b) Find 

Using Trapezoidal rule, calculate  by dividing the interval ]1,0[ in 5 equal subintervals. Hence evaluate π.

c) Evaluate 

Is the function f , defined by 

 f(4)=0 continuous at x = 4? Give reasons for your answer.

a) The curve  has a loop between . Find the area of this loop.

c) Find the derivatives of 

b) Use Simpson’s method to approximate  with 8 sub-intervals.

a) Evaluate 

Find the angle between the curves  at the points of intersection other than the origin.

Find the length of the curve given by  in 

Trace the curve  by the stating all the properties used to trace it.

c) Find 

b) Evaluate 

vii) Find the kernel of the linear transformation  defined by 

find  if 

vi) If  is an ordered basis of  and  is the corresponding dual basis find   and 

v) Check whether  defined by  is a linear transformation. 

vectors in  the vector space of polynomials of degree

iv) Check whether the set of vector  is a linearly independent set of 

iii) Check whether