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Suppose f(x) \to 100 and g(x) \to 0 with g(x) 0 as x \to 2. Determine \lim\limits_{ x \to 2}...

Question:

Suppose {eq}f(x) \to 100 {/eq} and {eq}g(x)\to 0 {/eq} with {eq}g(x) > 0 {/eq} as {eq}x \to 2 {/eq}.

Determine {eq}\lim \limits_{x \to 2} \frac {f(x)}{g(x)} {/eq}

Limit

By the basic principles of the limit the continuity and the discontinuity is calculated. The limit is a particular value for a function at given value of the independent variable of the function. Sometimes the derivatives and integral are defined by the limits of the functions.

Answer and Explanation:


Given Data

  • The value of first function is {eq}f\left( x \right) \to 100 {/eq}
  • The value of second function is {eq}g\left( x \right) \to 0 {/eq}


The limit value of the given function is,

{eq}\mathop {\lim }\limits_{x \to 2} \dfrac{{f\left( x \right)}}{{g\left( x \right)}} {/eq}


Hence, the value of function {eq}g\left( x \right) {/eq} is approx {eq}0 {/eq} and positive.


Substitute the values.

{eq}\begin{align*} \mathop {\lim }\limits_{x \to 2} \dfrac{{f\left( x \right)}}{{g\left( x \right)}} &= \dfrac{{100}}{0}\\ &= \infty \end{align*} {/eq}


Thus, the value of {eq}\mathop {\lim }\limits_{x \to 2} \dfrac{{f\left( x \right)}}{{g\left( x \right)}} {/eq} is {eq}\infty {/eq}.


Learn more about this topic:

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How to Determine the Limits of Functions

from Math 104: Calculus

Chapter 6 / Lesson 4
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