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Chapter 14: Q. 3 (page 905)

find the limit $\lim_{x \to 3} \sqrt{x^{2} + 7}$

Short Answer

Expert verified

$\lim_{x \to 3} \sqrt{x^{2} + 7} = 4$

Step by step solution

01

Step 1. Given information

$\lim_{x \to 3} \sqrt{x^{2} + 7}$

02

Step 2. Limit of the function

We can find limit of root function by $\lim_{x \to c} f (x) = f (c)$ if c is in the domain of f(x) and the domain of f(x)= $\sqrt{x^{2} + 7}$ is all real numbers.

So we can use the above formula .

$\lim_{x \to 3} f (x) = f (3) = \sqrt{(3)^{2} + 7} = 4$

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Most popular questions from this chapter

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

Find the y-intercept(s), if any, of $f$ .

$\lim_{x \to c} b =_____.$

In Problems 7– 42, find each limit algebraically.

\lim_{x \to 1} {(x^{2} + 1)}^{3}

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

$\lim_{x \to - 1} f (x), f (x) = 2 x - 1$

In Problems 7– 42, find each limit algebraically.

$\lim_{x \to 2} \frac{3 x + 4}{x^{2} + x} .$

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