Question

Use a calculator to estimate the limit
Picture provided below

Answer 1

Answer:

b.∞

Step-by-step explanation:

Given:$\lim_{n \to \infty} \sqrt{x^2 + 10x + 5}  + x$

This can be written as

= $\lim_{n \to \infty} \sqrt{x^2+10x + 5}  +  \lim_{n \to \infty} x$

when applying the limit x -->∞, we get

$\lim_{n \to \infty} \sqrt{x^2 +10x + 5} =$ ∞

and

$\lim_{n \to \infty} x =$ = ∞

Therefore, we get

= ∞ + ∞

= ∞       [Since ∞ itself a largest number so there is no 2∞]

Answer: b.∞

Hope this will helpful.

Thank you.

Answer 2

Answer:

b is correct.

$L=\infty$

Step-by-step explanation:

We are given a limit $L=\lim_{x\rightarrow \infty}(\sqrt{x^2+10x+5}+x)$

Using calculator to find the value of limit.

First we check the limit exist or not.

We have to check left and right hand limit.

For Left hand limit, LHL

$L=\lim_{x\rightarrow \infty^-}(\sqrt{x^2+10x+5}+x)=\infty$

For Right hand limit, RHL

$L=\lim_{x\rightarrow \infty^+}(\sqrt{x^2+10x+5}+x)=\infty$

LHL=RHL=∞

$L=\lim_{x\rightarrow \infty}(\sqrt{x^2+10x+5}+x)$

$L=\sqrt{\infty^2+10\infty+5}+\infty$

$L=\infty$

Hence, b is correct.