Multiple choice general knowledge math & puzzles

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

  1. 5

  2. 0

  3. 20

  4. None of the above
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A Correct answer
Explanation

The limit expression is the definition of the derivative of the function $H(x) = f(x) + g(x)$ at $x=1$. Therefore, the limit equals $f'(1) + g'(1)$. Substituting $x=1$ into $f'(x)=3x$ and $g'(x)=2x^2$ gives $3(1) + 2(1)^2 = 5$.

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