MATH QUIZ 2

Question 1

If it is known that y=1 when x=1, what is the constant of integration of the following integral?
y(x)=|(e^2x-2x)dx

Answer 1

c=4-e^2

Question 2

Evaluate:
lim(x csc 2x)
x->0

Answer 2

1/2

Question 3

Find the area of the curve bounded by y=9-x^2 and the x-axis

Answer 3

36

Question 4

What is the slope of the graph y=-x^2 at points (2,3)?

Answer 4

-4

Question 5

Evaluate:
lim(pi-2x)tanx
x->pi/2

Answer 5

2

Question 6

Find the maximum value of y given:
y=x^3-9x^2+15x-3

Answer 6

(1,4)

Question 7

Find the maximum value of y given:
y=x+1/2

Answer 7

(-1, -2)

Question 8

Evaluate:
|pi/2 0 5cos^6(x)sin^2(x)dx

Answer 8

0.30679

Question 9

If y=arctan(In x) find the derivative of y at x= 1/e

Answer 9

1.36

Question 10

The cost, C, of a product is a function of the quantity x of the product c(x)=x^2-40000x+50 Find the quantity for which the cost is minimum.

Answer 10

2000

Question 11

Evaluate:
|2 0 |y 0 (x^2+3y^2)dxdy

Answer 11

40/3

Question 12

Evaluate:
|4 2 x/(x+1)(x+2) dx

Answer 12

0.3

Question 13

What is the point of inflection of the curve x-ln(x)?

Answer 13

no point of inflection

Question 14

What is the general solution to the following differential equation:
d^2y/dx^2-5dy/dx+6y=0

Answer 14

c1e^3x + c1e^5x

Question 15

Evaluate the determinant of the matrix:

Answer 15

82

Question 16

What is the rank of matrix A?

Answer 16

Rank 2

Question 17

What is the general solution of the differential equation:
d^2y/dx^2+4y=0

Answer 17

y=sin(2x)+cos(2x)+c

Question 18

Find the differential equation whose general solution is
y=c1x+c2e^x

Answer 18

y”(x-1)-xy’+y=0

Question 19

What is the general solution of the given differential equation:
y”-8y’+16y=0

Answer 19

(c1+c2x)e^4x

Question 20

Solve the constant of integration of the given differential equation
xdx+6y^5dy=0

Answer 20

64

Question 21

What is the general solution for the following differential equation?
2 d^2y/dx^2 -4 dy/dx + y = 0

Answer 21

y=e^x(c1cosx+c2sinx)

Question 22

What is the specific solution to the given differential equation:
x”+4x’-3x=0; x’(0)=1

Answer 22

x=1/4e^-3/2t+11/4e^1/2t

Question 23

The complex expression 3 +4i is equivalent to?

Answer 23

5(cos53.13+jsin53.13)

Question 24

Find the general solution for the following differential equation:
(d^2y/dx^2 + 5dy/dx + 4y)(2 d^2y/dx^2 + 5dy/dx + 2y) = 0

Answer 24

c1e^-1/2x + c2e^-x + c3e^-2x + c4e^-4x

Question 25

The population in a certain city is 50,000 and is increasing at a rate numerically equal to the square root of the population. What will be the population 20 years hence?

Answer 25

54,571

Question 26

Write in rectangular form:
i^3217-i^427+i^18

Answer 26

2i-1

Question 27

The rate of population growth of a country is proportional to the number of inhabitants. If a population of a country now is 40 million and is expected to double in 25 years, how many years will the population be 3 times the present?

Answer 27

39.62 years