Assignment 2

Faculty of Science; Department of Mathematics
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The assignment can be found here.

Discussion, Questions, and Comments

Feel free to use this space to discuss the assignment. Ask questions, or answer questions posted by classmates. Remember that this is not a place to post full solutions to assignment problems.

Solutions

The assignment solutions can be found here.

Question/Clarification

Question 1 and 2: I'm confused with these questions.

"Use the Fundamental Theorem of Calculus to find the derivative of the function"

where f(x) = some integral

I'm guessing the first step is to evaluate the integral? Is this the right track?

Not quite. According to the fundamental theorem of calculus, you can compute the derivative of these functions without evaluating the integrals. The fundamental theorem has two parts to it: The first concerns taking derivatives of integrals, the second involves taking integrals of derivatives. This question relates to the first part. For more info, you can refer to this page, or you can continue the discussion here, or contact me through email or office hours. CameronChristou 10:34, 26 January 2011 (PST)

What does taking the derivative of an integrated function (with respect to the bounds) mean?

You can think of this as taking the derivative of the area function (the graph from Quiz 3). CameronChristou 10:34, 26 January 2011 (PST)

For Number one, do I just take the anti-derivative of the function then evaluate the function at the upper and lower limits?

No. Anti-derivatives are not required to answer this question. The Fundamental Theorem of Calculus has two parts, and one of those parts will tell you how to take the derivative of this integral function without evaluating the integral itself. CameronChristou 11:37, 28 January 2011 (PST)

So if I take the antiderivative will you mark the question wrong? Also, could you please give me a hint on how to start question 6?

Solving the integral before taking the derivative will not get you full marks on this question (It will get you some marks though. It would be worthwhile to write down that solution if it is the only solution you have.) Chapter 3, page 47 of the course notes may be a good place to start if you don't know what I'm talking about there.

To start question 6, you need to show that the inequalities are true; that 1 is less than or equal to

{\sqrt {1+x^{3}}}

for all values of x. You can do this in a number of ways, such as analysing the derivative of

{\sqrt {1+x^{3}}}

, finding the zeros of

{\sqrt {1+x^{3}}}-1

, finding the minimum value of

{\sqrt {1+x^{3}}}

, etc. if you can't come up with any methods that work, come and talk to me and we can brainstorm. CameronChristou 10:04, 31 January 2011 (PST)