Question

Select the correct answer. What is the value of this limit?

A. 7
B. 5
C. 3
D. 10
E. 9

Answer 1

The Value of Given Limit is option E) 9

`\lim_(x \to 3)(\sqrt{(x^(2)+7)} + 5) =9`

Explanation:

Given:

`\lim_(x \to 3)(\sqrt{(x^(2)+7)} + 5)`

To Find:

`\lim_(x \to 3)(\sqrt{(x^(2)+7)} + 5) = ?`

Solution:

x → 3 Implies that x is approaching to 3 not equal to 3

For taking Limit out we need to put x = 3

∴
`L = \lim_(x \to 3)(\sqrt{(x^(2)+7)} + 5) \\\\= \lim_(x \to 3)\sqrt{(x^(2)+7) } +\lim_(x \to 3)5\\\\=\sqrt{(3^(2) +7)} + 5\\\\=√(16) +5\\\\=4+5\\\\\therefore L =9`

∴ L = 9