MATH QUIZ 2 Flashcards

1
Q

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

A

c=4-e^2

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2
Q

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

A

1/2

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3
Q

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

A

36

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4
Q

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

A

-4

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5
Q

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

A

2

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6
Q

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

A

(1,4)

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7
Q

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

A

(-1, -2)

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8
Q

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

A

0.30679

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9
Q

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

A

1.36

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10
Q

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.

A

2000

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11
Q

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

A

40/3

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12
Q

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

A

0.3

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13
Q

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

A

no point of inflection

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14
Q

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

A

c1e^3x + c1e^5x

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15
Q

Evaluate the determinant of the matrix:

A

82

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16
Q

What is the rank of matrix A?

A

Rank 2

17
Q

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

A

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

18
Q

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

A

y”(x-1)-xy’+y=0

19
Q

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

A

(c1+c2x)e^4x

20
Q

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

A

64

21
Q

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

A

y=e^x(c1cosx+c2sinx)

22
Q

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

A

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

23
Q

The complex expression 3 +4i is equivalent to?

A

5(cos53.13+jsin53.13)

24
Q

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

A

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

25
Q

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?

A

54,571

26
Q

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

A

2i-1

27
Q

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?

A

39.62 years