EBK WEBASSIGN FOR STEWART'S ESSENTIAL C
2nd Edition
ISBN: 9781337772020
Author: Stewart
Publisher: VST
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 1, Problem 40RE
To determine
To prove: The limit of the function
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
The graph of f(x) is given below. Select each true statement about the continuity of f(x) at x = 1.
Select all that apply:
☐ f(x) is not continuous at x = 1 because it is not defined at x = 1.
☐ f(x) is not continuous at x = 1 because lim f(x) does not exist.
x+1
☐ f(x) is not continuous at x = 1 because lim f(x) ‡ f(1).
x+→1
☐ f(x) is continuous at x = 1.
a is done please show b
A homeware company has been approached to manufacture a cake tin in the shape
of a "ghost" from the Pac-Man video game to celebrate the 45th Anniversary of the
games launch. The base of the cake tin has a characteristic dimension / and is
illustrated in Figure 1 below, you should assume the top and bottom of the shape
can be represented by semi-circles. The vertical sides of the cake tin have a height of
h. As the company's resident mathematician, you need to find the values of r and h
that minimise the internal surface area of the cake tin given that the volume of the
tin is Vfixed-
2r
Figure 1 - Plan view of the "ghost" cake tin base.
(a) Show that the Volume (V) of the cake tin as a function of r and his
2(+1)²h
V = 2
Chapter 1 Solutions
EBK WEBASSIGN FOR STEWART'S ESSENTIAL C
Ch. 1.1 - 1. If f(x)=x+2x and g(u)=u+2u, is it true that f =...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 - Prob. 5ECh. 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 - Prob. 9ECh. 1.1 - The graph shows the height of the water in a...
Ch. 1.1 - Prob. 11ECh. 1.1 - Sketch a rough graph of the number of hours of...Ch. 1.1 - Prob. 13ECh. 1.1 - Sketch a rough graph of the market value of a new...Ch. 1.1 - Prob. 15ECh. 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 - 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 - Prob. 24ECh. 1.1 - Find the domain of the function. 31. f(x)=x+4x29Ch. 1.1 - Prob. 26ECh. 1.1 - Prob. 28ECh. 1.1 - Prob. 29ECh. 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 - Prob. 31ECh. 1.1 - Prob. 34ECh. 1.1 - Find the domain and sketch the graph of the...Ch. 1.1 - Prob. 33ECh. 1.1 - Prob. 35ECh. 1.1 - Prob. 36ECh. 1.1 - Find the domain and sketch the graph of the...Ch. 1.1 - Prob. 38ECh. 1.1 - Prob. 39ECh. 1.1 - Prob. 40ECh. 1.1 - Prob. 41ECh. 1.1 - Find the domain and sketch the graph of the...Ch. 1.1 - Find an expression for the function whose graph is...Ch. 1.1 - Prob. 44ECh. 1.1 - Prob. 45ECh. 1.1 - Prob. 46ECh. 1.1 - Prob. 47ECh. 1.1 - Find a formula for the described function and...Ch. 1.1 - Prob. 49ECh. 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 cell phone plan has a basic charge of 35 a...Ch. 1.1 - In a certain country, income tax is assessed as...Ch. 1.1 - The functions in Example 6 and Exercises 52 and...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 - (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 - Prob. 5ECh. 1.2 - Prob. 6ECh. 1.2 - Prob. 7ECh. 1.2 - Prob. 8ECh. 1.2 - Prob. 9ECh. 1.2 - Prob. 10ECh. 1.2 - Prob. 11ECh. 1.2 - Prob. 12ECh. 1.2 - Prob. 13ECh. 1.2 - The monthly cost of driving a car depends on the...Ch. 1.2 - Prob. 15ECh. 1.2 - Prob. 16ECh. 1.2 - Prob. 17ECh. 1.2 - Explain how each graph is obtained from the graph...Ch. 1.2 - Prob. 19ECh. 1.2 - Prob. 20ECh. 1.2 - Prob. 21ECh. 1.2 - Prob. 22ECh. 1.2 - Prob. 23ECh. 1.2 - Prob. 24ECh. 1.2 - Prob. 25ECh. 1.2 - Prob. 30ECh. 1.2 - Prob. 27ECh. 1.2 - Prob. 32ECh. 1.2 - Prob. 26ECh. 1.2 - Prob. 28ECh. 1.2 - Prob. 31ECh. 1.2 - Prob. 29ECh. 1.2 - Prob. 34ECh. 1.2 - Prob. 33ECh. 1.2 - Prob. 36ECh. 1.2 - Prob. 35ECh. 1.2 - Prob. 37ECh. 1.2 - Prob. 38ECh. 1.2 - Prob. 40ECh. 1.2 - Prob. 39ECh. 1.2 - Prob. 41ECh. 1.2 - Prob. 42ECh. 1.2 - Prob. 43ECh. 1.2 - Prob. 44ECh. 1.2 - Prob. 45ECh. 1.2 - Prob. 46ECh. 1.2 - Prob. 47ECh. 1.2 - Prob. 48ECh. 1.2 - Prob. 49ECh. 1.2 - Express the function in the form f g. 48....Ch. 1.2 - Prob. 51ECh. 1.2 - Prob. 52ECh. 1.2 - Prob. 53ECh. 1.2 - Prob. 54ECh. 1.2 - Prob. 55ECh. 1.2 - Prob. 57ECh. 1.2 - Prob. 56ECh. 1.2 - Prob. 58ECh. 1.2 - Prob. 59ECh. 1.2 - Prob. 60ECh. 1.2 - Prob. 61ECh. 1.2 - Prob. 62ECh. 1.2 - Prob. 63ECh. 1.2 - Prob. 64ECh. 1.2 - Prob. 65ECh. 1.2 - Prob. 66ECh. 1.3 - If a ball is thrown into the air with a velocity...Ch. 1.3 - If a rock is thrown upward on the planet Mars with...Ch. 1.3 - Use the given graph of f to state the value of...Ch. 1.3 - For the function f whose graph is given, state the...Ch. 1.3 - Prob. 5ECh. 1.3 - Prob. 6ECh. 1.3 - Prob. 7ECh. 1.3 - Prob. 8ECh. 1.3 - Prob. 9ECh. 1.3 - Sketch the graph of an example of a function f...Ch. 1.3 - Prob. 11ECh. 1.3 - Guess the value of the limit (if it exists) by...Ch. 1.3 - Prob. 13ECh. 1.3 - Guess the value of the limit (if it exists) by...Ch. 1.3 - Prob. 15ECh. 1.3 - Prob. 16ECh. 1.3 - Prob. 17ECh. 1.3 - Prob. 18ECh. 1.3 - Prob. 19ECh. 1.3 - Prob. 20ECh. 1.3 - Prob. 21ECh. 1.3 - Prob. 22ECh. 1.3 - Prob. 23ECh. 1.3 - Use the given graph of f(x) =x2 to find a number ...Ch. 1.3 - Prob. 25ECh. 1.3 - Use a graph to find a number such that if...Ch. 1.3 - Prob. 27ECh. 1.3 - Prob. 28ECh. 1.3 - Prob. 29ECh. 1.3 - Prove the statement using the , definition of a...Ch. 1.3 - Prob. 31ECh. 1.3 - Prove the statement using the , definition of a...Ch. 1.3 - Prob. 33ECh. 1.3 - Prob. 34ECh. 1.3 - Prob. 35ECh. 1.3 - Prob. 36ECh. 1.3 - Prob. 37ECh. 1.3 - Prob. 38ECh. 1.3 - Prob. 39ECh. 1.3 - Prove the statement using the , definition of a...Ch. 1.3 - Prob. 41ECh. 1.3 - Prob. 42ECh. 1.3 - Prob. 43ECh. 1.3 - Prob. 44ECh. 1.3 - Prob. 46ECh. 1.4 - Given that limx2f(x)=4limx2g(x)=2limx2h(x)=0 find...Ch. 1.4 - The graphs of f and g are given. Use them to...Ch. 1.4 - Evaluate the limit and justify each step by...Ch. 1.4 - Prob. 4ECh. 1.4 - Prob. 5ECh. 1.4 - Prob. 6ECh. 1.4 - Evaluate the limit and justify each step by...Ch. 1.4 - Prob. 8ECh. 1.4 - Prob. 9ECh. 1.4 - (a) What is wrong with the following equation?...Ch. 1.4 - Prob. 11ECh. 1.4 - Evaluate the limit, if it exists. limx4x24xx23x4Ch. 1.4 - Evaluate the limit, if it exists. limx5x25x+6x5Ch. 1.4 - Evaluate the limit, if it exists. limx1x24xx23x4Ch. 1.4 - Prob. 15ECh. 1.4 - Prob. 16ECh. 1.4 - Prob. 17ECh. 1.4 - Evaluate the limit, if it exists. limh0(2+h)38hCh. 1.4 - Prob. 19ECh. 1.4 - Prob. 20ECh. 1.4 - Evaluate the limit, if it exists. limh09+h3hCh. 1.4 - Evaluate the limit, if it exists. limu24u+13u2Ch. 1.4 - Prob. 25ECh. 1.4 - Evaluate the limit, if it exists. limt0(1t1t2+t)Ch. 1.4 - Prob. 23ECh. 1.4 - Evaluate the limit, if it exists. limx4x2+95x+4Ch. 1.4 - Prob. 27ECh. 1.4 - Evaluate the limit, if it exists. limh01(xh)21x2hCh. 1.4 - Prob. 29ECh. 1.4 - Prob. 30ECh. 1.4 - Prob. 31ECh. 1.4 - Use the Squeeze Theorem to show that...Ch. 1.4 - Prob. 33ECh. 1.4 - If 2x g(x) x4 x2 + 2 for all x, evaluate...Ch. 1.4 - Prove that limx0x4cos2x=0.Ch. 1.4 - Prove that limx0+x[1+sin2(2/x)]=0.Ch. 1.4 - Prob. 37ECh. 1.4 - Find the limit, if it exists. If the limit does...Ch. 1.4 - Prob. 39ECh. 1.4 - Find the limit, if it exists. If the limit does...Ch. 1.4 - Find the limit, if it exists. If the limit does...Ch. 1.4 - Prob. 42ECh. 1.4 - Let g(x)=x2+x6x2 (a) Find (i) limx2+g(x) (ii)...Ch. 1.4 - Prob. 44ECh. 1.4 - Prob. 45ECh. 1.4 - Prob. 46ECh. 1.4 - Prob. 47ECh. 1.4 - Prob. 48ECh. 1.4 - Prob. 49ECh. 1.4 - Find the limit. limx0sin4xsin6xCh. 1.4 - Find the limit. limt0tan6tsin2tCh. 1.4 - Prob. 52ECh. 1.4 - Find the limit. limx0sin3x5x34xCh. 1.4 - Prob. 54ECh. 1.4 - Prob. 55ECh. 1.4 - Find the limit. limx0sin(x2)xCh. 1.4 - If p is a polynomial, Show that limxa p(x) = p(a)Ch. 1.4 - If r is a rational function. use Exercise 57 to...Ch. 1.4 - If limx1f(x)8x1=10, find limx1f(x).Ch. 1.4 - To prove that sine has the Direct Substitution...Ch. 1.4 - Prove that cosine has the Direct Substitution...Ch. 1.4 - Show by means of an example that limxa[f(x)+g(x)]...Ch. 1.4 - Prob. 64ECh. 1.4 - Prove that if limxag(x)=0 and limxaf(x) exists and...Ch. 1.4 - Prob. 65ECh. 1.4 - Prob. 66ECh. 1.5 - Write an equation that expresses the fact that a...Ch. 1.5 - If f is continuous on ( , ).what can you say about...Ch. 1.5 - (a) From the graph of f , state the numbers at...Ch. 1.5 - From the graph of g, state the intervals on which...Ch. 1.5 - Sketch the graph of a function f that is...Ch. 1.5 - Sketch the graph of a function f that is...Ch. 1.5 - Sketch the graph of a function f that is...Ch. 1.5 - Sketch the graph of a function f that is...Ch. 1.5 - The toll T charged for driving on a certain...Ch. 1.5 - Explain why each function is continuous or...Ch. 1.5 - Use the definition of continuity and the...Ch. 1.5 - Use the definition of continuity and the...Ch. 1.5 - Use the definition of continuity and the...Ch. 1.5 - Explain why the function is discontinuous at the...Ch. 1.5 - Explain why the function is discontinuous at the...Ch. 1.5 - Explain why the function is discontinuous at the...Ch. 1.5 - Explain why the function is discontinuous at the...Ch. 1.5 - Explain, using Theorems 4, 5, 6, and 8, why the...Ch. 1.5 - Explain, using Theorems 4, 5, 6, and 8, why the...Ch. 1.5 - Explain, using Theorems 4, 5, 6, and 8, why the...Ch. 1.5 - Explain, using Theorems 4, 5, 6, and 8, why the...Ch. 1.5 - Explain, using Theorems 4, 5, 6, and 8, why the...Ch. 1.5 - Explain, using Theorems 4, 5, 6, and 8, why the...Ch. 1.5 - Locate the discontinuities of the function and...Ch. 1.5 - Locate the discontinuities of the function and...Ch. 1.5 - Prob. 27ECh. 1.5 - Use continuity to evaluate the limit....Ch. 1.5 - Show that f is continuous on (, )....Ch. 1.5 - Show that f is continuous on ( , )....Ch. 1.5 - Find the numbers at which the function...Ch. 1.5 - The gravitational force exerted by the planet...Ch. 1.5 - For what value of the constant c is the function f...Ch. 1.5 - Find the values of a and h that make f continuous...Ch. 1.5 - Suppose f and g are continuous functions such that...Ch. 1.5 - Which of the following functions .f has a...Ch. 1.5 - Suppose that a function f is continuous on [0, 1]...Ch. 1.5 - If f(x) = x2 + 10 sin x, show that there is a...Ch. 1.5 - Suppose f is continuous on [1, 5] and the only...Ch. 1.5 - Use the Intermediate Value Theorem to show that...Ch. 1.5 - Use the Intermediate Value Theorem to show that...Ch. 1.5 - Use the Intermediate Value Theorem to show that...Ch. 1.5 - Use the Intermediate Value Theorem to show that...Ch. 1.5 - Prob. 43ECh. 1.5 - Prob. 44ECh. 1.5 - Prob. 45ECh. 1.5 - (a) Prove that the equation has at least one real...Ch. 1.5 - Is there a number that is exactly 1 more than its...Ch. 1.5 - Prob. 48ECh. 1.5 - Prob. 49ECh. 1.5 - Prob. 50ECh. 1.5 - A Tibetan monk leaves the monastery at 7:00 AM and...Ch. 1.6 - How close to 3 do we have to take x so that...Ch. 1.6 - Prob. 52ECh. 1.6 - Prob. 53ECh. 1.6 - For the function f whose graph is given, state the...Ch. 1.6 - For the function g whose graph is given, state the...Ch. 1.6 - Sketch the graph of an example of a function f...Ch. 1.6 - Sketch the graph of an example of a function f...Ch. 1.6 - Sketch the graph of an example of a function f...Ch. 1.6 - Sketch the graph of an example of a function f...Ch. 1.6 - Sketch the graph of an example of a function f...Ch. 1.6 - Sketch the graph of an example of a function f...Ch. 1.6 - Guess the value of the limit limxx22x by...Ch. 1.6 - Determine limx11x31 and limx1+1x31 (a) by...Ch. 1.6 - Use a graph to estimate all the vertical and...Ch. 1.6 - (a) Use a graph of f(x)=(12x)x to estimate the...Ch. 1.6 - Find the limit or show that it does not exist....Ch. 1.6 - Find the limit or show that it does not exist....Ch. 1.6 - Find the limit. limx12x(x1)2Ch. 1.6 - Find the limit. limx2x22xx24x+4Ch. 1.6 - Find the limit or show that it does not exist....Ch. 1.6 - Find the limit or show that it does not exist....Ch. 1.6 - Find the limit or show that it does not exist....Ch. 1.6 - Prob. 24ECh. 1.6 - Prob. 13ECh. 1.6 - Find the limit. limx3x+2x+3Ch. 1.6 - Prob. 25ECh. 1.6 - Prob. 26ECh. 1.6 - Find the limit or show that it does not exist....Ch. 1.6 - Prob. 31ECh. 1.6 - Prob. 32ECh. 1.6 - Prob. 30ECh. 1.6 - Prob. 17ECh. 1.6 - Prob. 33ECh. 1.6 - Prob. 28ECh. 1.6 - Prob. 16ECh. 1.6 - Prob. 29ECh. 1.6 - Prob. 37ECh. 1.6 - Prob. 38ECh. 1.6 - Prob. 36ECh. 1.6 - Find the horizontal and vertical asymptotes of...Ch. 1.6 - Prob. 39ECh. 1.6 - Prob. 34ECh. 1.6 - Let P and Q be polynomials. Find limxP(x)Q(x) if...Ch. 1.6 - Prob. 46ECh. 1.6 - Prob. 41ECh. 1.6 - Prob. 40ECh. 1.6 - Evaluate the limits. (a) limxxsin1x (b) limxxsin1xCh. 1.6 - In the theory of relativity, the mass of a...Ch. 1.6 - (a) Show that limx4x25x2x2+1=2. (b) By graphing...Ch. 1.6 - A function f is a ratio of quadratic functions and...Ch. 1.6 - Prob. 44ECh. 1.6 - Prob. 47ECh. 1.6 - Prob. 49ECh. 1.6 - Prob. 55ECh. 1.6 - Prob. 54ECh. 1.6 - Prob. 56ECh. 1.6 - Prob. 57ECh. 1.6 - Prob. 58ECh. 1.6 - Prove that limxf(x)=limt0+f(1/t) and...Ch. 1 - Prob. 1RCCCh. 1 - Prob. 2RCCCh. 1 - Prob. 3RCCCh. 1 - Prob. 4RCCCh. 1 - Prob. 5RCCCh. 1 - Prob. 6RCCCh. 1 - Prob. 7RCCCh. 1 - Prob. 8RCCCh. 1 - Prob. 9RCCCh. 1 - Prob. 10RCCCh. 1 - Prob. 11RCCCh. 1 - Prob. 1RQCh. 1 - Prob. 2RQCh. 1 - Prob. 3RQCh. 1 - Prob. 4RQCh. 1 - Prob. 5RQCh. 1 - Prob. 6RQCh. 1 - Prob. 19RQCh. 1 - Prob. 1RECh. 1 - Prob. 2RECh. 1 - Prob. 3RECh. 1 - Prob. 4RECh. 1 - Prob. 5RECh. 1 - Prob. 6RECh. 1 - Prob. 7RECh. 1 - Prob. 8RECh. 1 - Prob. 9RECh. 1 - Prob. 10RECh. 1 - Prob. 11RECh. 1 - Use transformations to sketch the graph of the...Ch. 1 - Prob. 13RECh. 1 - Prob. 14RECh. 1 - Prob. 15RECh. 1 - Prob. 16RECh. 1 - Prob. 17RECh. 1 - Prob. 18RECh. 1 - Prob. 12RCCCh. 1 - Prob. 13RCCCh. 1 - Prob. 14RCCCh. 1 - Prob. 15RCCCh. 1 - Prob. 18RCCCh. 1 - Prob. 16RCCCh. 1 - Prob. 17RCCCh. 1 - Prob. 7RQCh. 1 - Prob. 8RQCh. 1 - Prob. 9RQCh. 1 - Prob. 10RQCh. 1 - Prob. 11RQCh. 1 - Determine whether the statement is true or false....Ch. 1 - Prob. 13RQCh. 1 - Prob. 14RQCh. 1 - Prob. 15RQCh. 1 - Prob. 16RQCh. 1 - Prob. 17RQCh. 1 - If f and g are polynomials and g(2) = 0, then the...Ch. 1 - Prob. 20RQCh. 1 - Prob. 21RQCh. 1 - Prob. 22RQCh. 1 - Prob. 23RQCh. 1 - Determine whether the statement is true or false....Ch. 1 - Prob. 25RQCh. 1 - Prob. 26RQCh. 1 - Prob. 19RECh. 1 - Prob. 20RECh. 1 - Prob. 21RECh. 1 - Prob. 22RECh. 1 - Prob. 23RECh. 1 - Prob. 24RECh. 1 - Find the limit. limh0(h1)3+1hCh. 1 - Prob. 26RECh. 1 - Prob. 27RECh. 1 - Prob. 28RECh. 1 - Prob. 29RECh. 1 - Prob. 30RECh. 1 - Prob. 31RECh. 1 - Prob. 32RECh. 1 - Prob. 33RECh. 1 - Prob. 35RECh. 1 - Prob. 36RECh. 1 - Prob. 34RECh. 1 - Prob. 37RECh. 1 - Prob. 38RECh. 1 - Prob. 39RECh. 1 - Prob. 40RECh. 1 - Prob. 41RECh. 1 - Prob. 42RECh. 1 - Prob. 43RECh. 1 - Prob. 44RECh. 1 - Prob. 45RECh. 1 - Prob. 46RECh. 1 - Prob. 47RECh. 1 - Prob. 48RE
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
- 15. Please solve this and show each and every step please. PLEASE no chatgpt can I have a real person solve it please!! I am stuck. I am doing pratice problems and I do not even know where to start with this. The question is Please compute the indicated functional value.arrow_forwardUse a graph of f to estimate lim f(x) or to show that the limit does not exist. Evaluate f(x) near x = a to support your conjecture. Complete parts (a) and (b). x-a f(x)= 1 - cos (4x-4) 3(x-1)² ; a = 1 a. Use a graphing utility to graph f. Select the correct graph below.. A. W → ✓ Each graph is displayed in a [- 1,3] by [0,5] window. B. in ✓ ○ C. und ☑ Use the graphing utility to estimate lim f(x). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. x-1 ○ A. The limit appears to be approximately ☐ . (Round to the nearest tenth as needed.) B. The limit does not exist. b. Evaluate f(x) for values of x near 1 to support your conjecture. X 0.9 0.99 0.999 1.001 1.01 1.1 f(x) ○ D. + ☑ (Round to six decimal places as needed.) Does the table from the previous step support your conjecture? A. No, it does not. The function f(x) approaches a different value in the table of values than in the graph, after the approached values are rounded to the…arrow_forwardx²-19x+90 Let f(x) = . Complete parts (a) through (c) below. x-a a. For what values of a, if any, does lim f(x) equal a finite number? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. x→a+ ○ A. a= (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There are no values of a for which the limit equals a finite number. b. For what values of a, if any, does lim f(x) = ∞o? Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. x→a+ A. (Type integers or simplified fractions) C. There are no values of a that satisfy lim f(x) = ∞. + x-a c. For what values of a, if any, does lim f(x) = -∞0? Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. x→a+ A. Either a (Type integers or simplified fractions) B.arrow_forwardSketch a possible graph of a function f, together with vertical asymptotes, that satisfies all of the following conditions. f(2)=0 f(4) is undefined lim f(x)=1 X-6 lim f(x) = -∞ x-0+ lim f(x) = ∞ lim f(x) = ∞ x-4 _8arrow_forwardDetermine the following limit. lim 35w² +8w+4 w→∞ √49w+w³ 3 Select the correct choice below, and, if necessary, fill in the answer box to complete your choice. ○ A. lim W→∞ 35w² +8w+4 49w+w3 (Simplify your answer.) B. The limit does not exist and is neither ∞ nor - ∞.arrow_forwardCalculate the limit lim X-a x-a 5 using the following factorization formula where n is a positive integer and x-➡a a is a real number. x-a = (x-a) (x1+x-2a+x lim x-a X - a x-a 5 = n- + xa an-2 + an−1)arrow_forwardThe function s(t) represents the position of an object at time t moving along a line. Suppose s(1) = 116 and s(5)=228. Find the average velocity of the object over the interval of time [1,5]. The average velocity over the interval [1,5] is Vav = (Simplify your answer.)arrow_forwardFor the position function s(t) = - 16t² + 105t, complete the following table with the appropriate average velocities. Then make a conjecture about the value of the instantaneous velocity at t = 1. Time Interval Average Velocity [1,2] Complete the following table. Time Interval Average Velocity [1, 1.5] [1, 1.1] [1, 1.01] [1, 1.001] [1,2] [1, 1.5] [1, 1.1] [1, 1.01] [1, 1.001] ப (Type exact answers. Type integers or decimals.) The value of the instantaneous velocity at t = 1 is (Round to the nearest integer as needed.)arrow_forwardFind the following limit or state that it does not exist. Assume b is a fixed real number. (x-b) 40 - 3x + 3b lim x-b x-b ... Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (x-b) 40 -3x+3b A. lim x-b x-b B. The limit does not exist. (Type an exact answer.)arrow_forwardx4 -289 Consider the function f(x) = 2 X-17 Complete parts a and b below. a. Analyze lim f(x) and lim f(x), and then identify the horizontal asymptotes. x+x X--∞ lim 4 X-289 2 X∞ X-17 X - 289 lim = 2 ... X∞ X - 17 Identify the horizontal asymptotes. Select the correct choice and, if necessary, fill in the answer box(es) to complete your choice. A. The function has a horizontal asymptote at y = B. The function has two horizontal asymptotes. The top asymptote is y = and the bottom asymptote is y = ☐ . C. The function has no horizontal asymptotes. b. Find the vertical asymptotes. For each vertical asymptote x = a, evaluate lim f(x) and lim f(x). Select the correct choice and, if necessary, fill in the answer boxes to complete your choice. earrow_forwardExplain why lim x²-2x-35 X-7 X-7 lim (x+5), and then evaluate lim X-7 x² -2x-35 x-7 x-7 Choose the correct answer below. A. x²-2x-35 The limits lim X-7 X-7 and lim (x+5) equal the same number when evaluated using X-7 direct substitution. B. Since each limit approaches 7, it follows that the limits are equal. C. The numerator of the expression X-2x-35 X-7 simplifies to x + 5 for all x, so the limits are equal. D. Since x²-2x-35 X-7 = x + 5 whenever x 7, it follows that the two expressions evaluate to the same number as x approaches 7. Now evaluate the limit. x²-2x-35 lim X-7 X-7 = (Simplify your answer.)arrow_forwardA function f is even if f(x) = f(x) for all x in the domain of f. If f is even, with lim f(x) = 4 and x-6+ lim f(x)=-3, find the following limits. X-6 a. lim f(x) b. +9-←x lim f(x) X-6 a. lim f(x)= +9-←x (Simplify your answer.) b. lim f(x)= X→-6 (Simplify your answer.) ...arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningLimits and Continuity; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=9brk313DjV8;License: Standard YouTube License, CC-BY