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Chapter 1: Problem 3

Find the limit. $$ \lim _{x \rightarrow 2} x^{4} $$

Short Answer

Expert verified
The limit of the function \(x^{4}\) as \(x\) approaches 2 is 16.

Step by step solution

01

Identify the function and the point of interest

The function given is \(x^{4}\) and the point of interest is when \(x\) is approaching 2.
02

Substitute x=2

Since the function is continuous at \(x=2\), substitute \(x\) with 2 into the function \(x^{4}\). Hence, when 2 is substituted in the function, it becomes \(2^{4}\)
03

Evaluate the expression

Evaluate the expression \(2^{4}\) to get 16.

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Most popular questions from this chapter

Sketch the graph of the function. Use a graphing utility to verify your graph. $$ f(x)=\arccos \frac{x}{4} $$

Write the expression in algebraic form. \(\csc \left(\arctan \frac{x}{\sqrt{2}}\right)\)

$$ \lim _{x \rightarrow 2} f(x)=3, \text { where } f(x)=\left\\{\begin{array}{ll} 3, & x \leq 2 \\ 0, & x>2 \end{array}\right. $$

Sketch the graph of the function. Use a graphing utility to verify your graph. $$ f(x)=\operatorname{arcsec} 2 x $$

Prove that if \(f\) has an inverse function, then \(\left(f^{-1}\right)^{-1}=f\).
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