Essential Calculus
2nd Edition
ISBN: 9781285209067
Author: Stewart
Publisher: Cengage
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Determine whether the statement is true or false.
lim x→0
x
ex
= 1
A) True
B) False
Use the Quotient Law to prove that if lim f (x) exists and is nonzero then
lim x→c 1/f(x)= 1/limf(x)
Considering the definition of f(x) below, find limx→5−f(x).
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- Find the value of the postive constant c, such that lim x->infinty ((x-c)/(x+c))^x=1/4arrow_forwardState whether the inequality provides sufficient information to determine lim f (x ), and if so, find the limit. x→ 1(a) 4x - 5 < f(x) < x 2(b) 2x - 1 < f(x) < x 2(c) 4x - x 2 < f(x) < x 2 + 2arrow_forwardLet g(x) = x2 + x − 30 |x − 5| . (a) Find the following limits. (If an answer does not exist, enter DNE.) (i) lim x → 5+ g(x) (ii) lim x → 5− g(x) (b) Does lim x → 5 g(x) exist?arrow_forward
- True or False: If f(c)=10, then lim f(x)=10 x-->carrow_forward(a) Estimate the value of lim x→ - infinity square root x^2+x+1 +1 by graphing the function f(x)=square root x^2+x+1 +1 b) use a table of values of f(x) to guess the value of the limit.arrow_forwardDetermine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If limxc f(x) = L and f(c) = L, then f is continuous at c.arrow_forward
- The graph of f(x) = 2x2/(x2 + 2) is shown. (a) Find L = limx ∞ f(x). (b) Determine x1 and x2 in terms of ε. (c) Determine M, where M > 0, such that ∣ f(x) − L∣ < ε for x > M. (d) Determine N, where N < 0, such that ∣ f(x) − L∣ < ε for x < N.arrow_forwardWhat is the lim f(x) x→1? f(x)= { 2x2-9, x<1 4x-11, x ≥ 1arrow_forward
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Limits and Continuity; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=9brk313DjV8;License: Standard YouTube License, CC-BY