 - Find the exact value of each expression. 35. (a)...Ch. 1.5 - Find the exact value of each expression. 37. (a)...Ch. 1.5 - Find the exact value of each expression. 38. (a)...Ch. 1.5 - Express the given quantity as a single logarithm....Ch. 1.5 - Express the given quantity as a single logarithm....Ch. 1.5 - Express the given quantity as a single logarithm....Ch. 1.5 - Use Formula 10 to evaluate each logarithm correct...Ch. 1.5 - Use Formula 10 to graph the given functions on a...Ch. 1.5 - Use Formula 10 to graph the given functions on a...Ch. 1.5 - Suppose that the graph of y = log2 x is drawn on a...Ch. 1.5 - Prob. 46ECh. 1.5 - Prob. 47ECh. 1.5 - Prob. 48ECh. 1.5 - (a) What are the domain and range of f? (b) What...Ch. 1.5 - (a) What are the domain and range of f? (b) What...Ch. 1.5 - Solve each equation for x. 51. (a) e74x=6 (b)...Ch. 1.5 - Solve each equation for x. 52. (a) ln(x2 1) = 3...Ch. 1.5 - Solve each equation for x. 53. (a) 2x5 = 3 (b) ln...Ch. 1.5 - Solve each equation for x. 54. (a) ln(ln x) = 1...Ch. 1.5 - Solve each inequality for x. 55. (a) ln x 0 (b)...Ch. 1.5 - Solve each inequality for x. 56. (a) 1 e3x1 2...Ch. 1.5 - (a) Find the domain of f(x) = ln(ex 3). (b) Find...Ch. 1.5 - (a) What are the values of eln 300 and ln(e300)?...Ch. 1.5 - If a bacteria population starts with 100 bacteria...Ch. 1.5 - When a camera flash goes off, the batteries...Ch. 1.5 - Find the exact value of each expression. 63. (a)...Ch. 1.5 - Find the exact value of each expression. 64. (a)...Ch. 1.5 - Prob. 65ECh. 1.5 - Find the exact value of each expression. 66. (a)...Ch. 1.5 - Find the exact value of each expression. 67. (a)...Ch. 1.5 - Find the exact value of each expression. 68. (a)...Ch. 1.5 - Prove that cos(sin1x)=1x2.Ch. 1.5 - Simplify the expression. 70. tan(sin1 x)Ch. 1.5 - Simplify the expression. 71. sin(tan1 x)Ch. 1.5 - Simplify the expression. 72. sin(2 arccos x)Ch. 1.5 - Prob. 73ECh. 1.5 - Prob. 74ECh. 1.5 - Find the domain and range of the function g(x) =...Ch. 1.5 - (a) Graph the function f(x) = sin(sin1 x) and...Ch. 1.5 - (a) If we shift a curve to the left, what happens...Ch. 1 - (a) What is a function? What are its domain and...Ch. 1 - Discuss four ways of representing a function....Ch. 1 - (a) What is an even function? How can you tell if...Ch. 1 - What is an increasing function?Ch. 1 - What is a mathematical model?Ch. 1 - Give an example of each type of function. (a)...Ch. 1 - Sketch by hand, on the same axes, the graphs of...Ch. 1 - Draw, by hand, a rough sketch of the graph of each...Ch. 1 - Suppose that f has domain A and g has domain B....Ch. 1 - How is the composite function f g defined? What...Ch. 1 - Suppose the graph of f is given. Write an equation...Ch. 1 - (a) What is a one-to-one function? How can you...Ch. 1 - (a) How is the inverse sine function f(x) = sin1 x...Ch. 1 - Determine whether the statement is true or false....Ch. 1 - Determine whether the statement is true or false....Ch. 1 - Determine whether the statement is true or false....Ch. 1 - Determine whether the statement is true or false....Ch. 1 - Determine whether the statement is true or false....Ch. 1 - Determine whether the statement is true or false....Ch. 1 - Determine whether the statement is true or false....Ch. 1 - Determine whether the statement is true or false....Ch. 1 - Determine whether the statement is true or false....Ch. 1 - Determine whether the statement is true or false....Ch. 1 - Determine whether the statement is true or false....Ch. 1 - Determine whether the statement is true or false....Ch. 1 - Determine whether the statement is true or false....Ch. 1 - Determine whether the statement is true or false....Ch. 1 - Let f be the function whose graph is given. (a)...Ch. 1 - The graph of g is given. (a) State the value of...Ch. 1 - lf f(x) = x2 2x + 3, evaluate the difference...Ch. 1 - Sketch a rough graph or the yield of a crop as a...Ch. 1 - Find the domain and range of the function. Write...Ch. 1 - Find the domain and range of the function. Write...Ch. 1 - Prob. 7RECh. 1 - Find the domain and range of the function. Write...Ch. 1 - Prob. 9RECh. 1 - The graph of .f is given. Draw the graphs of the...Ch. 1 - Prob. 11RECh. 1 - Use transformations to sketch the graph of the...Ch. 1 - Prob. 13RECh. 1 - Use transformations to sketch the graph of the...Ch. 1 - Use transformations to sketch the graph of the...Ch. 1 - Use transformations to sketch the graph of the...Ch. 1 - Determine whether f is even, odd, or neither even...Ch. 1 - Find an expression for the function whose graph...Ch. 1 - If f(x) = In x and g(x) = x2 9. find the...Ch. 1 - Express the function F(x)=1/x+x as a composition...Ch. 1 - A small-appliance manufacturer finds that it costs...Ch. 1 - If f(x) = 2x + In x, find f1(2).Ch. 1 - Find the inverse function of f(x)=x+12x+1.Ch. 1 - Find the exact value of each expression. 64. (a)...Ch. 1 - Prob. 26RECh. 1 - The half-life of palladium-100, 100Pd, is four...Ch. 1 - The population of a certain species in a limited...Ch. 1 - One of the legs of a right triangle has length 4...Ch. 1 - The altitude perpendicular to the hypotenuse of a...Ch. 1 - Solve the equation |2x 1| |x + 5| = 3.Ch. 1 - Solve the inequality |x 1| |x 3| 5.Ch. 1 - Prob. 5PCh. 1 - Sketch the graph of the function g(x) = |x2 1 | ...Ch. 1 - Prob. 7PCh. 1 - Prob. 8PCh. 1 - The notation max{a, b, } means the largest of the...Ch. 1 - Sketch the region in the plane defined by each of...Ch. 1 - Evaluate (log2 3)(log3 4)(log4 5)(log31 32).Ch. 1 - (a) Show that the function f(x)=ln(x+x2+1) is an...Ch. 1 - Solve the inequality ln(x2 2x 2) 0.Ch. 1 - Use indirect reasoning to prove that log2 5 is an...Ch. 1 - A driver sets out on a journey. For the first half...Ch. 1 - Is it true that f(g+h)=fg+fh?Ch. 1 - Prove that if n is a positive integer, then 7n 1...Ch. 1 - Prove that 1 + 3 + 5 + + (2n l ) = n2.Ch. 1 - If fo(x) = x2 and fn+1(x) = fo(fn(x)) for n = 0,...Ch. 1 - (a) If fo(x)=12x and fn+1=fofnforn=0,1,2,, find an...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Similar questions
- Provethat a) prove that for any irrational numbers there exists? asequence of rational numbers Xn converg to S. b) let S: RR be a sunctions-t. f(x)=(x-1) arc tan (x), xe Q 3(x-1) 1+x² x&Q Show that lim f(x)= 0 14x C) For any set A define the set -A=yarrow_forwardQ2: Find the interval and radius of convergence for the following series: Σ n=1 (-1)η-1 xn narrow_forward8. Evaluate arctan x dx a) xartanx 2 2 In(1 + x²) + C b) xartanx + 1½-3ln(1 + x²) + C c) xartanx + In(1 + x²) + C d) (arctanx)² + C 2 9) Evaluate Inx³ dx 3 a) +C b) ln x² + C c)¾½ (lnx)² d) 3x(lnx − 1) + C - x 10) Determine which integral is obtained when the substitution x = So¹² √1 - x²dx sine is made in the integral πT π π a) √ sin cos e de b) √ cos² de c) c Ꮎ Ꮎ cos² 0 de c) cos e de d) for cos² e de πT 11. Evaluate tan³xdx 1 a) b) c) [1 - In 2] 2 2 c) [1 − In2] d)½½[1+ In 2]arrow_forward12. Evaluate ſ √9-x2 -dx. x2 a) C 9-x2 √9-x2 - x2 b) C - x x arcsin ½-½ c) C + √9 - x² + arcsin x d) C + √9-x2 x2 13. Find the indefinite integral S cos³30 √sin 30 dᎾ . 2√√sin 30 (5+sin²30) √sin 30 (3+sin²30) a) C+ √sin 30(5-sin²30) b) C + c) C + 5 5 5 10 d) C + 2√√sin 30 (3-sin²30) 2√√sin 30 (5-sin²30) e) C + 5 15 14. Find the indefinite integral ( sin³ 4xcos 44xdx. a) C+ (7-5cos24x)cos54x b) C (7-5cos24x)cos54x (7-5cos24x)cos54x - 140 c) C - 120 140 d) C+ (7-5cos24x)cos54x e) C (7-5cos24x)cos54x 4 4 15. Find the indefinite integral S 2x2 dx. ex - a) C+ (x²+2x+2)ex b) C (x² + 2x + 2)e-* d) C2(x²+2x+2)e¯* e) C + 2(x² + 2x + 2)e¯* - c) C2x(x²+2x+2)e¯*arrow_forward4. Which substitution would you use to simplify the following integrand? S a) x = sin b) x = 2 tan 0 c) x = 2 sec 3√√3 3 x3 5. After making the substitution x = = tan 0, the definite integral 2 2 3 a) ៖ ស្លឺ sin s π - dᎾ 16 0 cos20 b) 2/4 10 cos 20 π sin30 6 - dᎾ c) Π 1 cos³0 3 · de 16 0 sin20 1 x²√x²+4 3 (4x²+9)2 π d) cos²8 16 0 sin³0 dx d) x = tan 0 dx simplifies to: de 6. In order to evaluate (tan 5xsec7xdx, which would be the most appropriate strategy? a) Separate a sec²x factor b) Separate a tan²x factor c) Separate a tan xsecx factor 7. Evaluate 3x x+4 - dx 1 a) 3x+41nx + 4 + C b) 31n|x + 4 + C c) 3 ln x + 4+ C d) 3x - 12 In|x + 4| + C x+4arrow_forward1. Abel's Theorem. The goal in this problem is to prove Abel's theorem by following a series of steps (each step must be justified). Theorem 0.1 (Abel's Theorem). If y1 and y2 are solutions of the differential equation y" + p(t) y′ + q(t) y = 0, where p and q are continuous on an open interval, then the Wronskian is given by W (¥1, v2)(t) = c exp(− [p(t) dt), where C is a constant that does not depend on t. Moreover, either W (y1, y2)(t) = 0 for every t in I or W (y1, y2)(t) = 0 for every t in I. 1. (a) From the two equations (which follow from the hypotheses), show that y" + p(t) y₁ + q(t) y₁ = 0 and y½ + p(t) y2 + q(t) y2 = 0, 2. (b) Observe that Hence, conclude that (YY2 - Y1 y2) + P(t) (y₁ Y2 - Y1 Y2) = 0. W'(y1, y2)(t) = yY2 - Y1 y2- W' + p(t) W = 0. 3. (c) Use the result from the previous step to complete the proof of the theorem.arrow_forward2. Observations on the Wronskian. Suppose the functions y₁ and y2 are solutions to the differential equation p(x)y" + q(x)y' + r(x) y = 0 on an open interval I. 1. (a) Prove that if y₁ and y2 both vanish at the same point in I, then y₁ and y2 cannot form a fundamental set of solutions. 2. (b) Prove that if y₁ and y2 both attain a maximum or minimum at the same point in I, then y₁ and Y2 cannot form a fundamental set of solutions. 3. (c) show that the functions & and t² are linearly independent on the interval (−1, 1). Verify that both are solutions to the differential equation t² y″ – 2ty' + 2y = 0. Then justify why this does not contradict Abel's theorem. 4. (d) What can you conclude about the possibility that t and t² are solutions to the differential equation y" + q(x) y′ + r(x)y = 0?arrow_forwardQuestion 4 Find an equation of (a) The plane through the point (2, 0, 1) and perpendicular to the line x = y=2-t, z=3+4t. 3t, (b) The plane through the point (3, −2, 8) and parallel to the plane z = x+y. (c) The plane that contains the line x = 1+t, y = 2 − t, z = 4 - 3t and is parallel to the plane 5x + 2y + z = 1. (d) The plane that passes through the point (1,2,3) and contains the line x = 3t, y = 1+t, and z = 2-t. (e) The plane that contains the lines L₁: x = 1 + t, y = 1 − t, z = 2t and L2 : x = 2 − s, y = s, z = 2.arrow_forwardPlease find all values of x.arrow_forward3. Consider the initial value problem 9y" +12y' + 4y = 0, y(0) = a>0: y′(0) = −1. Solve the problem and find the value of a such that the solution of the initial value problem is always positive.arrow_forward5. Euler's equation. Determine the values of a for which all solutions of the equation 5 x²y" + axy' + y = 0 that have the form (A + B log x) x* or Ax¹¹ + Bä” tend to zero as a approaches 0.arrow_forward4. Problem on variable change. The purpose of this problem is to perform an appropriate change of variables in order to reduce the problem to a second-order equation with constant coefficients. ty" + (t² − 1)y'′ + t³y = 0, 0arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell
Elementary AlgebraAlgebraISBN:9780998625713Author:Lynn Marecek, MaryAnne Anthony-SmithPublisher:OpenStax - Rice University
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGALAlgebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal LittellElementary AlgebraAlgebraISBN:9780998625713Author:Lynn Marecek, MaryAnne Anthony-SmithPublisher:OpenStax - Rice UniversityGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Probability & Statistics (28 of 62) Basic Definitions and Symbols Summarized; Author: Michel van Biezen;https://www.youtube.com/watch?v=21V9WBJLAL8;License: Standard YouTube License, CC-BY
Introduction to Probability, Basic Overview - Sample Space, & Tree Diagrams; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=SkidyDQuupA;License: Standard YouTube License, CC-BY