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Name: Student ID: Section: Instructor:
Math 112 (Calculus I)
Final Exam Form A
April 18, 7:00 p.m.
Instructions:
- Work on scratch paper will not be graded.
- For questions 10 to 17, show all your work in the space provided.. Full credit will be given only if the necessary work is shown justifying your answer. Please write neatly.
- Should you have need for more space than is alloted to answer a question, use the back of the page the problem is on and indicate this fact.
- Simplify your answers. Expressions such as ln(1), e^0 , sin(π/2), etc. must be simplified for full credit.
- Calculators are not allowed.
For Instructor use only.
Possible Earned
MC 24 9 11 10 7 11 7 12 7 13 7 14a 3 Sub 66
Possible Earned
14b 3 14c 3 15a 7 15b 7 16 7 17 7
Sub 34 Total 100
Multiple Choice. Fill in the answer to each problem on your scantron. Make sure your name, section and instructor is on your scantron.
- (^) dxd^ ∫^34 x^ √1 +^ t^3 t 5 dt = a) √1 + 1024^256 x^3 x 5 b) √1 + 1024^256 x^3 x 5 − √^27244 c) √1 + 1024^64 x^3 x 5
d) √1 +^4 x^3 x 5 e) √1 +^4 x^3 x 5 − √^27244 f) √1 +x^3 x 5
2.^ ∫^2
√ 3 √ 5 (4 + zz (^2) ) 3 / 2 dz^ = a) −^17 b) − 121 c) Does not exist. d) 121 e) 17 f) (^14) g) None of the above.
- Find the area of the largest rectangle that can be inscribed in a right triangle with legs of lengths 3 cm and 4 cm if two sides of the rectangle lie along the legs.square cm.) (All answers are in
a) 1 b) 13 c) 2 d) 3 e) 92 f) There is no largest rectan-gle. g) None of the above.
- lim x→ (^4) |^44 −−^ xx| = a) 0 b) 1 c) - d) ∞ e) −∞ f) Does not exist. g) None of the above.
TURN PAGE OVER
Short Answer Fill in the blank with the appropriate answer.
- (11 points) a) (^) xlim→π− ln(sin x) =
b) What kind of discontinuity exists at x = −1 for the function f (x) = (^) xx 2 + 1− 1?
c) (^) dxd(a^3 + cos^3 x) =
d) (^) dxd^22 (ex^2 ) =
e) If f ′(x) ≥ 2 for all x ∈ [0, 2], what theorem tells us that f (2)−f (0) ≥ 4?
f) (^) dxd(tan−^1 (x^2 )) =
g) (^) xlim→ 0 +^ ln(1 + x x)=
h)^ ∫ (√x + x^1 ) dx =
i)^ ∫^34 (1 + 3x) dx =
j)^ ∫^25 (2x − 1)^2 dx =
k) Set up a limit to find the derivative of g(x) = (^) x (^2 1) + 1. TURN PAGE OVER
Free Response. For problems 10 - 17, write your answers in the space provided. Use the back of the page if needed, indicating that fact. Neatly show all work.
- (7 points) Prove lim x→ 2 4 x − 3 = 5 using the − δ definition of the limit.
- (7 points) Estimate √^38 .012 by linear approximation.
TURN PAGE OVER
- Evaluate the following limits: (a) (7 points) limx→∞(√x^2 + x − x)
(b) (7 points) limx→∞ x^1 /x.
- (7 points) Find^ ∫^ x1 + + xx 2 dx.
TURN PAGE OVER
- (7 points) A dog owner has 1000 feet of fencing and wishes to make 4 dog runs side by side.(a dog run is a fenced rectangular area the dog can pace in). What dimensions will give the largest area? (Note: two dog runs that sit side by side share a common side.)
END OF EXAM
