Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
10th Edition
ISBN: 9781285464640
Author: Soo T. Tan
Publisher: Brooks Cole
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Chapter B, Problem 15E
To determine
To evaluate: The limit by using l’Hôpital’s Rule.
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Prove using the definition of a limit.
lim
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How do I find the limit?
2. Describe a strategy for solving limits of the form limx→∞f(x)g(x), where f(x) and g(x) are polynomials.
Chapter B Solutions
Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
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- Once you know lim x-->a+ f(x) and lim x-->a- ƒ(x) at an interior point of the domain of ƒ, do you then know limx-->a ƒ(x)? Give reasons for your answerarrow_forwardProve that limx->∞ f(x) =lim t->0+ f(1/t) and limx->∞ f(x) =lim t->0- f(1/t) if these limits exists.arrow_forwardEvaluate the limit limx>infinity x2e-xarrow_forward
- Evaluate the limitlimx->infinity8/(e^x-8)=limx->-infinity8/(e^x-8)=arrow_forwardIf lim f(x)=-2 x-->0+, lim f(x)=3 x-->0-, and f(0)=-2, what can you say about lim f(x) x-->0?arrow_forwardHow do you prove c), i.e. the third bullet point, using lim(x ->a) [ f(x) - f(a) ] / [ x -a ] with the domain (-inf, 1)? Is a = 1?arrow_forward
- Use Definition 4.2.1 ((Functional Limit).)to supply a proper proof for the following limit statements. (a) limx→2(3x + 4) = 10. (b) limx→0 x3 = 0. (c) limx→2(x2 + x − 1) = 5. (d) limx→3 1/x = 1/3.arrow_forwardusing theorems on infinite limits (not lhospitals rule), find the exact value of the limit. lim x goes to negative infinity, X^3 - 16 / 4x^2 - 13x -12arrow_forwardSolve it on a paper! Please use the limit rule, which is lim(x->c) f(g(x)) = f( lim_(x->c) g(x))!arrow_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