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Estimating limits graphically and numerically Use a graph of f to estimate
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Calculus, Single Variable: Early Transcendentals (3rd Edition)
- (x^3-x^2) divided by (x-1) lim x-> 1 Evaluate the limit.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_forwardlimx-->0 Evaluate the limit (-4+h)2-16/harrow_forward
- lim_(h->0)(h)/(sin (3h)) Find the limit algebraically, h approaching zero from the left hand sidearrow_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
- 3. Evaluate lim x→5 √x+4-3/ x-5. Show your complete solution. 4. Evaluate lim x→1 x-1/ √x-1. Show your complete solution. 5. Prove that lim t→-2 √1-t3/t +3/2 / t+2= 1/4. Show your complete solution.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_forwardhow to find limit of given function j(x)= kcosx x < 0 2x - k x > 0 Find the value of k Enter exact answerarrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning