Which of the following is the sum of (2k+1) where k goes from 1 to 4?

• A) 20
• B) 26
• C) 24
• D) 22

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

• A) 12.
• B) None of these.
• C) 10.
• D) 18

f(x) = (x^2)+1 is a continuous function on (-infinity ,+infinity ) , and ‘f’ has no absolute maximum on (-infinity ,+infinity ) because………

• A) lim (f(x)) = +infinity as ‘x’ tends to ±infinity
• B) lim (f(x)) = 1 as ‘x’ tends to ±infinity
• C) lim (f(x)) = -infinity as ‘x’ tends to ±infinity
• D) lim (f(x)) = 0 as ‘x’ tends to ±infinity

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

• A) 5
• B) 4
• C) 0
• D) 1

If x = 3 + 4 + . . . + 20, then x = ________.

• A) 210.
• B) 207.
• C) None of these.
• D) 250.

For the area under the curve f(x) = x+1 from x = 1 to x = 3 with mid points approximations for n = 1, what will be the value of xk* ?

• A) 1.5
• B) 1
• C) 2.5
• D) 2

Integral of 5^2 is

NOTE: x^n means ‘x’ to the power ‘n’

• A) 10
• B) (1/3)5^3
• C) 25x
• D) None of these

In [0,pi],if the area under the curve f(x)=Sinx is divided into ‘3’ equally spaced rectangles of width ‘pi/3’ then by choosing middle point for height, the area of middle rectangle is ---------.

• A) pi/2
• B) pi/3
• C) pi/6
• D) pi/4

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) 3
• B) 5
• C) 4
• D) 6

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

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

Right end point ,left end point, and midpoint evaluation all converges to same result as number of subintervals tends to +ive infinity.

• A) False
• B) True
• C)
• D)

summation of (ai) (i varies from 1 to n) , summation of (aj) (j varies from 1 to n),summation of (ak) (k varies from 1 to n)
All these three represents same summation.

• A) False
• B) True
• C)
• D)

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

• A) 5/n
• B) 6/n
• C) 1/n
• D) 7/n

$\begin{align} & \text{Let a function }f\text{ is twice differentiable at a stationary point }{{x}_{0}}, \\ & \text{then }f\text{ has relative maximum at }{{x}_{0}}\,\text{if} \\ \end{align}$

• A) $\text{ }{f}''({{x}_{0}})\ge 0$
• B) $\text{ }{f}''({{x}_{0}})=0$
• C) $\text{ }{f}''({{x}_{0}})>0$
• D) $\text{ }{f}''({{x}_{0}})<0$

1+2+3………+t equals

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

What is length of each subinterval if the interval [-1,1] is divided into n subintervals of equal length.

• A) None of these
• B) 0
• C) 2/n
• D) 1/n

Which geometrical figure is used for approximating the area under the curve?

• A) Circle
• B) None of these
• C) Pentagon
• D) Right angled triangle

If $f$ has a local maximum or minimum at c, and if $f'(c)$ exists, then_________.

• A) $f'(c) = 0$
• B) None of these
• C) $f'(c) < 0$
• D) $f'(c) > 0$

What will be the sigma notation for 32+52+72+92?

• A) summation of (2k-1)2 where (k varies from 1 to 4)
• B) summation of (k2) where (k varies from 3 to 9)
• C) summation of (2k2+1) where (k varies from 3 to 6)
• D) summation of (2k+1)2 where (k varies from 1 to 4)

The area of a rectangle can be found by simply …………its dimensions.

• A) subtracting
• B) multiplying
• C) dividing
• D) adding