lim x -> 0 sin (x^2) / x?

Question

thanks again. i'm hoping to find these answers without l'hospitals rule as it has not been covered yet

i give best answer

i think your answer is for sin^2(x) not sin(x^2)

Answer 1

lim x -> 0 sin (x^2) / x
apply the limit
sin(0^2)/0=0/0 indeterminate
apply l'hospital's rule
take the derivative of the numerator and denominator
cos(x^2)*2x/1
apply the limits
cos(0^2)*(2*0)/1
1*0/1
0
lim x -> 0 sin (x^2) / x =0

Answer 2

lim x-->0 sinx sinx /x
=lim x-->0 sinx/x . lim x--> 0 sinx .
=1 . sin0
=1.0
=0