Question

Find the limit of sin(x^2)/x as x approaches to 0.

Answer 1

Use L'hospital's rule. Take the derivatives of the numerator and denominator SEPARATELY.

Answer 2

I did. But I got 2x(cos x^2)/1, what's next?

Answer 3

Substitute x=0 into the equation.

Answer 4

I got 0/1=0, so is that the answer?

Answer 5

its simple
sinx^2/x=(sinx.sinx)/x
=(sinx/x)sinx
applying limit as x tends to 0, we know sinx/x=1
thus
=1*sinx
since x is 0 thus sinx=0 and 1*0=0
hence answer is =1*0=0