Cheenta
How 9 Cheenta students ranked in top 100 in ISI and CMI Entrances?
Learn More

Problem on Limit | ISI B.Stat Objective | TOMATO 728

Try this beautiful problem based on Limit, useful for ISI B.Stat Entrance

Problem on Limit | ISI B.Stat TOMATO 728


The limit lim \(\int\frac {h}{(h^2 + x^2)}\)dx (integration running from \(x =-1\)to \(x = 1\)) as\( h \to 0\)

  • equals 0
  • equals \(\pi\)
  • equals \(-\pi\)
  • deoes not exist

Key Concepts


Limit

Calculas

trigonometry

Check the Answer


Answer: does not exist

TOMATO, Problem 728

Challenges and Thrills in Pre College Mathematics

Try with Hints


Now, \(\int{h}{(h^2 + x^2)}\)dx (integration running from \(x = -1\) to \(x = 1\))
Let, \(x\) = h tany


\(\Rightarrow dx = h sec^2y dy\)
\(\Rightarrow \) \(x = -1\), \(y = -tan^{-1}(1/h)\) and \(x = 1\), \(y = tan^{-1}(1/h)\)


\(\Rightarrow \int \frac{h}{(h^2 + x^2)}\)dx =\(\int \frac{h(hsec^2ydy)}{h^2sec^2y}\) (integration running from\( y = -tan^{-1}(1/h) \) to \(y = tan^-1(1/h))\)


= y (upper limit =\( tan-1(1/h)\)) and lower limit = \(-tan^-1(1/h)\)


= \(2tan^-1(1/h)\)

Can you now finish the problem ..........


Now, lim \(2tan^-(1/h)\) as\( h \to 0\) doesn‟t exist

Subscribe to Cheenta at Youtube


Knowledge Partner

Cheenta is a knowledge partner of Aditya Birla Education Academy
Cheenta

Cheenta Academy

Aditya Birla Education Academy

Aditya Birla Education Academy

Cheenta. Passion for Mathematics

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.
JOIN TRIAL
support@cheenta.com