MTH101 Midterm Past Paper Fall 2008

FINALTERM EXAMINATION

Fall 2008 MTH101Calculus And Analytical Geometry (Session - 1) Marks: 70

Q1. If g is differentiable at a point x and f is differentiable at a point g(x), then the ------ -------- is differentiable at point x . (1 marks)

Composition f (g(x))

Product f (g(x))

Composition f (g(x+f))

Q2. Let f be a function on an interval, and (1 marks)

x and x denote the points in that interval,

if f x f x whenever x x then the we can say that f is

Increasing function

Decreasing function

Constant function

Q3. Sigma notation is represented by the (1 marks)

Greek letter. y x

x

x

Q6. The two curves (1 marks)

y x and y x intersect at the points

x and x

x and x

x and x

Q7. By using cylindrical shell to find the volume of the solid when the region R in (1 marks)

the first quadrent enclosed between y xand y x is revolved about yaxis,the volume will be represented by

V x x x dx 2 . V x dx

V x dx

Q8. If f is a smooth curve on the interval [a,b] ,the arc length L of the curve f(x) defined over the interval [a,b] is (1 marks)

max lim n k k x k L f x x

n k k k L f x x

max lim n k x k L f x