limitation

L'Hopitals' rule

According to L'Hopital's rule, the limit as x->0 of f(x)/g(x) is the same as the limit as x->0 of f'(x)/g'(x) . So your next step is to find those derivatives and see if your answer is not indeterminate any more. If it's still indeterminate, but getting less complicated, a second derivative might bring the answer.

If you show your work you can be helped more.
 
Find lim ( tan 3x^2 + sin^2 5x )/ x^2
x-0

urgent! need help!


Sorry,the lecturer havent teach this stuff but his assignment want us to solve this Q. so i hope to see a full answer and step here.
 
Find lim ( tan 3x^2 + sin^2 5x )/ x^2
x-0
You should know that limt0sin(t)t=1\displaystyle \lim _{t \to 0} \dfrac{{\sin (t)}}{t} = 1.

Now use the above: tan(3x2)x2=3cos(3x2)sin(3x2)3x2\displaystyle \dfrac{{\tan \left( {3x^2 } \right)}}{{x^2 }} = \dfrac{3}{{\cos \left( {3x^2 } \right)}}\dfrac{{\sin \left( {3x^2 } \right)}}{{3x^2 }}
 
Hey thankyou very much for u two's help,i think i solved this Q. I get 28 for this Q,shud be correct la hehe. really appreciate ur help!! :D
 
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