Let f(x) = x2 + 2x – 5 and g(x) = 5x + 30What are

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 Multiple Choice QuestionsMultiple Choice Questions

21.

If limx0ϕx = a2, where a  0, then what is limx0ϕxa = ?

  • a2

  • a - 2

  •  - a2

  •  - a


22.

What is limx0e - 1x2 = ?

  • 0

  • 1

  •  - 1

  • limit does not exist


23.

What is f'(x) = ? when x > 1 

  • 0

  • 2x - 1

  • 4x - 2

  • 8x - 4


24.

What if'(x) equal to when 0 x < 1 ?

  • 0

  • 2x - 1

  • 4x - 2

  • 8x - 4


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25.

Let f(x) = ex - 1x, x > 00,             x = 0

be a real valued function.

Which one of the following statements is correct ?

  • f (x) is a strictly decreasing function in (0, x)

  • f(x) is a strictly increasing function in (0, x)

  • f(x) is neither increasing nor decreasing in (0, x).

  • f(x) is not decreasing in (0, x)


26.

Let f(x) = ex - 1x, x > 00,             x = 0

be a real valued function.

Which one of the following statements is correct ?

  1. f(x) is right continuous at x = 0.
  2. f(x) is discontinuous at x = 1.

Select the correct answer using the code given below

  • 1 only

  • 2 only

  • Both 1 and 2

  • Neither 1 nor 2


27.

Let f(x) = x2 + 2x – 5 and g(x) = 5x + 30

If h(x) = 5 f(x) – xg(x), then what is the derivative of h(x)

  •  - 40

  •  - 20

  • - 10

  • 0


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28.

Let f(x) = x2 + 2x – 5 and g(x) = 5x + 30

What are the roots of the equation g[f(x)] = 0 ?

  • 1, - 1

  •  - 1, - 1

  • 1, 1

  • 0, 1


B.

 - 1, - 1

D.

0, 1

Given f(x) = x2 + 2x – 5 and g(x) = 5x + 30

Now we have to find the value of g[f(x)], then we have to put the value of x as f(x) in function g(x).

Then, g[f(x)] = 5(x2 + 2x 5) + 30 = 0 {it is given in the question that the value of g[f(x)] = 0}

now, it will become, g[f(x)] = 5x2 + 10x – 25 + 30 = 0

g[f(x)] = 5x2 + 10x + 5 = 0

g[f(x)] = 5{x2 + 2x + 1} = 0

g[f(x)] = 0 is possible only and only when the value of x2 + 2x + 1 = 0

then (x + 1 )2 = 0

it is possible only when x = - 1, - 1

hence, option B is correct.


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29.

Consider the equation xy = eyWhat is d2ydx2 at  x = 1 equal to ?

  • 0

  • 1

  • 2

  • 4


30.

Consider the equation xy = ey

What is dydx at  x = 1 equal to ?

  • 0

  • 1

  • 2

  • 4


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