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Questions › JNU › JNU SSS 2011 › Q57
1 mark, −0.25Mathematics › Limits, continuity and differentiability › Differentiability and its link to continuityModerateabout 1 min

JNU SSS 2011 Question 57: Limits, continuity and differentiability

If f(x)f(x)f(x) and g(x)g(x)g(x) are differentiable functions such that f′(x)=3xf'(x) = 3xf′(x)=3x and g′(x)=2x2g'(x) = 2x^2g′(x)=2x2, then the limit [(f(x)+g(x))−(f(1)+g(1))](x−1)\frac{[(f(x) + g(x)) - (f(1) + g(1))]}{(x - 1)}(x−1)[(f(x)+g(x))−(f(1)+g(1))]​ as xxx approaches 1 is equal to

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If f(x) and g(x) are differentiable functions such that f′(x) = 3x and g′(x) = 2x², then the limit ([(f(x) + g(x)) - (f(1) + g(1))])/((x - 1)) as x approaches 1 is equal to (A) 5 (B) 0 (C) 20 (D) None of the above

Also written as: If f(x) and g(x) are differentiable functions such that f'(x) = 3x and g'(x) = 2x^2, then the limit ([(f(x) + g(x)) - (f(1) + g(1))])/((x - 1)) as x approaches 1 is equal to

Limits, continuity and differentiability has come up 122 times in 7 exams since 2006.

What this question tests

This question is on Differentiability and its link to continuity, part of Limits, continuity and differentiability in Mathematics.

When a derivative exists and why differentiability implies continuity but not conversely.

TestStop has 12 past-paper questions on this subtopic; the nearest in year are below.

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Question from the JNU SSS 2011 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.