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# ISI MStat PSB 2007 Problem 3 | Application of L'hospital Rule This is a very beautiful sample problem from ISI MStat PSB 2007 Problem 3 based on use of L'hospital Rule . Let's give it a try !!

## Problem- ISI MStat PSB 2007 Problem 3

Let f be a function such that and f has derivatives of all order. Show that where is the second derivative of f at 0.

### Prerequisites

Differentiability

Continuity

L'hospital rule

## Solution :

Let L= it's a form as f(0)=0 .

So , here we can use L'hospital rule as f is differentiable .

We get L= = , taking -h=k .

= = . Hence done!

## Food For Thought

Let be a continuous function such and assume that there exists a positive integer m such that for all Prove that for all ## Subscribe to Cheenta at Youtube

This is a very beautiful sample problem from ISI MStat PSB 2007 Problem 3 based on use of L'hospital Rule . Let's give it a try !!

## Problem- ISI MStat PSB 2007 Problem 3

Let f be a function such that and f has derivatives of all order. Show that where is the second derivative of f at 0.

### Prerequisites

Differentiability

Continuity

L'hospital rule

## Solution :

Let L= it's a form as f(0)=0 .

So , here we can use L'hospital rule as f is differentiable .

We get L= = , taking -h=k .

= = . Hence done!

## Food For Thought

Let be a continuous function such and assume that there exists a positive integer m such that for all Prove that for all ## Subscribe to Cheenta at Youtube

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