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WAEC Further Mathematics 2019 Paper

Question : 39

Total: 39

Evaluate:

\lim\limits_{x\to 1}\left(\;\frac{1-x}{x^{2}-3x+2}\right)

Solution:

Concept:

Factorise the denominator and cancel the common factor to remove the indeterminate form.

Explanation:

We need to evaluate

\lim\limits_{x\to 1}\frac{1-x}{x^{2}-3x+2}

First, factorise the denominator:

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

Also, write the numerator as:

1-x=-(x-1)

Substitute these into the given expression:

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

Cancel the common factor

(x-1)

, valid for

x\neq1

\frac{-(x-1)}{(x-1)(x-2)}=\frac{-1}{x-2}

Now evaluate the limit as

x

approaches

1

\lim\limits_{x\to 1}\frac{-1}{x-2}=\frac{-1}{1-2}=\frac{-1}{-1}=1

Thus, the limit is

1

Answer:

1

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