If f(a) = 2, g(a) = −1, f'(a) =1,

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Continuity and Differentiability

Question:

If f(a) = 2, g(a) = −1, f'(a) =1, g'(a) = 2, then the value of $\underset{x→a}{\lim}\frac{f(x).g(a)-f(a).g(x)}{x-a}=$

Options:

-5

-6

none of these

Correct Answer:

-5

Explanation:

$\underset{x→a}{\lim}\frac{f(x).g(a)-f(a).g(x)}{x-a}$ $[\frac{0}{0}form]$

$\underset{x→a}{\lim}\frac{f'(x).g(a)-f(a).g'(x)}{1}=f'(a)g(a)-f(a).g'(a)=1.(-1)-2.2=-5$