$\text { Find the limit using } \lim _ { x = 0 } \frac { \sin x } { x } = 1 \text {. }$
-$\lim _ { h \rightarrow 0 ^ { - } } \frac { \sqrt { 10 } - \sqrt { 2 h ^ { 2 } + 7 h + 10 } } { h }$
A) $\frac { - 7 } { 2 \sqrt { 10 } }$
B) $\frac { 7 } { 2 \sqrt { 10 } }$
C) $\frac { - 7 } { \sqrt { 20 } }$
D) Does not exist

Question

Quizplus · Accepted Answer

To solve this limit, we can multiply the numerator and denominator by the conjugate of the numerator, $\sqrt{10} + \sqrt{2h^2 + 7h + 10}$, to rationalize the numerator. This process eliminates the square root in the numerator and simplifies the expression, allowing us to find the limit as $h$ approaches 0 from the left. After simplification, the limit evaluates to $\frac{-7}{2\sqrt{10}}$, making choice A correct.

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.

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