devotion & mathematics

Problems & Solutions :   Test for convergence of Σ (2n-1)/n(n+1)(n+2).                                                                Back Solution : Test for convergence of  1+ 4/5 + 6/10+ 8/17+ …+ 2n/(n 2 +1)+ … Solution: Test for convergence of  1.2/3.4.5 + 2.3/4.5.6+ 3.4/5.6.7 + … Solution : Test for convergence of Σ1/ n^( 𝜶+( 𝜷/n)). Solution : Test for convergence of Σ 1/( 2 n +3 n ). Solution : Test for convergence of Σ (√(n+1) - √n ). Solution : Test for convergence of Σ ( √ (n 2 +1) – n ). Solution : Test for convergence of  Σ ( √(n 3 +1) - √( n 3 )  ). Solution :  Test for convergence of Σ ( √ (n 4 +1) - √ ( n 4 -1) ).

  Leibnitz-Test : Problems & Solutions :                             *       Examine the character of the series Σ (-1) n-1 n /2n-1                                    Back                                                  Solution :   *      Examine the convergence of 1/1.2 – 1/3.4 + 1/5.6 -1/7.8 +…        Solution : *            Examine the convergence of Σ (-1) n 1/n ( 1+ 1/2 + 1/3+ …+ 1/n). Solution : *   Prove that   1- 1/2 + 1/3 - … converges. Solution : *      Prove that Σ (-1) n / n! = 1- 1/1! + 1/2! - 1/3!+… converges. Solution :  Leibnitz-Test : #Problems #...

Comparison Test : Problems & Solutions               Test for convergence of Σ 1/(n 2 +n)                                                                            Back Test for convergence of Σ 1/ logn Test for convergence of Σ n 3 /(n 5 +4n 4 +7) Test for convergence of Σ 1/n! Test for convergence of Σ log(1/n) Test for convergence of Σ logn/(2n 3 -1)  #comparison #test #problems #& #solutions #infinite #series

 LINE INTEGRALS - PROBLEMS &SOLUTIONS :       We have discussed about the definitions and development of line integrals.  Here we going to solve some problems regarding line integrals.                      Back  PROBLEM 1 :  .   Evaluate  ∫ dx/(x+y),  Where C  is the curve x=at 2 ,y=2at, 0 ≤ t ≤ 2. SOLUTION :                          PROBLEM 2:   Show that ∫ xy dx  =4/5, where C is the arc of the parabola y 2 =x from (1,-1) to   (1,1). SOLUTION :                         3.   PROBLEM 3 :  Show that ∫  [ (x-y) 3 dx+(x-y) 3 dy]=3 πa 4 , where C Is the circle x 2 +y 2 =a 2  in       the counter clockwise sense.         SOLUTION :            ...

 Double Integrals : Integration over Rectangular Regions :                                                                           This page having some problems on Double Integrals followed by solutions.                                                                                                                         Back        1.   Evaluate ∬   xy (x 2 +y 2 )dx dy over [0,a;0,a]. SOLUTION :   2.       2 .  Evaluate   ...