Check the solution to "Evaluate each of the following limits. a) limx→−32x2+13x+21x+3..." - Plainmath

Emily-Jane Bray

Answered question

2021-10-19

Evaluate each of the following limits.
a)

lim_{x \to - 3} \frac{2 x^{2} + 13 x + 21}{x + 3}

b)

lim_{x \to 9} \frac{2 - \sqrt{x - 5}}{x - 9}

Answer & Explanation

Viktor Wiley

Skilled2021-10-20Added 84 answers

Solution:
a)

lim_{x \to - 3} \frac{2 x^{2} + 13 x + 21}{x + 3}

Apply L hopital rule

= lim_{x \to - 3} \frac{\frac{d}{d x} (2 x^{2} + 13 x + 21)}{\frac{d}{d x} (x + 3)}

= lim_{x \to - 3} \frac{4 x + 13}{1} = 4 x - 3 + 13 = 1

b)

lim_{x \to 9} \frac{2 - \sqrt{x - 5}}{x - 9} = lim_{x \to 9} \frac{(2 - \sqrt{x - 5}) (2 + \sqrt{x - 5})}{(x - 9) (2 + \sqrt{x - 5})}

= lim_{x \to 9} \frac{(4 - (x - 5))}{(x - 9) (2 + \sqrt{x - 5})}

= lim_{x \to 9} \frac{- (x - 9)}{(x - 9) (2 + \sqrt{x - 5})}

= \frac{- 1}{2 + \sqrt{9 - 5}} = \frac{- 1}{4}

Jeffrey Jordon

Expert2022-06-28Added 2605 answers

Answer is given below (on video)

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