Get inspired by the success stories of our students in IIT JAM MS, ISI MStat, CMI MSc DS. Learn More

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 !!

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.

Differentiability

Continuity

L'hospital rule

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!

Let be a continuous function such and assume that there exists a positive integer m such that for all Prove that for all

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 !!

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.

Differentiability

Continuity

L'hospital rule

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!

Let be a continuous function such and assume that there exists a positive integer m such that for all Prove that for all

Cheenta is a knowledge partner of Aditya Birla Education Academy

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.

JOIN TRIALAcademic Programs

Free Resources

Why Cheenta?

Online Live Classroom Programs

Online Self Paced Programs [*New]

Past Papers

More