Show that converges for p > 1.
[ marks]Evaluate the following limits using L’Hospital’s Rule: .07
[4 marks]If then find the values of
[ marks]and (ii)
[ marks]Find the local extreme values of the function
[3 marks]The lengths a, b, and c of the edges of a rectangular box are changing with time. At the instant a = 1 m, b = 2 m, c = 3 m, = = 1 m/sec, and = – 3 m/sec . At what rates are the box’s volume Vand surface area Achanging at that instant?
[4 marks]Adelivery company accepts only rectangular boxes the sum of whose length and girth (perimeter of a cross section) does not exceed 108 inch. Find the dimensions of an acceptable box of largest volume using Lagrange’s multipliers method.
[7 marks]Evaluate:
[ marks]Evaluate by reversing the order of the integration:
[ marks]Evaluate using the Polar Coordinates: (1) , where Ris the semicircular region bounded by the x- axis and the curve . (2) .
[7 marks]Discuss the convergence of
[3 marks]Test the convergence of :
[4 marks]Examine for which values of x, the following series is convergent.
[7 marks]Discuss the continuity of the function
[3 marks]Check the convergence of
[4 marks]Find the Taylor’s series expansion of up to fourth term. Apply it to find
[7 marks]Using the method of slicing find the volume of the cone with height 4 cm and radius of the base 4 cm.
[3 marks]The region enclosed by the parabola y = x2 +1 and the straight line y = 2x +1 is revolved about the x- axis. Find the volume of solid of revolution.
[4 marks]Trace the curve x3 + y3 = 3axy, a > 0.
[7 marks]