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ISI MStat PSA 2019 Problem 17 | Limit of a function

This is a beautiful problem from ISI Mstat 2019 PSA problem 17 based on limit of a function . We provide sequential hints so that you can try this.

Limit of a function

If f(a)=2, f'(a)=1 , g(a)=-1 and g'(a)=2 , then what is

 \lim\limits_{x\to a}\frac{(g(x)f(a) - g(a)f(x))}{(x - a)} ?

  • 5
  • 3
  • - 3
  • -5

Key Concepts

Algebraic manipulation

Limit form of the Derivative

Check the Answer

Answer: is 5

ISI MStat 2019 PSA Problem 17

Introduction to real analysis Robert G. Bartle, Donald R., Sherbert.

Try with Hints

Try to manipulate \frac{(g(x)f(a) - g(a)f(x))}{(x - a)} so that you can use the Limit form of the Derivative . Let's give a try .

\frac{(g(x)f(a) - g(a)f(x))}{(x - a)} =

\frac{(g(x)f(a) -g(a)f(a) +g(a)f(a) - g(a)f(x))}{(x - a)} =

f(a)\frac{g(x)-g(a)}{(x-a)} - g(a)\frac{f(x)-f(a)}{(x-a)} .

Now calculate the limit using Limit form of the Derivative.

So, we have \lim\limits_{x\to a}\frac{(g(x)f(a) - g(a)f(x)}{(x - a)} =

\lim\limits_{x\to a} f(a)\frac{g(x)-g(a)}{(x-a)} - \lim\limits_{x\to a} g(a)\frac{f(x)-f(a)}{(x-a)} =

f(a) g'(a) - g(a)f'(a)= 2.(2)-1.(-1)=5.

Similar Problems and Solutions

Related Program

Outstanding Statistics Program with Applications

Outstanding Statistics Program with Applications

Subscribe to Cheenta at Youtube

This is a beautiful problem from ISI Mstat 2019 PSA problem 17 based on limit of a function . We provide sequential hints so that you can try this.

Limit of a function

If f(a)=2, f'(a)=1 , g(a)=-1 and g'(a)=2 , then what is

 \lim\limits_{x\to a}\frac{(g(x)f(a) - g(a)f(x))}{(x - a)} ?

  • 5
  • 3
  • - 3
  • -5

Key Concepts

Algebraic manipulation

Limit form of the Derivative

Check the Answer

Answer: is 5

ISI MStat 2019 PSA Problem 17

Introduction to real analysis Robert G. Bartle, Donald R., Sherbert.

Try with Hints

Try to manipulate \frac{(g(x)f(a) - g(a)f(x))}{(x - a)} so that you can use the Limit form of the Derivative . Let's give a try .

\frac{(g(x)f(a) - g(a)f(x))}{(x - a)} =

\frac{(g(x)f(a) -g(a)f(a) +g(a)f(a) - g(a)f(x))}{(x - a)} =

f(a)\frac{g(x)-g(a)}{(x-a)} - g(a)\frac{f(x)-f(a)}{(x-a)} .

Now calculate the limit using Limit form of the Derivative.

So, we have \lim\limits_{x\to a}\frac{(g(x)f(a) - g(a)f(x)}{(x - a)} =

\lim\limits_{x\to a} f(a)\frac{g(x)-g(a)}{(x-a)} - \lim\limits_{x\to a} g(a)\frac{f(x)-f(a)}{(x-a)} =

f(a) g'(a) - g(a)f'(a)= 2.(2)-1.(-1)=5.

Similar Problems and Solutions

Related Program

Outstanding Statistics Program with Applications

Outstanding Statistics Program with Applications

Subscribe to Cheenta at Youtube

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