MATH QUIZ 2 Flashcards
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
c=4-e^2
Evaluate:
lim(x csc 2x)
x->0
1/2
Find the area of the curve bounded by y=9-x^2 and the x-axis
36
What is the slope of the graph y=-x^2 at points (2,3)?
-4
Evaluate:
lim(pi-2x)tanx
x->pi/2
2
Find the maximum value of y given:
y=x^3-9x^2+15x-3
(1,4)
Find the maximum value of y given:
y=x+1/2
(-1, -2)
Evaluate:
|pi/2 0 5cos^6(x)sin^2(x)dx
0.30679
If y=arctan(In x) find the derivative of y at x= 1/e
1.36
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.
2000
Evaluate:
|2 0 |y 0 (x^2+3y^2)dxdy
40/3
Evaluate:
|4 2 x/(x+1)(x+2) dx
0.3
What is the point of inflection of the curve x-ln(x)?
no point of inflection
What is the general solution to the following differential equation:
d^2y/dx^2-5dy/dx+6y=0
c1e^3x + c1e^5x
Evaluate the determinant of the matrix:
82
What is the rank of matrix A?
Rank 2
What is the general solution of the differential equation:
d^2y/dx^2+4y=0
y=sin(2x)+cos(2x)+c
Find the differential equation whose general solution is
y=c1x+c2e^x
y”(x-1)-xy’+y=0
What is the general solution of the given differential equation:
y”-8y’+16y=0
(c1+c2x)e^4x
Solve the constant of integration of the given differential equation
xdx+6y^5dy=0
64
What is the general solution for the following differential equation?
2 d^2y/dx^2 -4 dy/dx + y = 0
y=e^x(c1cosx+c2sinx)
What is the specific solution to the given differential equation:
x”+4x’-3x=0; x’(0)=1
x=1/4e^-3/2t+11/4e^1/2t
The complex expression 3 +4i is equivalent to?
5(cos53.13+jsin53.13)
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
c1e^-1/2x + c2e^-x + c3e^-2x + c4e^-4x
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?
54,571
Write in rectangular form:
i^3217-i^427+i^18
2i-1
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?
39.62 years
