Algebraically evaluate the limit (if it exists)by the appropriate technique(s). $\lim _ { x \rightarrow 100 ^ { + } } \frac { 10 - \sqrt { x } } { x - 100 }$
A) $\lim _ { x \rightarrow 100 ^ { + } } \frac { 10 - \sqrt { x } } { x - 100 } = \frac { 1 } { 22 }$
B) $\lim _ { x \rightarrow 100 ^ { + } } \frac { 10 - \sqrt { x } } { x - 100 } = - \frac { 1 } { 21 }$
C) $\lim _ { x \rightarrow 100 ^ { + } } \frac { 10 - \sqrt { x } } { x - 100 } = \frac { 1 } { 21 }$
D) $\lim _ { x \rightarrow 100 ^ { + } } \frac { 10 - \sqrt { x } } { x - 100 } = \frac { 1 } { 20 }$
E) $\lim _ { x \rightarrow 100 ^ { + } } \frac { 10 - \sqrt { x } } { x - 100 } = - \frac { 1 } { 20 }$

Question

Algebraically evaluate the limit (if it exists)by the appropriate technique(s).  $\lim _ { x \rightarrow 100 ^ { + } } \frac { 10 - \sqrt { x } } { x - 100 }$ 
A) $\lim _ { x \rightarrow 100 ^ { + } } \frac { 10 - \sqrt { x } } { x - 100 } = \frac { 1 } { 22 }$
B) $\lim _ { x \rightarrow 100 ^ { + } } \frac { 10 - \sqrt { x } } { x - 100 } = - \frac { 1 } { 21 }$
C) $\lim _ { x \rightarrow 100 ^ { + } } \frac { 10 - \sqrt { x } } { x - 100 } = \frac { 1 } { 21 }$
D) $\lim _ { x \rightarrow 100 ^ { + } } \frac { 10 - \sqrt { x } } { x - 100 } = \frac { 1 } { 20 }$ 
E) $\lim _ { x \rightarrow 100 ^ { + } } \frac { 10 - \sqrt { x } } { x - 100 } = - \frac { 1 } { 20 }$

Quizplus · Accepted Answer

The expression can be simplified by multiplying the numerator and denominator by the conjugate of the numerator, $10 + \sqrt{x}$. This results in $\frac{(10 - \sqrt{x})(10 + \sqrt{x})}{(x - 100)(10 + \sqrt{x})}$. The numerator simplifies to $100 - x$, which cancels with the denominator $x - 100$, leaving $-1/(10 + \sqrt{x})$. Evaluating the limit as $x$ approaches 100 from the right gives $-1/20$.

Algebraically Evaluate the Limit (If It Exists)by the Appropriate Technique(s) lim⁡x→100+10−xx−100\lim _ { x \rightarrow 100 ^ { + } } \frac { 10 - \sqrt { x } } { x - 100 }limx→100+​x−10010−x​​

Algebraically Evaluate the Limit (If It Exists)by the Appropriate Technique(s) $\lim _ { x \rightarrow 100 ^ { + } } \frac { 10 - \sqrt { x } } { x - 100 }$