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VED1
          E\L-LOVELY-H\math3-1 IInd 6-8-11 IIIrd  24-1-12 IVth 21-4-12 Vth 20-8-12 VIth  10-9-12



          vFkZ'kkfL=k;ksa dk xf.kr




                   uksV
                                                                 iz'ukoyh 3-2

                                fuEufyf[kr iQyuksa dk   osQ lkis{k vody&xq.kkad Kkr dhft, %

                                                                                1

                                   " 	 ;   *   ; !                          #"  2x   ; %

                                                     3 x
                                  )"  x 3  log x + e  x −  x e              '"     *   ;
                                              x 3


                                   "     *   ;    ;                         +"      ;     ;



                                   " 	  ; 
  ;                               "   *       *


                                   "   *                                   %" %        ;   *

                                        x
                                      xe − 1
                                                                                            3 2x
                                   "                                       #"   a +  2a e +  2 x  a e
                                         x

                                  )"  3 1 +  3 log x +  a  3 (log x ) +  2  (log x ) 3   '"   *    x   ; 
  ;

                                                         a
                                                                  a
                                       1
                                   "      ;   *
                                      a x
                                                                     mÙkj
                                           1                           1     x           1     − 3  x
                                        e +  x  +  l x  log l       −    +  7e             −  2x  −  e
                                            x       e                 2x 2               x
                                       5                            3   3


                                         log e                        +   x 1/2       #    ;     ; 
    *
                                            10
                                       x                            x   2
                                                                    1        2           1


                                     %  	  ; 
    *  
          '     log a +         +    log e
                                                                         e
                                                                                              10
                                                                    x        x           x
                                                1
                                    -  −  2x − 9/7  +  log e       	  ;


                                                x   2
                                       1                             1
                                         log e                         +  a x  log a      −  a − x  log a +  1  log e
                                                                              e
                                            a
                                       x                            2x                           e    x   a
                                3-11 nks iQyuksa osQ HkkxiQy dk vody&xq.kkad
                                              
     3        
      $        
     /)
                                                             f 1 ()            f 1 (x +  ) h
                                                               x
                                eku yks                    :       rks     ; ,  :
                                                             f 2 () x          f 2 (x +  ) h
                                                                              x
                                                                  f 1 (x +  ) h  f 1 ( )
                                                   d              f  (x +  ) h  −  f  ( ) x
                                ∴                           :  lim    2     2
                                                   dx        h→ 0       h
                                                                                  x
                                                                                 ( ) f
                                                                            x
                                                           :  lim 0    f 1 (x +  ) h f 2 2 ( ) −  (x +  h f 1 ) ( ) 2 (x +  ) h
                                                             h→
                                                                                   x
                                                                        hf
                                                                                 f
                                                                                  2
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