Chapter 14: Q. 8 (page 905)

$\lim_{x \to - 3} \frac{x^{2} - 9}{x^{2} - x - 12}$ find the limit

Short Answer

Expert verified

$\lim_{x \to - 3} \frac{x^{2} - 9}{x^{2} - x - 12} = \frac{6}{7}$

Step by step solution

Step 1. Given information

$\lim_{x \to - 3} \frac{x^{2} - 9}{x^{2} - x - 12}$

Step 2. Domain of the function

We can find limit of rational function by $\lim_{x \to c} f (x) = f (c)$ if c is in the domain of f(x) .So to find the domain of f(x)= $\frac{x^{2} - 9}{x^{2} - x - 12}$ we have to put denominator =0

role="math" localid="1647084893764" $x^{2} - x - 12 x = - 3 x = 4$

So domain of the f(x) is all real number except 4and -3.

Step 3. limit of the function

As here c= -3which is not in the domain . So we have to simplify the f(x)

$\lim_{x \to - 3} \frac{x^{2} - 9}{x^{2} - x - 12} = \lim_{x \to - 3} \frac{(x - 3) (x + 3)}{(x - 4) (x + 3)} = \lim_{x \to - 3} \frac{x - 3}{x - 4} = \frac{- 3 - 3}{- 3 - 4} = \frac{6}{7}$

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$\lim_{x \to - 3} \frac{x^{2} - 9}{x^{2} - x - 12}$ find the limit

Short Answer

Step by step solution

Step 1. Given information

Step 2. Domain of the function

Step 3. limit of the function

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limx→-3x2-9x2-x-12find the limit

Short Answer

Step by step solution

Step 1. Given information

Step 2. Domain of the function

Step 3. limit of the function

One App. One Place for Learning.

Most popular questions from this chapter

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$\lim_{x \to - 3} \frac{x^{2} - 9}{x^{2} - x - 12}$ find the limit