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

• A) 4.5
• B) 6.5
• C) 5.0
• D) 3.5

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

• A) There is no such point in the interval (-2, 2) where f(x) has a horizontal tangent.
• B) None of these.
• C) It is discontinuous on the interval [-2, 2].
• D) There is a point in the interval (-2, 2) where f(x) has a horizontal tangent

Let f(x)=x^3 and a=-3 ,b=3 and n = no. of partition of [-3,3]= 4
Let the widths of first, second, third and fourth intervals are 2, 1, 1, 2 respectively. Then “Mesh size” of this partition of [-3,3] is-------

• A) 1
• B) -1
• C) 2
• D) 0

12+22+32+…+152 equals _____.

• A) 15(16)(31) / 6
• B) 15(16)(30) / 6
• C) 15(16)(29) / 6
• D) 15(16)(17) / 6

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

• A) 3, 7 and 11
• B) 2, 6 and10
• C) 1, 5 and 9
• D) 2, 5 and 8

Integral of x^(-10) is

NOTE: x^n means ‘x’ to the power ‘n’

• A) None of these
• B) -10x^(-11)+C
• C) 1/(9x^9)+C
• D) - 1/(9x^9)+C

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

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

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

• A) True
• B) False
• C)
• D)

$${\text{The integral }}\int {\frac{{10x}}{{{{(5{x^2} + 1)}^2}}}\,dx\,} {\text{will be equal to ?}}$$

• A) $$- \frac{1}{{5{x^2} + 1}} + c$$
• B) $$- \frac{1}{{5x + 1}} + c$$
• C) $$\frac{1}{{5{x^2} + 1}} + c$$
• D) $$- \frac{1}{{{{(5{x^2} + 1)}^3}}} + c$$

1+2+3……….+1000 equals -------

• A) 3000
• B) None of these
• C) 500500
• D) 1000

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

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

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

• A) 5.
• B) None of these.
• C) 13.
• D) 6.

If f(x) = Sin(x) + x, then which of the following is true about it

• A) Its anti – derivative is Cos(x) + x^2/2 + 10.
• B) None of these.
• C) Its anti – derivative is Cos(x) + 1.
• D) Its anti – derivative is –Cos(x) + x^2/2 + 10.

$${\text{The integral }}\int {\sec (x).\tan (x)\,dx\,} {\text{will be equal to ?}}$$

• A) $$\cos ec(x) + c$$
• B) $${\text{None of these}}$$
• C) $$- \ln \left| {\cos (x)} \right| + c$$
• D) $$\sec (x) + c$$

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

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

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

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

\[\text{If we say a function }f\text{ have a relative extremum at a point }{{x}_{0}},\text{ then it means that }f\text{ has }\!\!~\!\!\text{ }\_\_\_\_\_\_\_\_\text{ at }{{x}_{0}}.\]

• A) Relative minimum
• B) Relative maximum
• C) None of these
• D) Either a relative maximum or relative minimum

The indefinite integral of ‘sec(x)tan(x)’ is…………….

• A) Tanx+c
• B) Cotx +c
• C) Sinx+c
• D) Secx+c

\[\text{If a function }f\text{ has a relative extrema at }{{x}_{0}}\text{, then}\]

• A) \[\text{either}\,{f}'\left( {{x}_{0}} \right)=0\,\text{or }f\text{ is not differentiable at }{{x}_{0}}\]
• B) \[f\text{ is differentiable at }{{x}_{0}}\]
• C) \[{f}'\left( {{x}_{0}} \right)\le 0\]
• D) \[{f}'\left( {{x}_{0}} \right)>0\]

Critical point for f(x) = -Cosx on [-pi/2,pi/2] are ------

• A) pi/2
• B) -pi/2
• C) pi/4
• D) 0