Concept explainers
Estimating limits graphically and numerically Use a graph of f estimate
31.
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Calculus: Early Transcendentals (3rd Edition)
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University Calculus: Early Transcendentals (3rd Edition)
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Calculus and Its Applications (11th Edition)
Precalculus (10th Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
- Given lim (4x-3) as x approaches 1. Use the definition of a limt to find a number delta such that the absolute value of x-a is less than delta when the absolute value of f(x)-L is less than 0.08arrow_forwardlimx-->0 Evaluate the limit (-4+h)2-16/harrow_forwardlim x to infinity x-2/x2+1 find the limitarrow_forward
- lim_(h->0)(h)/(sin (3h)) Find the limit algebraically, h approaching zero from the left hand sidearrow_forwardlim X^3-2x^2+3x-4 / 4x^3-3x^2+2x-1 x---infinite Question? Evaluate the limitarrow_forwardTrue or False: If limit as xà0 of f(x) equals zero then f(0)=0. If false provide an illustrative example to support your conclusion.arrow_forward
- Let f(x)= 2x-2 if x<1 f(x)=x^2-1 if x is greater than or equal to 1 Evaluate Lim h-->0+ f(1+h)-f(1)/h Evaluate Lim h-->0- f(1+h)-f(1)/h Is the function f differentiable at a=1? Justify your answer.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_forwarda) value of f(1) b) lim x→1-f(x) c) lim x→1+f(x) d) Does lim x→1 f(x) exist? If so, find value. If not, explain why. e) lim x→2+f(x) f) lim x→2-f(x)arrow_forward
- lim x→8 f(x) = 4 and limx→8 g(x)=8 , evaluate limx→8 f(x) +g(x) /7f(x) Limit =arrow_forwardThe graph of the function f(x)=cotxf(x)=cotx is given above for the interval x∈[0,2π]x∈[0,2π] ONLY.Determine the one-sided limit. Then indicate the equation of the vertical asymptote.Find limx→π− f(x)=limx→π- f(x)= This indicates the equation of a vertical asymptote is x= .Find limx→0+ f(x)=limx→0+ f(x)= This indicates the equation of a vertical asymptote is x=.arrow_forwardSketch the graph of a function f which incorporates all the limit & derivative information below: (Be sure to include any asymptotes in your sketch of the graph f) • lim f(x)=0 lim f(x)=−∞ lim f(x)=∞ limf(x)=−∞ lim f(x)=1 • The function values of f, and its first derivative f′(x), and its second derivative, f′′(x), are undefined at x = −2 and at x = 0, and are defined for all other real number values of x. • The first derivative f′(x) is negative on the x-intervals (−∞, −2) and (−2, 0), is positive on the interval (0, 2), is zero at x = 2, and is negative on the interval (2, ∞). • The second derivative f′′(x) is negative on the x-interval (−∞,−2), positive on the interval (−2, −1), has value zero at x = −1, is negative on the intervals (−1, 0) and (0, 3), has value zero at x = 3, and is positive on the interval (3, ∞).arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning