MATH105 April 2011
• Q1 (a) • Q1 (b) • Q2 • Q3 • Q4 • Q5 (a) • Q5 (b) • Q5 (c) • Q6 • Q7 • Q8 (a) • Q8 (b) • Q8 (c) • Q9 (a) • Q9 (b) • Q9 (c) • Q9 (d) • Q9 (e) • Q9 (f) • Q9 (g) •
Question 09 (b)
Each of the short-answer questions below is worth 5 points. Put your answer in the box provided and show your work. No credit will be given for the answer without the correct accompanying work.
What is the slope of the curve
at the point
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.
Apply the fundamental theorem of calculus to the integral. i.e:
where F'(x) = f(x).
Consider the first hint. Can you take the derivative of
with respect to where is a function of ?
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To evaluate the slope of the curve at , we let
and evaluate . By the fundamental theorem of calculus, we know that
where is the antiderivative of the integrand (i.e: ). Taking the derivative with respect to , we find
So the slope of the curve at is 2.
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