Lim x tends to 3 x^5- 243/x^2-9
dhruvsh:
what's the x tending to?
Limit X tends to 3
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Solution :
Lim ( x ->3 )[ (x^5 - 3^5 )/(x² - 3²) ]
=Lim (x->3){[(x^5-3^5)/(x-3)]/[(x²-3²)/(x-3)}
= [ 5* 3^5-1 ]/[ 2*3^2-1 ]
= [ 5*3⁴ ]/( 2*3 )
= ( 5/2 ) * 3³
= 137/2
••••
Lim ( x ->3 )[ (x^5 - 3^5 )/(x² - 3²) ]
=Lim (x->3){[(x^5-3^5)/(x-3)]/[(x²-3²)/(x-3)}
= [ 5* 3^5-1 ]/[ 2*3^2-1 ]
= [ 5*3⁴ ]/( 2*3 )
= ( 5/2 ) * 3³
= 137/2
••••
In third step ??
Lim( x-> a) [ xⁿ - aⁿ ]/( x - a )
= n * a^n-1
thanks
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