If x =(3+4+5+...+10)+{(3^3)+(4^3)+(5^3)+...+ (10^3)}, then x = _______.

• A) 3068.
• B) 3080.
• C) None of these.
• D) 55.

Approximation to an area improves as number of partitions is decreased.

• A) True
• B) False
• C)
• D)

By applying mean value theorem to the function
f(x)=lnx in the interval [1,e], the corresponding value of ‘c’ is ------------(Hint: lne=1, ln1=0)

• A) 1-e
• B) e-1
• C) -e
• D) e

Subdivide the interval [1, 5] into ‘n’ equally spaced subintervals then the width of each sub-interval is ------

• A) 1/n
• B) 5/n
• C) 5
• D) 4/n

Given a function f(x) = 1 / (x-1) and the interval is (0,2) ,then mean value theorem cannot be applied due to ……….

• A) Discontinuity of the function in the given interval
• B) Open interval
• C) Rational function
• D) None of these

If ‘n’ goes from 1 to 3 and the summation of ‘na’ = 6a, then the value of ‘a’ is ----------

• A) -6
• B) Undetermined
• C) 1
• D) 6

If x = 1 + 2 +3 + 4 + . . . + 20, then
x = ________.

• A) 500.
• B) None of these.
• C) 200.
• D) 210.

If we subdivide the interval [2,4] into n equal parts, then what will be the length ∆x of each part?

• A) 6/n
• B) 8/n
• C) 2/n
• D) 1/n

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)

What is the estimated area under f(x) = x2+2 from x = 1 to x = 5 with mid points for n = 2

• A) 48
• B) 38
• C) 76
• D) 26

If the interval [3,7] is divided into ‘4’ equal subintervals ,then right endpoint of each subinterval will be………

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

In Rolle’s theorem, f(x) is continuous in closed interval [a,b] and differentiable in open interval (a,b).Then why we don’t discuss its differentiability in the closed interval [a,b] because ---------

• A) f(a)=f(b)=0
• B) f ‘(a) and f ‘(b) never exist
• C) f(a) and f(b) never exist
• D) f ‘(a)=f ‘(b)=0

What are critical points of the function f(x) =x^2-1?
NOTE: x^n means ‘x’ to the power ‘n’

• A) No critical point
• B) None of these
• C) x=0
• D) x=1

How many subintervals of length ‘2’ will be formed for the interval [4,16] ?

• A) 4
• B) 6
• C) 5
• D) 7

Integral of x^2+x^3 is

NOTE: x^n means ‘x’ to the power ‘n’

• A) (1/3)x^4+(1/4)x^3 +C
• B) (1/4)x^4+(1/3)x^3 +C
• C) None of these
• D) x^3+x^4+C

What is the estimated area under f(x) = x from x = 0 to x = 3 with mid points for n = 3?

• A) 3.5
• B) 5.0
• C) 6.5
• D) 4.5

Let A be the area of a rectangle under a continuous function f(x) over a closed interval
[a, b]. If this area is divided in to ‘n’ sub-rectangles then width of each approximated sub-intervals is ---------

• A) (b-a)/n
• B) (a-b)/2
• C) (b-a)/2n
• D) (a-b)/n

Newton’s Method fails to find the approximate solution of an equation if _____________.

• A) the tangent line (at any approximated point) is not parallel to x-axis.
• B) None of these
• C) the tangent line(at any approximated point) is parallel to x-axis.
• D) the slope of the tangent line(at any approximated point) is non-zero

If x=-3 and x=3 are the two critical points of the function: f(x)=81x-3(x^3) then by using the 2nd derivative test, we can conclude that f(x) is relatively maximum at-----

• A) x= -9
• B) x=0
• C) x= 3
• D) x=-3

If the interval [3,7] is divided into ‘4’ equal subintervals ,then left endpoint of each subinterval will be………

• A) 4,5,6,7
• B) 5,6,7,8
• C) 3,4,5,6
• D) 3,6,8,9