What is the derivative of tan-1(x) with respect to cot-1(x) ? fr

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 Multiple Choice QuestionsMultiple Choice Questions

41.

For what value of k is the function fx = 2x + 14 x < 0k              x = 0x + 122 x > 0 continuous?

  • 14

  • 12

  • 1

  • 2


42.

What is the derivative of 2sinx2 with respect to sin(x) ?

  • sinx2sinx2ln4

  • 2sinx2sinx2ln4

  • lnsinx2sinx2

  • 2sinxcosx2sinx2


43.

Consider the following statements in respect of the function fx = sin1x for x ≠ 0 and f(0) = 0 :

1) limx0fx exists

2) f(x) is continuous at x = 0

Which of the above statements is/are correct ?

  • 1 only

  • 2 only

  • Both 1 and 2

  • Neither 1 nor 2


Advertisement

44.

What is the derivative of tan-1(x) with respect to cot-1(x) ?

  •  - 1

  • 1

  • 1x2 + 1

  • xx2 + 1


A.

 - 1

As we know that differentiation of tan-1x w.r.t. x is 11 + x2

and cot-1x = - 11 + x2Now, dtan-1xdcot-1x = ddxtan-1x . ddx1cot-1x= 11 + x2 x  -1 + x21  = - 1


Advertisement
Advertisement
45.

Consider the following statements:

f(x) = e-|x|:

1) The function is continuous at x = 0.

2) The function is differentiable at x = 0.

Which of the above statements is/are correct ?

  • 1 only

  • 2 only

  • Both 1 and 2

  • Neither 1 nor 2


46.

If fx = sinxx where x ∈ R, is to be continuous at x = 0, then the value of the function at x = 0

  • should be 0

  • should be 1

  • should be 2

  • cannot be determined


47.

If eθφ = c + 4θφ, where c is an arbitrary constant and φ is a function of θ, then what is φdθ equal to ?

  • θdφ

  • θdφ

  • 4θ dφ

  • 4θ dφ


Advertisement