Question

mit: \\( \lim _ { x \
ightarrow 64 } \frac { - 128 + 2 x } { 8 - \sqrt { x } } \\)

Explanation:

Step1: Factor numerator

Factor out \(2\) from \(-128 + 2x\): \(2(x - 64)\).
So, the limit becomes \(\lim_{x
ightarrow64}\frac{2(x - 64)}{8-\sqrt{x}}\).

Step2: Rationalize denominator

Multiply numerator and denominator by \(8+\sqrt{x}\):

$$
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$$

Step3: Cancel out common factor

Cancel out \((64 - x)\):
\(\lim_{x
ightarrow64}-2(8+\sqrt{x})\)

Step4: Substitute \(x = 64\)

Substitute \(x = 64\) into \(-2(8+\sqrt{x})\):
\(-2(8+\sqrt{64})=-2(8 + 8)=-32\)

Answer:

\(-32\)