Using L’Hospital’s rule find the limit of the following function
 

Using L’Hospital’s rule find the limit of the following function
 

Using L’Hospital’s rule find the limit of the following function
 

Using L’Hospital’s rule find the limit of the following function

Using L’Hospital’s rule find the limit of the following function  

Using L’Hospital’s rule find the limit of the following function
 

Using L’Hospital’s rule find the limit of the following function
 

Using L’Hospital’s rule find the limit of the following function
 

Using L’Hospital’s rule find the limit of the following function
 

Using L’Hospital’s rule find the limit of the following function
 

Using L’Hospital’s rule find the limit of the following function
 

Using L’Hospital’s rule find the limit of the following function
 

The number of solutions of the equation xe^sinxcosx = 0 in the interval (0, π/2)

f (x) = x^3/2 (3x – 10), x ≥ 0 then f (x) is increasing in

Consider the polynomial f (x) = 1 + 2x + 3x² + 4x³. Let s be the sum of all distinct real roots of f (x) and let t = |s|. The real number s lies in the interval

a)

b)

c)

d)

If F (x) =

where  =  and  and given that F (5) = 5
then F (10) is equal to

a) 5

b) 10

c) 0

d) 15

 If f (x) = cos [π²] x + cos [-π²] x where [x] stands of the greatest integer function then

a) f  = −1

b)

c) f (−π) = 0

d) f  = 1

Let f (x + y) = f (x) f (y) for all x, y. Suppose that f (5) = 2 and  (0) = 3. Find f (5).

a) 1

b) 2

c) 3

d) 6

Let a + b + c = 0, then the quadratic equation  has

a) at least one root in (0, 1)

b) one root in (2, 3) and the other in

c) imaginary roots

d) none of these

If f (x) =

a) f (x) is a strictly increasing function

b) f (x) has a local maxima

c) f (x) is a strictly decreasing function

d) f (x) is bounded

Suppose p(x) =
If  prove that
 

In (- 4, 4) the function  has

a) No extrema

b) One extrema

c) Two extremas

d) None of the above

The length of longest interval in which the function  is increasing is

a)

b)

c)

d)