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