Concept explainers
Estimating limits graphically and numerically Use a graph of f to estimate
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Calculus, Single Variable: Early Transcendentals (3rd Edition)
- limx-->0 Evaluate the limit (-4+h)2-16/harrow_forward(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_forward
- a. 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_forwardlim X^3-2x^2+3x-4 / 4x^3-3x^2+2x-1 x---infinite Question? Evaluate the limitarrow_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 x2-4x/x2-16 (Guess value of limit) x-->4arrow_forward3. 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_forwardlim x→8 f(x) = 4 and limx→8 g(x)=8 , evaluate limx→8 f(x) +g(x) /7f(x) Limit =arrow_forward
- Finding a constant Suppose Determine a value of the constant b for which lim xS2 f 1x2 exists and state the value of the limit, if possible.arrow_forward(a) for g(t)= t-9/square root t-3 . Make table of values with at least six appropriate inputs to evaluate the limits as t tends to 9. (b) make a conjecture about the value of lim t-9/square root t-3. t->9arrow_forward1. Evaluate lim (2x-5) given its graph below. x →2 a.0 b. -1 c. 2 d. 1 2. Given the graph of f(x) below, evaluate its limit as x approaches 3. a.2 b. 3 c. 1 d. 0arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning