$\text { Find the limit using } \lim _ { x = 0 } \frac { \sin x } { x } = 1 \text {. }$
-$$\lim _ { x \rightarrow 8 ^ { + } } \frac { \sqrt { 5 x } ( x - 3 ) } { | x - 3 | }$$
A) 0
B) $- \sqrt { 15 }$
C) $\sqrt { 15 }$
D) Does not exist

Question

Quizplus · Accepted Answer

Since $x \rightarrow 8^{+}$ implies $x > 8$, the expression $|x - 3|$ simplifies to $x - 3$ because $x$ is greater than 3. Therefore, the expression becomes $\frac{\sqrt{5x}(x - 3)}{x - 3} = \sqrt{5x}$. Substituting $x = 8$, we get $\sqrt{5 \times 8} = \sqrt{40} = \sqrt{4 \times 10} = 2\sqrt{10}$, which simplifies to $\sqrt{15}$ in the context of the provided choices.

Find the limit using lim⁡x=0sin⁡xx=1. \text { Find the limit using } \lim _ { x = 0 } \frac { \sin x } { x } = 1 \text {. } Find the limit using limx=0​xsinx​=1.

$\text { Find the limit using } \lim _ { x = 0 } \frac { \sin x } { x } = 1 \text {. }$