Consider the function f(x) = ((x - 1)^3)/((x + 1)^3 (x - 4)^3). Find the following limits. A)...

Question:

Consider the function {eq}f(x) = \frac{(x - 1)^3}{(x + 1)^3 (x - 4)^3} {/eq}. Find the following limits.

A) {eq}\lim_{x\rightarrow -1^+} f(x) {/eq}

B) {eq}\lim_{x\rightarrow -1^-} f(x) {/eq}

C) {eq}\lim_{x\rightarrow 1^+} f(x) {/eq}

D) {eq}\lim_{x\rightarrow 1^-} f(x) {/eq}

E) {eq}\lim_{x\rightarrow 4^+} f(x) {/eq}

F) {eq}\lim_{x\rightarrow 4^-} f(x) {/eq}

Limit:


Limit is a crucial part of integral as well as differential calculus. Limits are used to evaluate the sum of sequence and series, differential equation, and the average value of the function. Limits are also used to define where the function is continuous and differentiable.


Answer and Explanation: 1

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Given:


  • The function is, {eq}f\left( x \right) = \frac{{{{\left( {x - 1} \right)}^3}}}{{{{\left( {x + 1} \right)}^3}{{\left( {x - 4}...

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How to Determine the Limits of Functions

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Chapter 6 / Lesson 4
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Develop an intuition for the limit of a function. Learn the properties of the limit of a function. Apply the rules to compute the limits of functions through examples.


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