Science:Math Exam Resources/Courses/MATH110/December 2014/Question 04 (a)

MATH110 December 2014

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Question 04 (a)
The following limit $$\lim _{h\to 0}{\frac {{\frac {1}{(2+h)^{2}}}-{\frac {1}{4}}}{h}}$$ equals the derivative ${\textstyle f'(a)}$ for some function ${\textstyle f}$ and some point ${\textstyle a}$. (a) Give an example of one such function ${\textstyle f}$ and point ${\textstyle a}$.

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?

If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!

Hint
Recall the definition of $f'(a)$.

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Solution

Found a typo? Is this solution unclear? Let us know here. Please rate my easiness! It's quick and helps everyone guide their studies. Recall the definition of the derivative of a function $f$ at a point $a$: $f'(a)=\lim _{h\to 0}{\frac {f(a+h)-f(a)}{h}}$. Comparing this with the given limit $\lim _{h\to 0}{\frac {{\frac {1}{(2+h)^{2}}}-{\frac {1}{4}}}{h}}$, possible choices of $f$ and $a$ are $\color {blue}f(x)={\frac {1}{x^{2}}},a=2$.