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I'm trying to solve a test and I have a doubt. Knowing the following limit

$$\lim_{s\to 0} \frac{f(2+s)-f(2)}{2s} = 1$$

can someone help me to choose the right option?

a) $f'(2) = 1 $

b) $f'(2) = 2 $

c) $f'(0) = 1 $

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  • $\begingroup$ hopefully $f$ is differentiable $\endgroup$ Jan 4, 2018 at 21:03

3 Answers 3

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You know that $$\lim_{s\to0}\frac{f(2+s)-f(2)}s=2.$$ Hence, $f'(2)=2$.

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I would avoid asking test question on stack exchange. It only hinders your learning, but you get to choose how much you want to learn. What is shown in the question is the definition of the derivative multiplied by 1/2. i.e

$1/2 *f'(2)= 1$

Therefore, the answer is b.

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  • $\begingroup$ thanks for answering I have understood it. $\endgroup$ Jan 4, 2018 at 20:56
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Hint

$$\lim_{s\to 0}\frac{f(2+s)-f(2)}{s}=f'(2).$$

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    $\begingroup$ Are you sure of what you wrote? $\endgroup$
    – egreg
    Jan 4, 2018 at 21:00
  • $\begingroup$ @egreg: what do you mean ? $\endgroup$
    – idm
    Jan 5, 2018 at 8:00
  • $\begingroup$ The edit by idm has fixed it. What you wrote was quite wrong. $\endgroup$
    – egreg
    Jan 5, 2018 at 10:00

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