Question:

If $ y=tan^{-1}\left(\frac{2x}{1+3x^{2}}\right)+tan^{-1}\left(\frac{5+x}{1-5x}\right) $ , then $ \frac{dy}{dx}= $

Updated On: Jun 23, 2024
  • $ \frac{9}{1+9x^{2}} $
  • $ \frac{3}{1+9x^{2}} $
  • $ \frac{1}{1+9x^{2}} $
  • $ \frac{3}{1+3x^{2}} $
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The Correct Option is B

Solution and Explanation

Answer (b) $ \frac{3}{1+9x^{2}} $
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Concepts Used:

Continuity

A function is said to be continuous at a point x = a,  if

limx→a

f(x) Exists, and

limx→a

f(x) = f(a)

It implies that if the left hand limit (L.H.L), right hand limit (R.H.L) and the value of the function at x=a exists and these parameters are equal to each other, then the function f is said to be continuous at x=a.

If the function is undefined or does not exist, then we say that the function is discontinuous.

Conditions for continuity of a function: For any function to be continuous, it must meet the following conditions:

  • The function f(x) specified at x = a, is continuous only if f(a) belongs to real number.
  • The limit of the function as x approaches a, exists.
  • The limit of the function as x approaches a, must be equal to the function value at x = a.