If $f (2) = g(2)$ and $f'(2) = a, g'(2) - CUETMOCK

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Continuity and Differentiability

Question:

If $f (2) = g(2)$ and $f'(2) = a, g'(2) = 2a$, then $\underset{x→2}{\lim}\frac{f(x)-g(x)}{x-2}$ is equal to

Options:

1

a

-a

none of these

Correct Answer:

-a

Explanation:

$\underset{x→2}{\lim}\frac{f(x)-g(x)}{x-2}=\underset{x→2}{\lim}\frac{f'(x)-g'(x)}{1}=f'(2)-g'(2)=a-2a=-a$

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