Name Exam 1
Math 105, section B October 11, 2002
1. (12) 3. (22) 5. (22)
2. (26) 4. (18)
Total
1. (12 points) If f(x) = ln (ex), calculate f0(x). Simplify your answer if possible.
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Explanation - Calculus - Exam, Exams of Calculus
This is the Exam of Calculus which includes Find, Differentiable, Function, Limit Definition, Derivative, Limits, Evaluate, Calculus, Respect, Elliptic Track etc. Key important points are: Explanation, Calculate, Continuous, Calculate, Function, Graph, Sketched, Points, Corresponding Points, Partial Credit
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Name Exam 1 Math 105, section B October 11, 2002
- (12) 3. (22) 5. (22)
- (26) 4. (18)
Total
- (12 points) If f (x) = ln (ex), calculate f ′(x). Simplify your answer if possible.
- (26 points) Suppose g(x) =
x^2 + 6x + 7 if x < 1 x^2 + 7x + 6 if 1 < x < 3 13 x − 3 if x ≥ 3.
(a) Is g(x) continuous at x = 1? At x = 3? Explain. (b) Calculate g′(x). Does g′(1) exist? Does g′(3) exist? Explain. (c) Calculate g′′(x). Does g′′(1) exist? Does g′′(3) exist? Explain.
- (18 points) Use the fact that d dx
|x| = |x| x
, and whatever other derivative rules you may need, to
calculate the following derivatives. Simplify your answers if possible.
(a) a(x) = x |x| (b) b(x) = |ex|
- (22 points) Calculate the derivatives of the following functions. Do not try to simplify your answers!
(i) c(x) =
x^8 − 6 x^5 + 3 − 4 x−^3
x^12 + 7x^7 + 3x−^8
(ii) d(x) = ec(x), where c(x) is the function in (i). (Use your answer to (i) in this answer if you like.)