If f(x)=Tan(x) then mean value theorem can be applied to it on the interval (0,2pi)

• A) False
• B) True
• C)
• D)

By using Newton method, which of the following is the poorest initial approximate solution of equation:x+Cosx=0?

• A) x=-pi/3
• B) x=0
• C) x=pi/2
• D) x=-pi/4

For the given function f(x)= 2(x^2)+1 in the interval [-1,2] , which condition of Rolle’s theorem is not satisfied.

• A) f (-1) = f (2)
• B) The function is continuous in the interval
• C) The function is differentiable in the interval
• D) None of these.

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

• A) 5
• B) 7
• C) 4
• D) 6

$${\text{For}}\,{\text{Rolle's}}\,{\text{Theorem,}}\,f\,{\text{is}}\,{\text{differentiable}}\,{\text{on}}\,{\text{the}}\,{\text{interval __________}}{\text{.}}$$

• A) $$(a,b)$$
• B) $$[a,b]$$
• C) $$(a,b]$$
• D) $$[a,b)$$

If a function f has a relative extrema at a point c, then c is a critical point for f .

• A) True
• B) False
• C)
• D)

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

• A) 5.0
• B) 3.5
• C) 6.5
• D) 4.5

$\text{A critical point for a function }f\text{ is any value of }x\text{ in the domain of }f\text{ at which}$

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

What are critical points of the function f(x) =x-1?

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

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

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

In approximation to an area Rn (where n is subscript) when limit is taken as n goes to infinity, approximation becomes actual area.

• A) True
• B) False
• C)
• D)

If $f''(x) > 0\,\forall \,x \in I$, then the graph of $f$ is___________ on $I$.

• A) concave downward
• B) None of these
• C) concave upward
• D) constant

Integration of (Cosx/Sinx).Cosecx with respect to x…………

• A) -Cosecx
• B) Cosecx
• C) Cotx
• D) Secx

If f(x)=(x^3)+(x^2)+x+1 , then ‘f’ is continuous and differentiable everywhere because ‘f’ is a ……..

• A) Function
• B) Equation
• C) Polynomial
• D) Relation

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

• A) False
• B) True
• C)
• D)

The anitderivative of the function f(x)=2-7Cosx, is -------

• A) All choices are true
• B) 2x-7Sinx-100
• C) 2x-7Sinx+C
• D) 2x-7Sinx+100

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

• A) Its relative maximum value is 9.
• B) Its absolute maximum value is 0.
• C) Its absolute maximum value is 9.
• D) None of these.

If ‘n’ goes from 1 to 4 and the summation of ‘na’ =Maxima of (e^x) in the interval[-e,0], then the value of ‘a’ is -----------

• A) 10
• B) -10
• C) -1/10
• D) 1/10

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

• A) 1/n
• B) 6/n
• C) 2/n
• D) 8/n

Integral of 5^2 is

NOTE: x^n means ‘x’ to the power ‘n’

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