21 May Calculus Homework about Derivatives and Limits
MTH 271—001L Spring 2018
Quiz 2 (Take-home, Due February 20): Be sure to demonstrate good math
work habits.
Please follow these instructions:
Use standard 8 ½ by 11 white paper for your work on questions 1 through 4.
Be neat. Be complete. Show all the steps required for each problem.
Neatly staple your pages together in the upper left hand corner.
Submit your final draft of your work (not a first draft reflecting your
scribbles, corrections, false starts, messy papers, and the like). Show me
what your very best work is.
Use the limit definition of derivative to find the derivative of the following
functions in questions 1 through 4:
1. (15) [Find this problem in the exercise set for Chapter 3, section 4 and read about it before you attempt to answer this question. Hint:
Rationalize the numerator as per Example 7 in section 4.]
xxf 3)(
2. (15) 632)( 2 xxxf
3. (15) x
xf 4
)(
4. (15) 852 3 xxy
5. (10) Find the equation of the secant line from 2x to 5x for the function xxxf 6)( 2 . Graph the function and the line. What
does the slope of your line indicate? (What is it?)
6. (10) Find the equation of the line tangent to 132)( 2 xxxf
when 3x . Graph the function and the line.
7. (5) Explain what this means: 0 1
lim nx x
8. (5) Find the limit if it exists: 2
6 lim
2
2
x
xx
x
9. (5) Find the limit if it exists: 122
23 lim
2
2
xx
xx
x
10. (5) Explain what it means when we say a function is continuous.
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