Question

Evalute the following given in the picture.

Topic - Calculus
Level - Hard
Class - 11th , 12th or Graduates.

Answer 1

Ans--

0

Explanation--

First i did, integration by parts to solve the integration. Which took many steps and lengthy but it was worthy. Then i used simple L'Hospital rule in lim to solve the question.

Answer 2

Answer:

Step-by-step explanation:

Definite integration:-

Here, at first we substitute n as 1/t,where t will tend to 0,as n tends to infinity.

After this substitution,we get a 0/0 form.

So,we apply L hospital rule,by differentiating both numerator and denominator to remove the indeterminate form.

In numerator,a definite integral is there.

So,we apply Newton Leibnitz rule for antiderivative of definite integral.

We assume y=t*2018^t

Applying log both sides,we get an indeterminate form again which is at power of e.

Again applying L hospital rule,we get y=1

But,there was a denominator of 2(y/2) if you observe carefully.

Hence required limit is 1/2.