Limit Solving Strategies for Non-L'Hôpital's Rule Problems

[Infinitum]

We have not such rule in Limits but in differential calculus we were taught,
y=f(x)g(x)
$\frac{dy}{dx}$=g(x)f'(x)+f(x)g'(x)

Exactly. Use this rule to differentiate y*sec(y), that's the answer you are looking for!

 

[shalikadm]

what about the [3] one?

 

[Infinitum]

what about the [3] one?

Convert $\frac{1}{\sqrt{2}}$ into $cos(\frac{\pi}{4})$, and apply the formula that changes the difference of two trigonometric terms into their product. In the denominator, after writing cot in terms of cos and sin, try getting a single trigonometric ratio and simplify.

 

[shalikadm]

thanks Infinitum and Pranav-Arora...Successfully solved the 2nd and 3rd limits..I'm going to ask about 1st one from a teacher...thanks for the help !