MA 112 - 01PC Applied Calculus for Aviation Summer 2022
Exam 1 Review Exercises
Remark: Do not rely solely on this problem set to study for the exam. It is highly recommended to do
the Exam Review on MyMathLab, and also study the class notes and previous homework.
1. The graph of f (x) is given below. Use the graph to answer questions (a)-(d) below.
(a) Compute the following. If it does not exist (DNE), explain why.
(i)
lim f (x) =
x→−8−
(ii)
lim f (x) =
(iii) lim f (x) =
x→−8
x→−8+
(iv) f (−8) =
(b) Compute the following. If it does not exist (DNE), explain why.
(i) lim− f (x) =
x→6
(ii) lim+ f (x) =
(iii) lim f (x) =
x→6
x→6
(iv) f (6) =
(c) Compute the following. If it does not exist (DNE), explain why.
(i)
lim f (x) =
x→10−
(ii)
lim f (x) =
(iii) lim f (x) =
x→10
x→10+
(d) State the value(s) of x at which f is discontinuous.
2. Compute
lim (x5 + 2x2 − 3x2 − x + 9)
x→−1
3. Compute
x3 − 8x + 3
x→0 x2 + x − 1
lim
4. Compute
x2 − 3x − 4
x→4
x−4
lim
5. Compute
lim
x→2
1
x
− 12
x−2
6. Compute
x2 − x − 6
x→1 (x + 1)2
lim
(iv) f (10) =
7. Compute
x3 + x2 − x + 10
x→∞
1 − x3
lim
8. Compute
lim
x→∞
20x + 3
x2 + x + 1
9. Compute
20x3 + 3
x→∞ x2 + x + 1
lim
10. Use the definition of the derivative to compute f 0 (x) where f (x) = 3x2 + x − 5.
11. Use the definition of the derivative to compute f 0 (x) where f (x) = 4x + 7.
For questions 12–20, compute the derivative of each function. You do not need to simplify.
1
12. y = x5 + x6 − 7
5
13. f (x) = −2x5 + 9x4 −
14. g(t) =
√
x − 9x
5
− 100
t4
15. f (x) = (1 + x5 )(5x3 + 1)
t4 − 1
t4 + 1
√
17. f (x) = x3 + x
16. h(t) =
18. f (x) = (4x3 + 9x2 − 1)9
19. h(t) =
(3x2
1
+ 1)5
20. g(z) = 8z 3 (4z + 9)3
21. Find the slope of tangent line to the curve y =
22. For the following equations, compute
dy
dx
x2 − 1
at (1, 1).
x2 + 1
using implicit differentiation.
(a) xy 4 + y 3 = x2 + 3y
(b) xy = y 3 − 1
2