Get the solution to "Find the following limits or state that they..."

texelaare

Answered question

2021-10-28

Find the following limits or state that they do not exist. Assume a, b, c, and k are fixed real numbers.

lim_{x \to 4} \frac{\frac{1}{x} - \frac{1}{4}}{x - 4}

Answer & Explanation

Sally Cresswell

Skilled2021-10-29Added 91 answers

Given limit:

lim_{x \to 4} (\frac{\frac{1}{x} - \frac{1}{4}}{x - 4})

Now,

lim_{x \to 4} (\frac{\frac{1}{x} - \frac{1}{4}}{x - 4}) = lim_{x \to 4} (\frac{\frac{4 - x}{4 x}}{x - 4})

= lim_{x \to 4} (\frac{4 - x}{4 x (x - 4)})

= lim_{x \to 4} (\frac{- (x - 4)}{4 x (x - 4)})

lim_{x \to 4} (- \frac{1}{4 x})

Plug in the value x=4:

= - \frac{1}{4.4}

= - \frac{1}{16}

Thus,

lim_{x \to 4} (\frac{\frac{1}{x} - \frac{1}{4}}{x - 4}) = - \frac{1}{16}

Jeffrey Jordon

Expert2022-07-03Added 2575 answers

Answer is given below (on video)

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