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JAMB Mathematics 2023 Paper

Question : 16

Total: 80

\lim\limits_{x\to 2} \frac{x^2 + 4x - 12}{x^2 - 2x}

Solution:

Concept:

Direct substitution gives an indeterminate form, so factor and simplify the rational expression before evaluating the limit.

Explanation:

First, factor both the numerator and the denominator.

x^2 + 4x - 12 = (x-2)(x+6)

x^2 - 2x = x(x-2)

So the expression becomes:

\lim\limits_{x\to 2} \frac{(x-2)(x+6)}{x(x-2)}

Cancel the common factor

(x-2)

, since

x \neq 2

in the limit process.

\lim\limits_{x\to 2} \frac{x+6}{x}

Now substitute

x = 2

\frac{2+6}{2} = \frac{8}{2} = 4

Thus, the limit is

4

Answer:

A. 4

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