Question

limit 4 nd 5 krna hi .. plz help nd tell me the theorem

Answer 1

Final Answer : C) e^(1/12)

Steps :
1) We will check form of limit.
We know that
$\cos(hx) = \frac{ {e}^{x} + {e}^{ - x} }{2}$
x By series expansion of e^x and e^-x,
Series of cosh(x) looks like.

cosh(x) = 1 + x^2/2 + x^4/24+ .......

From here in calculation, we get form is 1^inf.

2) Now, after getting form is 1^inf
We will use that
limit will be e^[(f(x)-1)g(x)]

We will neglect higher order terms after x^4.

After calculating, limit tends to e.^(1/12).

For Calculation, see pic