Science:Math Exam Resources/Courses/MATH110/April 2019/Question 10 (b)
Work in progress: this question page is incomplete, there might be mistakes in the material you are seeing here.
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q1 (e) • Q1 (f) • Q1 (g) • Q1 (h) • Q1 (i) • Q2 (a)(i) • Q2 (a)(ii) • Q2 (a)(iii) • Q2 (b) • Q2 (c) • Q3 • Q4 (a) • Q4 (b) • Q5 (a) • Q5 (b) • Q5 (c) • Q6 • Q7 (a) • Q7 (b) • Q7 (c) • Q8 • Q9 • Q10 (a) • Q10 (b) •
Question 10 (b) 

Suppose that is a function such that and . Evaluate

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 hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

This limit looks like the one from the definition of the derivative. Try comparing the two. 
Hint 2 


Checking a solution serves two purposes: helping you if, after having used all the hints, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

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. Comparing this limit with the one appearing in the definition of the derivative, we see that we need to rewrite 1. Using and , we get:
So the limit is none other than the definition of derivative:
We can compute this derivative by the chain rule:
