

If x + y = e^{(x + y)}, then the value of dy/dx at the point (1/2 , 1/2) is
A) 1
B) e  1
C) 1  e
D) e
E) 1

Evaluate the integral
A) 0
B) 1
C) 2
D) 1
E) 2

The acceleration a(t) of a body in motion along a straight line is given by a(t) = 2t  4, where t is the time. If x(t) is the distance of the body from the origin at the time t and x(6)  x(2) = 10, then the velocity v(t) of the body is given by
A) t^{2}  4t
B) t^{2}  4t + 7/6
C) t
D) t^{2}
E) 2t^{2}  4t

Evaluate
A) 1
B) e
C) e  1
D) e + 1
E) 0

Which of these series is/are convergent?
A) A only
B) B only
C) A, B and C
D) A and B only
E) B and C only

Evaluate
A) ln(3/4)
B) ln(2)
C) 1
D) ln(2)
E) ln(2)

What is true about the graph of f(x) = ln(x^{2} + 2x + 1)?
A) It has no x intercept
B) It has a horizontal asymptote
C) It is exactly the same as the graph of g(x) = 2 ln x + 1 
D) It is exactly the same as the graph of g(x) = 2 ln(x + 1)
E) It has no y intercept

For what value of C we have the following
A) e
B) e  1
C) 1  e
D) 1
E) 2e

Find constant K, K positive, so that the volume of the solid of revolution determined by rotating the area bounded by f(x) = x^{2} and g(x) =  x(x  K) is equal to 200 Pi.
A) 4 ^{.} 5^{2/3}
B) 1 / 2
C) 120
D) ^{.} 1200^{1/5}
E) 2 ^{.} 600^{1/5}
Answers to the Above Questions
 E
 A
 B
 C
 D
 D
 C
 B
 E
