Concept explainers
Sketching graphs Sketch a possible graph of a function f that satisfies all the given conditions. Be sure to identify all vertical and horizontal asymptotes.
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Calculus: Early Transcendentals (3rd Edition)
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Precalculus (10th Edition)
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- The function f is defined by the graph represented in the figure below. Find: a) lim f(x) x--> -4 ^+ b) lim f(x) x--> -4^ - c) lim f(x) x--> -4 d) lim f(x) x--> 0 e) lim f(x) x--> 6 f) lim f(x) x--> -2arrow_forwardExplain why the function is discontinuous at the given number a. (Select all that apply.) f(x) = 1 x + 3 a = −3 lim x→−3 f(x) does not exist. f(−3) and lim x→−3 f(x) are finite, but are not equal. lim x→−3+ f(x) and lim x→−3− f(x) are not finite, and are not equal. f(−3) is undefined. none of the above Sketch the graph of the function.arrow_forward5) a function with a domain of (-2, infinity): Consider: Is the function continuous at x=1? If not, what type of discontinuity does the function have at x=1?arrow_forward
- reate a table of values for the function and use the result to estimate the limit. Use a graphing utility to graph the function to confirm your result. (Round your answers to four decimal places. If an answer does not exist, enter DNE.) lim x→−3 Root 46 − x-7/x+3 x -3.1 -3.01 -3.001 -2.999 -2.99 -2.9 f(x) lim x→−3 Root 46 − x-7/x+3 ≈arrow_forwardreate a table of values for the function and use the result to estimate the limit. Use a graphing utility to graph the function to confirm your result. (Round your answers to four decimal places. If an answer does not exist, enter DNE.) lim x→−3 Sq.Root 46 − x-7/x+3 x -3.1 -3.01 -3.001 -2.999 -2.99 -2.9 f(x) lim x→−3 Sq.Root 46 − x-7/x+3 ≈arrow_forwardTrue or False. If a statement below must always be true, write True and give the brief justification . Otherwise, write False, and give an example in which the statement is not true. Your example may be a graph. a. If lim x->a+ f(x)= lim x->a- f(x), then f(x) is continuous at x=a b. If f(2) = 6 and f"(2)= 8, then f(x) is increasing at x=2arrow_forward
- True or false? if f'(x)>0 for all real x values, then the limit as x goes to infinity of f(x) = infinity. Show a graph to illustrate your answer.arrow_forwardDetermine whether the graph of the function has a vertical asymptote or a removable discontinuity at x = −1. Graph the function using a graphing utility to confirm your answer.arrow_forwardDescribe how the graph of the given function can be obtained by transforming the graph of the reciprocal function g(x)=1/x. Identify horizontal and vertical asymptotes and use limits to describe the corresponding behavior. Sketch a graph of the function. f(x) = (2x-1) / (x+3)arrow_forward
- (Question pertaining to indeterminate limits) It is not uncommon for people to write: lim x approaches a f(x) = 0/0 a) Why is this not correct? b) Is 0/0 a number? No. Explain what 0/0 means in terms of the numerator and the denominator.arrow_forwarda. What is the domain of f? Express your answer in interval notation. f(x)= 1 - x^4 / x^2 - 1 b. Use a sequence of values of x near a=1 to estimate the value of limx→1 f(x). The sequence should include values such as 1.01, 1.001, etc. c. Use algebra to simplify the expression 1 - x^4 / x^2 - 1 d. True or false: f(1)=-2 e. Based on all of your work above, construct an accurate, labeled graph of y=f(x) on the interval [0,2].arrow_forwardSketch a graph of the functiony = x^3e^−xshowing clearly where it is concave up or concave down. Indicate the x-coordinatesof any maxima, minima and points of inflection and find the asymptotic behaviour.Show all your reasoning.arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning