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Math 1210, Fall 2020, Exam 1
• Answer the following questions on any paper that you have
handy.
• When you are done, take pictures of your work and upload
these to Canvas. Please merge your files into a single file before
uploading.
• Please show working where appropriate to receive full credit.
An answer without appropriate working may receive no credit.
• You are encouraged to to write something for every problem.
Even if you are not sure exactly how to answer a question it
is good practice to do as much as you can; you might surprise
yourself. Good Luck!
Answer the following questions using any method you prefer. Show all relevant work-
ing/steps and/or use words to explain your thoughts/method if necessary. Just writing the
answer will not be accepted for any of these. For some of these there is not much working to
show, but at the very least say what rules you’re using (power,multiplication,division,chain).
Don’t wo
y about simplifying. So long as your final answer is a co
ect expression and it is
clear that it was obtained via a valid method you will receive full credit.
1. What is the slope of the tangent line to the curve y = 1+2x+3x2 +4x3 +5
√
x+ 6√
x
+ 7x at the point
(1, 35)?
2. Compute the derivative of (x2 + x)(3x+ 5)
3. Compute the derivative of x
2+x
3x+5
4. Compute the derivative of (x2 + x)4
5. Compute the derivative of x4ex
6. Compute the derivative of x4ex sin(x)
7. Compute the derivative of e4x
8. Compute the derivative of 1e4x
9. Compute the derivative of sin4(x)
10. Compute the derivative of e
x
sin(x)
11. Compute the derivative of tan2(x)
12. Compute the derivative of sec2(x)
Determine the exact values of the following limits. You must show or explain how these
exact values are determined. You can do this via alge
a, or by recognizing the limit
as the definition of the derivative of a function at a specific point. Just evaluating at
numbers close to the limiting value is not sufficient and will not be accepted. Neithe
will just writing the answer with no explanation.
13. lim
x→5
1
x−
1
5
x−5
14. lim
x→5
x2−25
x−5
15. lim
x→5
x3+125
x+5
16. lim
x→5
√
x−
√
5
x−5