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Chapter 14: Q. 4 (page 883)

True or False The limit of a polynomial function as $x$ approaches $5$ equals the value of the polynomial at $5$

Short Answer

Expert verified

True

Step by step solution

01

Step 1. Limit of a polynomial theorem

If $P (x)$ is a polynomial function then,

$\lim_{x \to c} P (x) = P (c)$ .

02

Step 2. Theorem in words

To find the limit of a polynomial as $x$ approaches $c$ all we need to do is evaluate the polynomial at $c$ .

Therefore the statement "the limit of a polynomial function as $x$ approaches $5$ equals the value of the polynomial at $5$ " is TRUE.

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Most popular questions from this chapter

In Problems 13–32, use the accompanying graph of y = f(x).

Find $\lim_{x \to 2^{+}} f (x) .$

Graph each function. Use the graph to find the indicated limit, if it exists.

$\lim_{x \to 4} f (x), f (x) = 3 x + 1$

In Problem, graph each function. Use the graph to find the indicated limit, if it exists.

$\underset{x \to 2}{l i m} f (x), f (x) = \{\begin{cases} x^{2} & i f x \leq 2 \\ 2 x - 1 & i f x > 2 \end{cases}$

In Problem, graph each function. Use the graph to find the indicated limit, if it exists.
$\underset{}{\underset{x \to 2}{l i m} f (x), f (x) = 1}$

Use the graph shown to determine if the limit exists. If it does, find its value.

See all solutions

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