Test-2

B.Sc. (Hons.) Mathematics – III year

Test

Analysis – IV

Time: 1Hr. Max. Marks: 25

(This question paper consists of 6 questions. All questions carry 5 marks each.)

(Attempt any 5 questions.)


 * 1) Test for convergence of the integral $$\int_0^1x^p(log\frac{1}{x})^q~dx$$
 * 2) Show that [[Image:]] exists  iff n < m+1
 * 3) Discuss the convergence of [[Image:]]
 * 4) State Green's theorem and verify it for I = [[Image:]] ; where C is the closed curve formed by y 3 = x2 and y=x between (0,0) and (1,1).
 * 5) Change the order of integration in the inegral[[Image:]]and evaluate it.
 * 6) Evaluate[[Image:]]taken over the upper half of the circle x2 + y2 = 2ax.
 * 7) State and prove Abel's Test for the convergence of Improper Integrals.