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Standardgränsvärden

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cobbe's version from 2016-08-21 16:49

Section

Question Answer
lim x -> 0 ( sin(x) / x )1
lim x -> 0 ( tan (x) / x )1
lim x -> 0 ( (e^x - 1) / x )1
lim x -> 0 ( ln( x+1 ) / x )1
lim x -> 0+ ( x^a * ln (x) )0 ( a > 0 )
lim x -> 0 ( ( 1+x )^( 1/x ) )e
lim x -> 0 ( arcsin(x) / x )1
lim x -> 0 ( arctan (x) / x )1
memorize

 

Question Answer
lim x - > inf ( ln(x) / x^a )0 ( a > 0 )
lim x - > inf ( x^a / b^x )0 ( a >= 0, b > 1 )
lim x - > inf ( ( 1 + (1+x) )^x )e
lim x - > inf ( a^x / x! )0 ( för alla konstanter a )
lim x - > inf ( x! / x^x )0
memorize

 

Question Answer
Hastighetstabell då x -> infln(x) << x^a << b^x ( a > 0, b > 1 )
memorize