Find the lim as h approaches 0 of (sqrt(16 + h) + 4) / h.

Question:

Find the {eq}\lim_{h \to 0} \frac{\sqrt{16+h}+4}{h} {/eq}.

Limit Function:


The general formula of limit for a function {eq}g(x) {/eq} can be shown as below;

{eq}\mathop {\lim }\limits_{h \to 0} \dfrac{{g\left( {x + h} \right) - g\left( x \right)}}{h} {/eq}

Where, {eq}g(x+h) {/eq} can be found by replacing the term x with {eq}x+h {/eq} in the given function. This formula also tells the differentiability of the function.

Answer and Explanation: 1

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Given

  • The function is given as {eq}\mathop {\lim }\limits_{h \to 0} \dfrac{{\sqrt {16 + h} + 4}}{h} {/eq}.


Solve the given function to find the...

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How to Determine the Limits of Functions

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Chapter 6 / Lesson 4
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A limit can tell us the value that a function approaches as that function's inputs get closer and closer to a number. Learn more about how to determine the limits of functions, properties of limits and read examples.


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