Continuity Assignments Class 12 (1)

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For Guru Dakshina  @ 9990781319   ashishkumarhdfc@hdfcbank    SOME FREQUENTLY USED LIMITS in radians not in degrees    010 sin tan 1 cos 1lim 1 lim 1 lim 0 lim 1log (1 ) 1lim 1 lim lim log x x n n x neex x a ex x  x a ana ax x a x  → → → →−→ → →   −  −= = = =  + − −= = =−  Discuss the continuity of following functions: 1.   2 3, if 2( )2 3, if 2 x x  f x x x  + = −    2.   | |, if 0( )0, if 0 x x x  f x x  = =   3.   2 1, if 1( )1, if 1 x x  f x x x  + = +    4.   102 1, if 1( ), if 1 x x  f x x x   − =     5.   , if 0| |( )1, if 0 x x x  f x x  = −    6.   32 3, if 2( )1, if 2 x x  f x x x   − =  +    7.   5, if 1( )5, if 1 x x  f x x x  + = −    8.   | | 3, if 3( ) 2 , if 3 36 2, if 3 x x  f x x x x x  +  −= − −  +    9.   3, if 0 1( ) 4, if 1 35, if 3 10 x  f x x x   =      10.   2 , if 0( ) 0, if 0 14 , if 1 x x  f x x x x  =     11.   2, if 1( ) 2 , if 1 12, if 1 x  f x x x x  −  −= −     12.   1, 0log(1 2 )( )7, 0 x  ex x  f x x   −+= =   13.   sin, if 0( )1, if 0 x x x  f x x x  = +    14.   2  1sin , if 0( )0, if 0 x x x  f x x  = =   15.   sin cos , if 0( )1, if 0 x x x  f x x  − = − =   16.   2 sin3, 0tan23( ) , 02log(1 3 ), 01 x  x x x  f x x x x e = =+ −   LIMITS – 2    For Guru Dakshina  @ 9990781319   ashishkumarhdfc@hdfcbank    Find the value k, a,   b , c , or any other unknown, if following functions are continuous: 1.   2 , if 2( )3, if 2 kx x  f x x   =    2.   1, if ( )cos , if  kx x  f x x x  +  =     3.   1, if 5( )3 5, if 5 kx x  f x x x  + = −    4.   2 2 3, 11( ), 1 x x x x  f x k x   − − −+= = −   5.   =−= 2if ,32if ,2cos)( x x x x kx  f    6.   += 10if ,21 102if , 2if ,5 )( x x bax x x  f    7.   =−= 0,0,22cos1)(  2 x kx x x x  f    8.   =−−+= 0,0,)1log()1log( )( x kx x bx ax x  f    9.   == 0,10,sin)(  22 x x x kx x  f    10.   −+=−= 0,4160,0,4cos1)( 2 x x x x kx x x x  f    11.   =+= 0,0,2||)(  2 x kx x x x x  f    12.   −+=++= 0,0,0,sin)1sin( )( 232 x bx x bx x x cx x x x ax  f    13.   =−= 0,210,sincos1)( x x x x kx x  f    14.   +−−=++−−= 4,|4|44,4,|4|4)( x bx x x bax ax x x  f    15.   −−=−= 2,)2()sin1( 2,2,cos3sin1)( 223 x x x bx ax x x x  f    16.   −+−−−+= 10,21201,11)( x x x x x  px  px x  f    17.   −+= 0,sintan0),1( 2sin)( 3  x x x x x x ax  f    18.   =−−+= 0,0,)21log()31log( )( x kx x x x x  f    19.   −+=−= 0,256250,0,10cos1)( 2 x x x x ax x x x  f    LIMITS – 3    For Guru Dakshina  @ 9990781319   ashishkumarhdfc@hdfcbank

Sep 10, 2019

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Sep 10, 2019
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