If eθφ = c + 4θφ, where c is an arbitrar

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 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


44.

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

  •  - 1

  • 1

  • 1x2 + 1

  • xx2 + 1


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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


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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


B.

θdφ

Given eθφ = c + 4θφAnd φ = fθ, φdθ = ?Taking log both sides eθφ = c + 4θφlogeθφ = logc + 4θφθφ = logc + 4θφφ + θ = 1c + 4θφ0 +4φ +4θφ + θ = 4φeθφ +4φeθφθ - 4θeθφ = 4θeθφ - φθeθφ - 4eθφ = φ - eθφ - 4eθφθ = - φθdφ = - φdθφdθ = - θdφ


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