Course:MATH110/Archive/2010-2011/003/Teams/Uri/Homework/14 Part3

Homework

Midterm Question 1

For each derivative, compute the actual answer and explain what you didn't do correctly in your midterm (if you did your computation correctly, that's great). Compute the derivative of each of the following functions.

• $f(x)=\displaystyle {3^{x}}$
• $g(x)=\ln \left({\frac {3x+3}{x^{2}+1}}\right)$
• $h(x)=\ln(x\cdot x^{2}\cdot x^{3}\cdot x^{4}\cdot x^{5}\cdot x^{6})+e^{x\cdot x^{2}\cdot x^{3}\cdot x^{4}\cdot x^{5}\cdot x^{6}}$

Midterm Question 2

As a woman walks away from a streetlight, her shadow lengthens. Prove that it does so at a rate which depends on her speed but not on her position. Explain in details how to solve this problem and what you have learned from this problem. What could you have done differently during the midterm to solve the problem? Can you use some of those new ideas to get a good start at the problem in the second part of the homework? HINT: The question 5 of this week's webwork should help you get started if you're stuck.