Test Index

WAEC Further Mathematics 2025 Paper

Question : 15

Total: 40

Evaluate lim

_{x→1}

\frac{1-x}{x^2 - 3x + 2}

Solution:

Concept:

This is a limit of the form

\frac{0}{0}

, so factorise the denominator and cancel the common factor.

Explanation:

Factorise the denominator:

x^2 - 3x + 2 = (x-1)(x-2)

Rewrite the numerator:

1-x = -(x-1)

Substitute into the limit:

\lim_{x\to 1}\frac{1-x}{x^2-3x+2} = \lim_{x\to 1}\frac{-(x-1)}{(x-1)(x-2)}.

Cancel

(x-1)

since

x \neq 1

in the limit:

= \lim_{x\to 1}\frac{-1}{x-2}.

Evaluate directly at

x=1

\frac{-1}{1-2} = \frac{-1}{-1} = 1.

Answer:

1

This corresponds to option B.

Go to Question:

Prev Question

Next Question