Evaluate

a) 0

b)

c)

d) 1

Evaluate

a) 0

b)

c)

d) 1

Evaluate

a) 0

b)

c) 1

d) 2

Evaluate

a) 2asina

b) a²cosa

c) 2asina + a²cosa

d) 2a

If f (x + y) = f (x) + f (y) for all x and y. If the function f is continuous at x = 0 then f is continuous for all x.

a) True

b) False

Determine the values of a, b, c for which the function

is continuous at x = 0

a)

b)

c)

d)

Let f be a twice differentiable function such that  and , . Find h (10) if

h (5) = 1.

a) 0

b) 1

c) 2

d) 4

Let

Determine the function g (x) = f (f(x)) and hence find the points of discontinuity of g if any.

a) g(x) is continuous for all x except x = 1 and x = 2

b) g(x) is continuous for all x except x = 1

c) g(x) is continuous for all x except x = 2

d) g(x) is continuous for all x

Let f(x) =

Discuss the continuity of  on [0, 2]

a)  is continuous for all x  ℝ

b)  is continuous for all x  ℝ except at x = 1

c)  is continuous for all x  ℝ except at x = 1 and x = 2

d)  is continuous for all x  ℝ except at x = 0, x = 1 and x = 2

Let f (x) be a continuous function satisfying  If  exists, find its value.

a) 0

b) 1

c) 2

d) 4

Let ℝ be the set of real numbers and f : ℝ → ℝ such that for all x and y in ℝ, . Then f (x) is a constant.

a) True

b) False

A function f : ℝ → ℝ satisfies the equation

f(x + y) = f(x) . f(y)  x, y in ℝ and f(x) ≠ 0 for any x in ℝ. Let the function be differentiable at x = 0 and . Show that. Hence determine f(x).

a) e^x

b) e^2x

c) 2e^x

d) 2e^2x

Find

a) 0

b) e

c) e^z

d) e³

Let

Determine a and b so that f is continuous at x = 0.

a)

b)

c)

d)

Let

Test whether

f(x) is continuous at x = 0

f(x) is differentiable at x = 0

a) f(x) is differentiable and continuous at x = 0

b) f(x) is continuous but not differentiable at x = 0

c) f(x) is neither continuous nor differentiable at x = 0

If a function f : is an odd function such that  for x ε [a, 2a] and the left hand derivative at

x = a is 0 then find the left hand derivative at x =  

a) 0

b) 1

c) a

d) 2a

P(x) is a polynomial function such that P(1) = 0, > P(x)

 x > 1. Then  x > 1,

a) P(x) > 0

b) P(x) = 0

c) P(x) < 1

If  and = and f(0) = 0. Find the value of . Given that 0 < <

a)

b)

c)

d) 1

f(x) is a function such that  and the tangent at any point passes through (1, 2). Find the equation of the tangent.

a) x = 2

b) y = 2

c) x + y = 2

d) x – y = 2

If  exists then both the limits  and  exist

a) True

b) False

A =  is equal to

a) 0

b) 1

c)

d)

Let f(x) =

If f is continuous for all x, then k is equal to

a) 3

b) 5

c) 7

d) 9

Identify a discontinuous function y = f(x) satisfying