1+2+3+…+539 equals _____.

• A) 538(540)/2
• B) 539(540)/2
• C) 538(539)/6
• D) 538(540)/6

$$\text{If }{f}'(x)={{x}^{2}}-1.\text{ Then the critical points of the function }f\text{ are}$$

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

What is the estimated area under f(x) = 2x from x = 0 to x = 4 with left end points for n = 2?

• A) 8
• B) 10
• C) 18
• D) 24

If a function has an extreme value (either a maximum or a minimum) on an open interval (a,b), then the extreme value occurs at a ........

• A) Any point in the open interval (a,b)
• B) Critical point of f(x)
• C)
• D)

Integral of (5/2)cos(x) is

• A) None of these
• B) (5/2)sin(x)+C
• C) (3/2)csc(x)+C
• D) (5/2)tan(x)+C

For the area under the curve f(x) = x+2 from x = 2 to x = 4 with mid points approximations for n = 1, what will be the value of f(xk*) ?

• A) 6
• B) 5
• C) 3
• D) 4

$\begin{align} & \text{If a function }f\text{ is twice differentiable at a stationary point }{{x}_{0}}\text{ and }{f}''({{x}_{0}})>0, \\ & \text{then }f\text{ has relative }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ at }{{x}_{0}}. \\ \end{align}$

• A) c. Both a and b
• B) d. None of these
• C) a. Maximum
• D) b. Minimum

f(x) = 8x-x^2 on the closed interval [0, 6]
has the critical point at x=………

• A) 1
• B) 5
• C) 0
• D) 4

Let y = f(x) be a discontinuous function on a finite closed interval, then which of the following is true about it.

• A) It has only absolute minimum value.
• B) It must have absolute extreme values.
• C) It may or may not have absolute extreme values.
• D) None of these.

If f (x) = 2 x + 7 is defined on the interval
[2, 4), then which of the following is true about it.

• A) It has only absolute minimum value.
• B) It has both absolute maximum and minimum values.
• C) None of these.
• D) It has only absolute maximum value.

If the function is continuous on the closed interval [a,b], then the function has …………

• A) Only maximum value on the [a,b]
• B) Only minimum value on the [a,b]
• C) Only minimum value on the [a,b]
• D) Both maximum and minimum values on the [a,b]

For the area under the curve f(x) = x+2 from x = 2 to x = 8 with left end points approximations for n = 3, what will be the values of xk* ?

• A) 4, 6 and 8
• B) 2, 6 and 8
• C) 2, 4 and 6
• D) 3, 5 and 7

The approximate solution is possible to generate using Newton’s Method if ___________.

• A) the tangent line(at approximated points) must crosses the x - axis.
• B) the slope of tangent line(at any approximated point) is zero.
• C) the tangent line(at any approximated point) is parallel to x- axis.
• D) None of these.

If ‘n’ goes from 1 to 3 and the summation of ‘na’ = derivative of Cosx at (pi/2), then the value of ‘a’=------

• A) -1/6
• B) 1/6
• C) 6
• D) -6

$\text{A critical point for a function }f,\text{ where }{f}'(x)=0\text{ is called as}\,\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\,\text{ point}\text{.}$

• A) Mid
• B) Tangent
• C) Stationary
• D) Corner

If f(x) = Cos(x) + Sin(x) + x, then which of the following is NOT true about it.

• A) None of these.
• B) Its anti – derivative is Sin(x) – Cos(x) + x^2/2 + 5.
• C) Its anti – derivative is -Sin(x) – Cos(x) + x^2/2 + 4.
• D) Its anti – derivative is Sin(x) – Cos(x) + x^2/2 + 4.

What will be the value of summation of k2 where k goes from 11 to 12

• A) 212
• B) 244
• C) 281
• D) 265

What is the estimated area under f(x) = 9 - x2 from x = 0 to x = 4 with mid points for n = 1?

• A) 24
• B) 21
• C) 20
• D) 28

If ‘n’ goes from 1 to 3 and the summation of ‘na’ = definite integral of ‘1’ on closed interval [0,1], then the value of ‘a’=------------

• A) 1/6
• B) -6
• C) -1/6
• D) 6

The estimated area under f(x) = 12 / x from
x = 1 to x = 3 with right end points for
n = 2 is ________.

• A) 18.
• B) 10
• C) 20.
• D) None of these.