f(x)=x^3-3x, is increasing on the interval (0 ,infinity)

• A) True
• B) False
• C)
• D)

Integration of 5 with respect to x is…………

• A) 5x^2
• B) 5x
• C) 5
• D) x

Absolute minimum of the function f(x)=x in the semi open interval (0,2] is-------

• A) 0
• B) Undefined
• C) 1
• D) 2

Newton’s method is not applicable when ‘f’ is a …………

• A) Trignometric function
• B) Exponential function.
• C) Polynomial
• D) Constant function

Which of the following is the regular partition of the interval [0,2]?

• A) [0,0.25],[0.25,0.75],[0.75,1.25],[1.25,2]
• B) [0,0.5],[0.5,1.25],[1.25,1.50],[1.50,2]
• C) [0,0.50],[0.50,1],[1,1.50],[1.50,2]
• D) [0,0.25],[0.25,1],[1,1.50],[1.50,2]

\[{\text{What}}\,{\text{does}}\,{\text{the}}\,{\text{indefinite}}\,{\text{integral }}\int_{}^{} {f(x)} dx\,{\text{represent?}}\]

• A) \[{\text{None}}\,{\text{of}}\,{\text{these}}\]
• B) \[{\text{Families}}\,{\text{of}}\,{\text{antiderivative}}\,{\text{of}}\,{\text{the}}\,{\text{function }}f(x)\]
• C) \[{\text{Area}}\,{\text{under}}\,{\text{the}}\,{\text{curve}}\]
• D) \[{\text{Curvature}}\,{\text{of}}\,{\text{the}}\,{\text{curve}}\]

If we subdivide the interval [1,6] into n equal parts, then what will be the length ∆x of each part?

• A) 1/n
• B) 6/n
• C) 5/n
• D) 7/n

The dimensions of a rectangle are given to be 8ft by 12ft. The perimeter of rectangle will be…………..

• A) 40 feet
• B) 30 feet
• C) 50feet
• D) 60 feet

The indefinite integral of 5sinx is ……….

• A) 5cosx +c
• B) -5cosx+c
• C) cosx/5+c
• D) -cosx/5+c

Integral of 3sec(x)tan(x) is

NOTE: x^n means ‘x’ to the power ‘n’

• A) (3/2)sec^2(x)+C
• B) 3tan(x)+C
• C) 3sec(x)+C
• D) None of these

To find out critical values of a function, we put it equal to zero and solve for x.

• A) True
• B) False
• C)
• D)

13+23+33+…+193 equals _____.

• A) [19(20)]2/2
• B) 19(20)2/2
• C) [19(20)/2]2
• D) 19(20)/22

Which of the following is the sum of (2k-1) where k goes from 0 to 2?

• A) -2
• B) 3
• C) 4
• D) -1

For the area under the curve f(x) = 2x from x = 0 to x = 12 with left points approximations for n = 3, what will be the values of xk* ?

• A) 0, 5 and 10
• B) 0, 4 and 8
• C) 0, 6 and 12
• D) 0, 3 and 6

1+2+3………+t equals

• A) n(n+1)(2n+1)/6
• B) None of these
• C) n(n+1)/2
• D) t(t+1)/2

If f(x) =cos(x) then mean value theorem can be applied on this in the interval (pi/2, 3pi/2)

• A) False
• B) True
• C)
• D)

What will be the sigma notation for 43+63+83+103?

• A) summation of (2k)3 where (k varies from 1 to 4)
• B) summation of (2k)3 where (k varies from 2 to 5)
• C) summation of (2k3) where (k varies from 2 to 5)
• D) summation of (2k+1)3 where (k varies from 2 to 5)

$$\text{If }{f}'(x)={{x}^{2}}-x\text{. Then the critical points of the function }f\text{ are}$$

• A) 1, -1
• B) 1, 2
• C) 0, 1
• D) 0, 2

If f (x) = x^3 is defined on the interval
[-1, 2], then which of the following is true about it

• A) Its relative minimum value exists at the critical point.
• B) Its relative minimum value does not exist at the critical point.
• C) Its absolute minimum value exists at the critical point.
• D) None of these.

If x = (1^2)+(2^2)+(3^2)+(4^2) + . . . + (30^2), then x = ________.

• A) 465.
• B) 9455.
• C) 900.
• D) None of these.