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If $ \displaystyle \lim_{x \to 0}\frac{f(x)}{x^2}…

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Problem 59 Medium Difficulty

If $ \displaystyle \lim_{x \to 1}\frac{f(x) - 8}{x - 1} = 10 $, find $ \displaystyle \lim_{x \to 1}f(x) $.

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Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 2

Limits and Derivatives

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Calculating Limits Using the Limit Laws

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Video Transcript

This is problem number 59 of this to calculus edition section 2.3. If the limit as x, approaches 1 of the function f of x minus 8 over x, minus 1 is equal to 10 point find the limit as x approaches 1 of the function f. So, since we're given this definitive statement that this limit is equal to 10, we'll use our limit laws to rewrite this limit. Instead, as the limit as x, approaches 1 have f minus the limit is f x, approaches 1 of a divided by the limit as x, riches 1 of the quantity x minus 1 equals to 10 point. So we've used the laws that allow us to separate this quotient within the limit into the division of 2 limits and then the difference of limits in the top and the difference in set of a limit to the difference of limits at the top and notice that This term here is the term we want to solve, for so, let's go ahead, and do that multiply both sides limit is x, plus 1 of f minus limit is x, plus is 1 of 8 is equal to 10 times. This limit as x, approaches 1 of x minus 1. We can move the other limit to the right hand side. So, on the left hand, side we have limit as x, which is 1 of f equals 10 times the limit and which is 1 of the quantity x. Minus 1 plus e limit as x approaches 1 of 8. Now, as x, proches 1, this quantity x, minus 1, is equal to 1 minus 1 or 0 and 10 times 0 is 0. So what we end up getting is that the limit, as x, pushes 1 of f is equal to 0, plus this limit the limit of just 188 being in a constant value, therefore telling what is equal to 8- and this is our final answer as to what The limit is toast, 1 of f is.

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Problem

If $ \displaystyle \lim_{x \to 0}\frac{f(x)}{x^2}…

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Related Courses

Calculus: Early Transcendentals

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Video Transcript

James Stewart

Calculus: Early Transcendentals

Anna Marie Vagnozzi

Caleb Elmore

Michael Jacobsen

Joseph Lentino

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Calculus: Early Transcendentals

Anna Marie Vagnozzi

Caleb Elmore

Michael Jacobsen

Joseph Lentino

James StewartCalculus: Early Transcendentals

Anna Marie Vagnozzi

Caleb Elmore

Michael Jacobsen

Joseph Lentino

James Stewart

Calculus: Early Transcendentals