\lim _{x\to \:-1}\frac{x^2+3x+2}{x+1}

Answered question

2022-02-17

\lim _{x\to \:-1}\frac{x^2+3x+2}{x+1}

Answer & Explanation

Vasquez

Vasquez

Expert2022-03-12Added 669 answers

limx1x2+3x+2x+1 - Given

Apply L'Hospital's rule.

Evaluate the limit of the numerator and the limit of the denominator.

Take the limit of the numerator and the limit of the denominator.

limx1x2+3x+2limx1x+1

Evaluate the limit of the numerator.

0limx1x+1

Evaluate the limit of the denominator.

00

Since 00 is of indeterminate form, apply L'Hospital's Rule. L'Hospital's Rule states that the limit of a quotient of functions is equal to the limit of the quotient of their derivatives.

limx1x2+3x+2x+1=limx1ddx[x2+3x+2]ddx[x+1]

Find the derivative of the numerator and denominator.

limx12x+31

Divide 2x+3 by 1

limx12x+3

Evaluate the limit.

2limx1x+3

Evaluate the limit of x by plugging in 1 for x

21+3

Simplify the answer.

1 - Answer

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