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Chapter 14: Q. 6 (page 883)

True or False The limit of a quotient equals the quotient of the limits.

Short Answer

Expert verified

The given statement is False.

Step by step solution

01

Step 1. Given Information

The statement given is, "The limit of a quotient equals the quotient of the limits.

02

Step 2. Example

Let us take for example,

$f (x) = \frac{x^{2} - x - 6}{x^{2} - 9}$

$\frac{x^{2} - x - 6}{x^{2} - 9} = \frac{(x - 3) (x + 2)}{(x - 3) (x + 3)}$

On Applying the limit,

$\lim_{x \to 3} \frac{(x - 3) (x + 2)}{(x - 3) (x + 3)}$

The limit of the quotient of the function $\lim_{x \to 3} \frac{1}{x^{2} - 9} = \frac{1}{0}$ which is undefined

03

Step 3. Conclusion

This statement is false because if in any case the limit of the denominator becomes zero, Then the limit is undefined.

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Most popular questions from this chapter

Use a graphing utility to find the indicated limit rounded to two decimal places.

$\lim_{x \to 2} \frac{x^{3} - 2 x^{2} + 4 x - 8}{x^{2} + x - 6}$

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