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MATH 171 Midterm: Math 171 TAMU Spring 15 Exam2M171Solutions

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turquoisegnu128
31 Jan 2019
School
Texas A&M University
Department
Mathematics
Course
MATH 171
Professor
All

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Document Summary

2 april 2015: (12) use the de nition of the derivative to calculate d dx(cid:0)x2(cid:1)(cid:12)(cid:12)(cid:12)(cid:12)x=3, (24) evaluate the following limits: d dx(cid:0)x2(cid:1) at x = 3. = lim h 0 (3 + h)2 9 h. = lim h 0 (6 + h) = 6 (a) (b) (c) (d) lim x . = 2 lim h 0 cos h 1 h. = 0 lim x 1 x3 + 4x 5 x 1 lim x 1 (x 1)(x2 + x + 5) x 1. = lim x 1 (x2 + x + 5) = 7: (24) di erentiate each of the following functions. [sec (cos x)] = sec (cos x) tan (cos x) ( sin x) (a) (b) (c) (d) d dx"(cid:18) 1 x. + tan x(cid:19)99(cid:18) 1 x2 + sec2 x(cid:19: (20) let f (x) = x2(x 2)2. The number line below indicates where f is positive and negative.

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Related Questions

Please help answer circled questions U substitution-exponential and logarithmic form.

Show transcribed image text

Q20. Find functions f and g so that f ∘ g = H(x) = (5 - 2x3)2.
a. f(x) = 5 - 2x3 ; g(x) = x2
b. f(x) = (5 - 2x)3 ; g(x) = x2
c. f(x) = x2 ; g(x) = 5 - 2x3
d. f(x) = x3 ; g(x) = (5 - 2x)2

Q29. Solve the system of equations using Cramer's Rule if it is applicable.


a. x = 9, y = 2, z = 5; (9, 2, 5)
b. x = 8, y = 4, z = 5; (8, 4, 5)
c. x = 4, y = 5, z = 4; (4, 5, 4)
d. x = 8, y = -4, z = -5; (8, -4, -5)

Q30. Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent.


a. x = 2, y = 3, z = -7; (2, 3, -7)
b. x = 1, y = 3, z = -4; (1, 3, -4)
c. x = 5, y = 13/2, z = -3; (5, 13/2, -3)
d. x = 1, y = -3, z = -16; (1, -3, -16)

Q33. Write the partial fraction decomposition of the rational expression (4x3 + 4x2)/(x2 + 5)2.
a. (4x - 4)/(x2 + 5) + (-20x + 20)/(x2 + 5)2
b. (4x + 4)/(x2 + 5) + (-20x - 20)/(x2 + 5)2
c. (4x + 4)/(x2 + 5) + (20x - 20)/(x2 + 5)2
d. (4x + 4)/(x2 + 5) + (20x + 20)/(x2 + 5)2

Q34. Solve the linear programming problem. Minimize z = 11x + 6y + 7 subject to: x = 0, y = 0, x + y = 1.
a. minimum: 7
b. minimum: 18
c. minimum: 24
d. minimum: 13

Q35. Solve the system of equations by elimination.


a. x = 10, y = 0; (10, 0)
b. x = 10, y = 10; (10, 10)
c. x = 0, y = 10; (0, 10)
d. x = 0, y = 0; (0, 0)

Q36. Perform the row operations on the given augmented matrix.


a.
b.
c.
d.

Q37. Solve the system of equations using Cramer's Rule if it is applicable.


a. x = -4, y = 3; (-4, 3)
b. x = -3, y = -4; (-3, -4)
c. x = 4, y = 3; (4, 3)
d. x = 3, y = 4; (3, 4)

Q38. Write the partial fraction decomposition of the rational expression x/(x2 - 9x + 20).
a. -4/(x - 4) + 5/(x - 5)
b. -5/(x - 4) + 4/(x - 5)
c. 4/(x - 4) + -5/(x - 5)
d. -4/(x - 4) + -5/(x - 5)

Q39. Solve the system of equations.


a. x = -4, y = 4, z = -3; (-4, 4, -3)
b. x = -3, y = 4, z = -4; (-3, 4, -4)
c. x = -4, y = -3, z = 4; (-4, -3, 4)
d. inconsistent

Q40. Find the value of the determinant.


a. 224
b. 24
c. -72
d. 72

Show transcribed image text

Q18. A size 6 dress in Country C is size 52 in Country D. A function that converts dress sizes in Country C to those in Country D is f(x) = 2(x + 20). Find a formula for the inverse of the function described.
a. f -1(x) = (x - 20)/2
b. f -1(x) = x - 20
c. f -1(x) = (x/2) - 20
d. f -1(x) = (x/2) + 20

Q19. If f(x) = 4x and g(x) = 12, find the point of intersection of the graphs of f and g by solving f(x) = g(x). Give an exact answer.
a. (log 4 12, 12)
b. (log 4 12, 4)
c. (log 4 12, 0)
d. (12, 12)

Q20. Find functions f and g so that f ∘ g = H(x) = (5 - 2x3)2.
a. f(x) = 5 - 2x3 ; g(x) = x2
b. f(x) = (5 - 2x)3 ; g(x) = x2
c. f(x) = x2 ; g(x) = 5 - 2x3
d. f(x) = x3 ; g(x) = (5 - 2x)2

Q29. Solve the system of equations using Cramer's Rule if it is applicable.


a. x = 9, y = 2, z = 5; (9, 2, 5)
b. x = 8, y = 4, z = 5; (8, 4, 5)
c. x = 4, y = 5, z = 4; (4, 5, 4)
d. x = 8, y = -4, z = -5; (8, -4, -5)

Q30. Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent.


a. x = 2, y = 3, z = -7; (2, 3, -7)
b. x = 1, y = 3, z = -4; (1, 3, -4)
c. x = 5, y = 13/2, z = -3; (5, 13/2, -3)
d. x = 1, y = -3, z = -16; (1, -3, -16)

Q33. Write the partial fraction decomposition of the rational expression (4x3 + 4x2)/(x2 + 5)2.
a. (4x - 4)/(x2 + 5) + (-20x + 20)/(x2 + 5)2
b. (4x + 4)/(x2 + 5) + (-20x - 20)/(x2 + 5)2
c. (4x + 4)/(x2 + 5) + (20x - 20)/(x2 + 5)2
d. (4x + 4)/(x2 + 5) + (20x + 20)/(x2 + 5)2

Q34. Solve the linear programming problem. Minimize z = 11x + 6y + 7 subject to: x = 0, y = 0, x + y = 1.
a. minimum: 7
b. minimum: 18
c. minimum: 24
d. minimum: 13

Q35. Solve the system of equations by elimination.


a. x = 10, y = 0; (10, 0)
b. x = 10, y = 10; (10, 10)
c. x = 0, y = 10; (0, 10)
d. x = 0, y = 0; (0, 0)

Q36. Perform the row operations on the given augmented matrix.


a.
b.
c.
d.

Q37. Solve the system of equations using Cramer's Rule if it is applicable.


a. x = -4, y = 3; (-4, 3)
b. x = -3, y = -4; (-3, -4)
c. x = 4, y = 3; (4, 3)
d. x = 3, y = 4; (3, 4)

Q38. Write the partial fraction decomposition of the rational expression x/(x2 - 9x + 20).
a. -4/(x - 4) + 5/(x - 5)
b. -5/(x - 4) + 4/(x - 5)
c. 4/(x - 4) + -5/(x - 5)
d. -4/(x - 4) + -5/(x - 5)

Q39. Solve the system of equations.


a. x = -4, y = 4, z = -3; (-4, 4, -3)
b. x = -3, y = 4, z = -4; (-3, 4, -4)
c. x = -4, y = -3, z = 4; (-4, -3, 4)
d. inconsistent

Q40. Find the value of the determinant.


a. 224
b. 24
c. -72
d. 72

Show transcribed image text