For what value of k is the function fx = 2x +

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41.

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

  • 14

  • 12

  • 1

  • 2


A.

14

For the function to be continuous at x = 0, the function should have valid limit equal to the value at that particular point at which we have to check the continuity, for this particular question, we have to check the continuity at x = 0, so, the limit should exist in the neighbours of x =0.

Then,

limx0+2x + 14 = limx0-x +122 = k

From above, we can clearly say that k = 14

So, option A is correct.


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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


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


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