Chapter 14: Q. 29 (page 883)

In Problems 7– 42, find each limit algebraically.
$\lim_{x \to 2} \frac{x^{2} - 4}{x^{2} - 2 x} .$

Short Answer

Expert verified

The answer is 2.

Step by step solution

Step. 1 Given Information

Firstly, we check whether the given function is in indeterminant form or not.

$f (x) = \frac{x^{2} - 4}{x^{2} - 2 x}$

Since if we put $x = 2$ we get,

$\frac{2^{2} - 4}{2^{2} - 2 (2)} = \frac{4 - 4}{4 - 4} = \frac{0}{0}$ .

So given the limit is in 0/0 indeterminant form.

Step. 2 Try to find factor which make the function indeterminant.

Since we have both polynomial functions in the numerator and denominator, So let's factorize them,

$\frac{x^{2} - 4}{x^{2} - 2 x} = \frac{x^{2} - 2^{2}}{x (x - 2)} = \frac{(x - 2) (x + 2)}{x (x - 2)},$

cancelling $(x - 2)$ from both numerator and denominator we get,

$\frac{x + 2}{x}$ .

Now if we put $x = 2$ then it is not in indeterminant from. So, now we can directly put the limit in it.

Step. 3 Solving the limit

$\lim_{x \to 2} \frac{x + 2}{x} = \frac{2 + 2}{2} = \frac{4}{2} = 2 .$

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In Problems 7– 42, find each limit algebraically.
$\lim_{x \to 2} \frac{x^{2} - 4}{x^{2} - 2 x} .$

Short Answer

Step by step solution

Step. 1 Given Information

Step. 2 Try to find factor which make the function indeterminant.

Step. 3 Solving the limit

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In Problems 7– 42, find each limit algebraically.limx→2x2-4x2-2x.

Short Answer

Step by step solution

Step. 1 Given Information

Step. 2 Try to find factor which make the function indeterminant.

Step. 3 Solving the limit

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Probability and Statistics

Theoretical and Mathematical Physics

Decision Maths

Calculus

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In Problems 7– 42, find each limit algebraically.
$\lim_{x \to 2} \frac{x^{2} - 4}{x^{2} - 2 x} .$