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Question

If f(a) = 2, f’(a) = 1, g(a) = –1, g’(a) = 2, then the value of limxag(x)f(a)g(a)f(x)xa is

A
5
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B
15
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C
25
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D
1
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Solution

The correct option is A 5
limxag(x)f(a)g(a)f(x)xa
limh0g(a+h)f(a)g(a)f(a)+g(a)f(a)g(a)f(a+h)h
[for x = a + h]
limh0[f(a)(g(a+h)g(a)h)]g(a)[f(a+h)f(a)h]
=f(a)g(a)g(a)f(a)=2×2(1)×1=5

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