Science:Math Exam Resources/Courses/MATH110/December 2016/Question 05 (b)

MATH110 December 2016

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Question 05 (b)
Consider the function ${\textstyle f(x)=x^{1/3}}$. (b) Let ${\textstyle m(h)}$ be the quantity computed in part (a). Explain in your own words what $\lim _{h\to 0}m(h)$ represents graphically.

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
We are taking a limit of the slope of the secant line.

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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. Since ${\textstyle m(h)}$ is the slope of the secant line joining ${\textstyle (0,f(0))}$ and ${\textstyle (h,f(h))}$, at the limit we have that ${\textstyle \lim \limits _{h\to 0}m(h)}$ is the slope of the tangent line of ${\textstyle y=f(x)}$ at the point ${\textstyle (0,f(0))=(0,0)}$. Answer: ${\textstyle \lim \limits _{h\to 0}m(h)}$ represents the ${\textstyle {\color {blue}{\mbox{slope of the tangent line at the origin.}}}}$