CALCULUS,VOLUME 1 (OER)
17th Edition
ISBN: 2810022307715
Author: OpenStax
Publisher: XANEDU C
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Textbook Question
Chapter 1.2, Problem 68E
For the following exercises, write the equation of the line satisfying the given conditions in slope-intercept form.
68. Slope = 3, passes through (-3. 2)
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Q5*) Write down an immediate first integral for the Euler-Lagrange equation for the integral
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Hence write down a first integral of the Euler-Lagrange equation for the integral
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Find the general solution of this ordinary differential equation, seeking first the complementary function and
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You are provided with three 2D data points, p1, p2 and p3. Solving A C = B for C provides youwith the coefficients of a natural cubic spline curve that interpolates these points.Additionally, you have been given A and B, but some elements are missing. Moreover, the last two rowsof A are entirely absent. Your task is to determine and fill in the missing elements. For the last two rows,enforce a zero tangent at the beginning (in p1) and a not-a-knot boundary condition in p2. The matricesA and B are given as follows:Explain how to find the entries of A and B . How would you adapt these matrices if the data pointswere 3D? What if your spline should go through five data points? How many “extra rows” would there thenbe (with “extra” meaning “in addition to securing C2-continuity”)?
Q2*) In question P3 we showed that a minimal surface of revolution is given by revolution (about the x-axis)
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Chapter 1 Solutions
CALCULUS,VOLUME 1 (OER)
Ch. 1.1 - For the following exercises, (a) determine the...Ch. 1.1 - For the following exercises, (a) determine the...Ch. 1.1 - For the following exercises, (a) determine the...Ch. 1.1 - For the following exercises, (a) determine the...Ch. 1.1 - For the following exercises, (a) determine the...Ch. 1.1 - For the following exercises, (a) determine the...Ch. 1.1 - For the following exercises, find the values for...Ch. 1.1 - For the following exercises, find the values for...Ch. 1.1 - For the following exercises, find the values for...Ch. 1.1 - For the following exercises, find the values for...
Ch. 1.1 - For the following exercises, find the values for...Ch. 1.1 - For the following exercises, find the values for...Ch. 1.1 - For the following exercises, find the values for...Ch. 1.1 - For the following exercises, find the domain,...Ch. 1.1 - For the following exercises, find the domain,...Ch. 1.1 - For the following exercises, find the domain,...Ch. 1.1 - For the following exercises, find the domain,...Ch. 1.1 - For the following exercises, find the domain,...Ch. 1.1 - For the following exercises, find the domain,...Ch. 1.1 - For the following exercises, find the domain,...Ch. 1.1 - For the following exercises, find the domain,...Ch. 1.1 - For the following exercises, set up a table to...Ch. 1.1 - For the following exercises, set up a table to...Ch. 1.1 - For the following exercises, set up a table to...Ch. 1.1 - For the following exercises, set up a table to...Ch. 1.1 - For the following exercises, set up a table to...Ch. 1.1 - For the following exercises, set up a table to...Ch. 1.1 - For the following exercises, use the vertical line...Ch. 1.1 - For the following exercises, use the vertical line...Ch. 1.1 - For the following exercises, use the vertical line...Ch. 1.1 - For the following exercises, use the vertical line...Ch. 1.1 - For the following exercises, use the vertical line...Ch. 1.1 - For the following exercises, use the vertical line...Ch. 1.1 - For the following exercises, use the vertical line...Ch. 1.1 - For the following exercises, use the vertical line...Ch. 1.1 - For the following exercises, for each pair of...Ch. 1.1 - For the following exercises, for each pair of...Ch. 1.1 - For the following exercises, for each pair of...Ch. 1.1 - For the following exercises, for each pair of...Ch. 1.1 - For the following exercises, for each pair of...Ch. 1.1 - For the following exercises, for each pair of...Ch. 1.1 - For the following exercises, for each pair of...Ch. 1.1 - For the following exercises, for each pair of...Ch. 1.1 - For the following exercises, for each pair of...Ch. 1.1 - For the following exercises, for each pair of...Ch. 1.1 - For the following exercises, for each pair of...Ch. 1.1 - For the following exercises, for each pair of...Ch. 1.1 - For the following exercises, for each pair of...Ch. 1.1 - The table below lists the NBA championship winners...Ch. 1.1 - The area A of a square depends on the length of...Ch. 1.1 - [T] The volume of a cube depends on the length of...Ch. 1.1 - [T] A rental car company rents cars for a flat fee...Ch. 1.1 - [T] A vehicle has a 20-gal tank and gets 15 mpg....Ch. 1.1 - [T] The volume V of a sphere depends on the length...Ch. 1.1 - [T] A certain bacterium grows in culture in a...Ch. 1.1 - [T] An American tourist visits Paris and must...Ch. 1.1 - [T] The manager at a skateboard shop pays his...Ch. 1.1 - Use a graphing calculator to graph the half-circle...Ch. 1.2 - For the following exercises, for each pair of...Ch. 1.2 - For the following exercises, for each pair of...Ch. 1.2 - For the following exercises, for each pair of...Ch. 1.2 - For the following exercises, for each pair of...Ch. 1.2 - For the following exercises, for each pair of...Ch. 1.2 - For the following exercises, for each pair of...Ch. 1.2 - For the following exercises, for each pair of...Ch. 1.2 - For the following exercises, for each pair of...Ch. 1.2 - For the following exercises, write the equation of...Ch. 1.2 - For the following exercises, write the equation of...Ch. 1.2 - For the following exercises, write the equation of...Ch. 1.2 - For the following exercises, write the equation of...Ch. 1.2 - For the following exercises, write the equation of...Ch. 1.2 - For the following exercises, write the equation of...Ch. 1.2 - For the following exercises, write the equation of...Ch. 1.2 - For the following exercises, write the equation of...Ch. 1.2 - For the following exercises, for each linear...Ch. 1.2 - For the following exercises, for each linear...Ch. 1.2 - For the following exercises, for each linear...Ch. 1.2 - For the following exercises, for each linear...Ch. 1.2 - For the following exercises, for each linear...Ch. 1.2 - For the following exercises, for each linear...Ch. 1.2 - For the following exercises, for each linear...Ch. 1.2 - For the following exercises, for each linear...Ch. 1.2 - For the following exercises, for each polynomial,...Ch. 1.2 - For the following exercises, for each polynomial,...Ch. 1.2 - For the following exercises, for each polynomial,...Ch. 1.2 - For the following exercises, for each polynomial,...Ch. 1.2 - For the following exercises, for each polynomial,...Ch. 1.2 - For the following exercises, use the graph of...Ch. 1.2 - For the following exercises, use the graph of...Ch. 1.2 - For the following exercises, use the graph of...Ch. 1.2 - For the following exercises, use the graph of...Ch. 1.2 - For the following exercises, use the graph of...Ch. 1.2 - For the following exercises, use the graph of...Ch. 1.2 - For the following exercises, for each of the...Ch. 1.2 - For the following exercises, for each of the...Ch. 1.2 - For the following exercises, for each of the...Ch. 1.2 - For the following exercises, for each of the...Ch. 1.2 - For the following exercises, determine whether the...Ch. 1.2 - For the following exercises, determine whether the...Ch. 1.2 - For the following exercises, determine whether the...Ch. 1.2 - For the following exercises, determine whether the...Ch. 1.2 - For the following exercises, determine whether the...Ch. 1.2 - [T] A company purchases some computer equipment...Ch. 1.2 - [T] Total online shopping during the Christmas...Ch. 1.2 - [T] A family bakery makes cupcakes and sells them...Ch. 1.2 - [T] A house purchased for $250,000 is expected to...Ch. 1.2 - [T] A car was purchased for $26,000. The value of...Ch. 1.2 - [T] A condominium in an upscale part of the city...Ch. 1.2 - [T] The total cost C (in thousands of dollars) to...Ch. 1.2 - [T] A professor asks her class to report the...Ch. 1.2 - [T] The output (as a percent of total capacity) of...Ch. 1.2 - [T] The admissions office at a public university...Ch. 1.3 - For the following exercises, convert each angle in...Ch. 1.3 - For the following exercises, convert each angle in...Ch. 1.3 - For the following exercises, convert each angle in...Ch. 1.3 - For the following exercises, convert each angle in...Ch. 1.3 - For the following exercises, convert each angle in...Ch. 1.3 - For the following exercises, convert each angle in...Ch. 1.3 - For the following exercises, convert each angle in...Ch. 1.3 - For the following exercises, convert each angle in...Ch. 1.3 - For the following exercises, convert each angle in...Ch. 1.3 - For the following exercises, convert each angle in...Ch. 1.3 - Evaluate the following functional values. 123....Ch. 1.3 - Evaluate the following functional values. 124....Ch. 1.3 - Evaluate the following functional values. 125....Ch. 1.3 - Evaluate the following functional values. 126....Ch. 1.3 - Evaluate the following functional values. 127....Ch. 1.3 - Evaluate the following functional values. 128....Ch. 1.3 - For the following exercises, consider triangle...Ch. 1.3 - For the following exercises, consider triangle...Ch. 1.3 - For the following exercises, consider triangle...Ch. 1.3 - For the following exercises, consider triangle...Ch. 1.3 - For the following exercises, consider triangle...Ch. 1.3 - For the following exercises, consider triangle...Ch. 1.3 - For the following exercises, P is a point on the...Ch. 1.3 - For the following exercises, P is a point on the...Ch. 1.3 - For the following exercises, P is a point on the...Ch. 1.3 - For the following exercises, P is a point on the...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, verify that each...Ch. 1.3 - For the following exercises, verify that each...Ch. 1.3 - For the following exercises, verify that each...Ch. 1.3 - For the following exercises, verify that each...Ch. 1.3 - For the following exercises, verify that each...Ch. 1.3 - For the following exercises, verify that each...Ch. 1.3 - For the following exercises, verify that each...Ch. 1.3 - For the following exercises, verify that each...Ch. 1.3 - For the following exercises, solve the...Ch. 1.3 - For the following exercises, solve the...Ch. 1.3 - For the following exercises, solve the...Ch. 1.3 - For the following exercises, solve the...Ch. 1.3 - For the following exercises, solve the...Ch. 1.3 - For the following exercises, solve the...Ch. 1.3 - For the following exercises, solve the...Ch. 1.3 - For the following exercises, solve the...Ch. 1.3 - For the following exercises, each graph is of the...Ch. 1.3 - For the following exercises, each graph is of the...Ch. 1.3 - For the following exercises, each graph is of the...Ch. 1.3 - For the following exercises, each graph is of the...Ch. 1.3 - For the following exercises, find a. the...Ch. 1.3 - For the following exercises, find a. the...Ch. 1.3 - For the following exercises, find a. the...Ch. 1.3 - For the following exercises, find a. the...Ch. 1.3 - For the following exercises, find a. the...Ch. 1.3 - For the following exercises, find a. the...Ch. 1.3 - [T] The diameter of a wheel rolling on the ground...Ch. 1.3 - [T] Find the length of the arc intercepted by...Ch. 1.3 - [T] As a point P moves around a circle, the...Ch. 1.3 - [T] A total of 250,000 m2 of land is needed to...Ch. 1.3 - [T] The area of an isosceles triangle with equal...Ch. 1.3 - [T] A panicle travels in a circular path at a...Ch. 1.3 - [T] An alternating current for outlets in a home...Ch. 1.3 - [T] The number of hours of daylight in a northeast...Ch. 1.3 - [T] Suppose that T=50+10sin[12(t8)] is a...Ch. 1.3 - [T] The function H(t)=8sin(6t) models the height H...Ch. 1.4 - Consider the graph in Figure 1.42 of the function...Ch. 1.4 - Now consider other graphs of the form...Ch. 1.4 - Repeat for A = 1, B = 2. Is there any relationship...Ch. 1.4 - Complete the following table, adding a few choices...Ch. 1.4 - 5. Try to figure out the formula for the y-values.Ch. 1.4 - 6. The formula for the x-values is a little...Ch. 1.4 - 7. If you found formulas for parts (5) and (6),...Ch. 1.4 - For the following exercises, use the horizontal...Ch. 1.4 - For the following exercises, use the horizontal...Ch. 1.4 - For the following exercises, use the horizontal...Ch. 1.4 - For the following exercises, use the horizontal...Ch. 1.4 - For the following exercises, use the horizontal...Ch. 1.4 - For the following exercises, use the horizontal...Ch. 1.4 - For the following exercises, a. find the inverse...Ch. 1.4 - For the following exercises, a. find the inverse...Ch. 1.4 - For the following exercises, a. find the inverse...Ch. 1.4 - For the following exercises, a. find the inverse...Ch. 1.4 - For the following exercises, a. find the inverse...Ch. 1.4 - For the following exercises, a. find the inverse...Ch. 1.4 - For the following exercises, use the graph of f...Ch. 1.4 - For the following exercises, use the graph of f...Ch. 1.4 - For the following exercises, use the graph of f...Ch. 1.4 - For the following exercises, use the graph of f to...Ch. 1.4 - 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[T] The velocity V (in centimeters per second) of...Ch. 1.4 - A function that converts dress sizes in the United...Ch. 1.4 - [T] The cost to remove a toxin from a lake is...Ch. 1.4 - [T] A race car is accelerating at a velocity given...Ch. 1.4 - [T] An airplane’s Mach number M is the ratio of...Ch. 1.4 - [T] Using =2sin1(1M) , find the Mach number M for...Ch. 1.4 - [T] The temperature (in degrees Celsius) of a city...Ch. 1.4 - [T] The depth (in feet) of water at a dock changes...Ch. 1.4 - [T] All object moving in simple harmonic motion is...Ch. 1.4 - A local art gallery has a portrait 3 ft in height...Ch. 1.4 - [T] Use a calculator to evaluate...Ch. 1.4 - [T] Use a calculator to evaluate...Ch. 1.5 - For the following exercises, evaluate the given...Ch. 1.5 - For the following exercises, evaluate the given...Ch. 1.5 - For the following exercises, evaluate the given...Ch. 1.5 - For the following exercises, evaluate the given...Ch. 1.5 - For the following exercises, match the exponential...Ch. 1.5 - For the following exercises, match the exponential...Ch. 1.5 - For the following exercises, match the exponential...Ch. 1.5 - For the following exercises, match the exponential...Ch. 1.5 - For the following exercises, match the exponential...Ch. 1.5 - For the following exercises, match the exponential...Ch. 1.5 - For the following exercises, sketch the graph of...Ch. 1.5 - For the following exercises, sketch the graph of...Ch. 1.5 - For the following exercises, sketch the graph of...Ch. 1.5 - For the following exercises, sketch the graph of...Ch. 1.5 - For the following exercises, sketch the graph of...Ch. 1.5 - For the following exercises, sketch the graph of...Ch. 1.5 - For the following exercises, sketch the graph of...Ch. 1.5 - For the following exercises, write the equation in...Ch. 1.5 - For the following exercises, write the equation in...Ch. 1.5 - For the following exercises, write the equation in...Ch. 1.5 - For the following exercises, write the equation in...Ch. 1.5 - For the following exercises, write the equation in...Ch. 1.5 - For the following exercises, write the equation in...Ch. 1.5 - For the following exercises, write the equation in...Ch. 1.5 - For the following exercises, write the equation in...Ch. 1.5 - For the following exercises, write the equation in...Ch. 1.5 - For the following exercises, write the equation in...Ch. 1.5 - For the following exercises, write the equation in...Ch. 1.5 - For the following exercises, write the equation in...Ch. 1.5 - For the following exercises, write the equation in...Ch. 1.5 - For the following exercises, write the equation in...Ch. 1.5 - For the following exercises, write the equation in...Ch. 1.5 - For the following exercises, write the equation in...Ch. 1.5 - For the following exercises, write the equation in...Ch. 1.5 - For the following exercises, write the equation in...Ch. 1.5 - For the following exercises, sketch the graph of...Ch. 1.5 - For the following exercises, sketch the graph of...Ch. 1.5 - For the following exercises, sketch the graph of...Ch. 1.5 - 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For the following exercises, solve the logarithmic...Ch. 1.5 - For the following exercises, solve the logarithmic...Ch. 1.5 - For the following exercises, solve the logarithmic...Ch. 1.5 - For the following exercises, solve the logarithmic...Ch. 1.5 - For the following exercises, solve the logarithmic...Ch. 1.5 - For the following exercises, solve the logarithmic...Ch. 1.5 - For the following exercises, solve the logarithmic...Ch. 1.5 - For the following exercises, solve the logarithmic...Ch. 1.5 - For the following exercises, rise the...Ch. 1.5 - For the following exercises, rise the...Ch. 1.5 - For the following exercises, rise the...Ch. 1.5 - For the following exercises, rise the...Ch. 1.5 - For the following exercises, rise the...Ch. 1.5 - For the following exercises, rise the...Ch. 1.5 - Rewrite the following expressions in terms of...Ch. 1.5 - [T] The number of bacteria N in a culture after t...Ch. 1.5 - [T] The demand D (in millions of barrels) for oil...Ch. 1.5 - [T] The amount A of a $100,000 investment paying...Ch. 1.5 - [T] An investment is compounded monthly,...Ch. 1.5 - [T] The concentration of hydrogen ions in a...Ch. 1.5 - [T] Iodine-131 is a radioactive substance that...Ch. 1.5 - [T] According to the World Bank, at the end of...Ch. 1.5 - [T] The amount A accumulated after 1000 dollar’s...Ch. 1.5 - [T] A bacterial colony grown in a lab is known to...Ch. 1.5 - [T] The rabbit population on a game reserve...Ch. 1.5 - [T] The 1906 earthquake in Sail Francisco had a...Ch. 1 - True or False? Justify your answer with a proof or...Ch. 1 - True or False? Justify your answer with a proof or...Ch. 1 - True or False? Justify your answer with a proof or...Ch. 1 - True or False? Justify your answer with a proof or...Ch. 1 - For the following problems, state the domain and...Ch. 1 - For the following problems, state the domain and...Ch. 1 - For the following problems, state the domain and...Ch. 1 - For the following problems, state the domain and...Ch. 1 - Find the degree, y-intercept, and zeros for the...Ch. 1 - Find the degree, y-intercept, and zeros for the...Ch. 1 - Simplify the following trigonometric expressions....Ch. 1 - Simplify the following trigonometric expressions....Ch. 1 - Solve the following trigonometric equations on the...Ch. 1 - Solve the following trigonometric equations on the...Ch. 1 - Solve the following logarithmic equations. 324....Ch. 1 - wSolve the following logarithmic equations. 325....Ch. 1 - Are the following functions one-to-one over their...Ch. 1 - Are the following functions one-to-one over their...Ch. 1 - For the following problems, determine the largest...Ch. 1 - For the following problems, determine the largest...Ch. 1 - A car is racing along a circular track with...Ch. 1 - For the following problems, consider a restaurant...Ch. 1 - For the following problems, consider a restaurant...Ch. 1 - For the following problems, consider a restaurant...Ch. 1 - For the following problems, consider a restaurant...Ch. 1 - For the following problems, consider radioactive...Ch. 1 - For the following problems, consider radioactive...
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- Q3*) Consider the integral I Yn, Y₁, Y2, . . ., Y'n) dã, [F(x, Y 1, Y2, · · Yng) = - where y1, 2, ...y are dependent variables, dependent on x. If F is not explicitly dependent on x, deduce the equivalent of the Beltrami identity. Optional: Give an example of a function F(y1, Y2, Y₁, y2), and write down the Euler-Lagrange equations and Beltrami Identity for your example. Does having this Beltrami Identity help solve the problem?arrow_forwardWrite an integral that is approximated by the following Riemann sum. Substitute a into the Riemann sum below where a is the last non-zero digit of your banner ID. You do not need to evaluate the integral. 2000 (10 1 ((10-a) +0.001) (0.001)arrow_forwardSolve the following problem over the interval from x=0 to 1 using a step size of 0.25 where y(0)= 1. dy = dt (1+4t)√√y (a) Euler's method. (b) Heun's methodarrow_forward
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