"Evaluate the following limits, where c and k..." solved and explained

Ava-May Nelson

Answered question

2021-10-17

Evaluate the following limits, where c and k are constants.

lim_{x \to 2} (\frac{1}{x - 2} - \frac{2}{x^{2} - 2 x})

wheezym

Skilled2021-10-18Added 103 answers

To evaluate:

lim_{x \to 2} (\frac{1}{x - 2} - \frac{2}{x^{2} - 2 x})

Solution:
Given,

lim_{x \to 2} (\frac{1}{x - 2} - \frac{2}{x^{2} - 2 x})

On simplifying further we get:

lim_{x \to 2} (\frac{1}{x - 2} - \frac{2}{x^{2} - 2 x}) = lim_{x \to 2} (\frac{1}{x - 2} - \frac{2}{x (x - 2)})

\Rightarrow lim_{x \to 2} (\frac{1}{x - 2} - \frac{2}{x^{2} - 2 x}) = lim_{x \to 2} (\frac{x - 2}{x (x - 2)})

\Rightarrow lim_{x \to 2} (\frac{1}{x - 2} - \frac{2}{x^{2} - 2 x}) = lim_{x \to 2} \frac{1}{x}

\Rightarrow lim_{x \to 2} (\frac{1}{x - 2} - \frac{2}{x^{2} - 2 x}) = \frac{1}{2}

Result:

lim_{x \to 2} (\frac{1}{x - 2} - \frac{2}{x^{2} - 2 x}) = \frac{1}{2}

Jeffrey Jordon

Expert2022-08-30Added 2605 answers

Answer is given below (on video)

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