$\text{A line }y={{y}_{\text{0}}}\text{ is called a horizontal asymptote for the graph of function }f\text{ if}$

• A) $\underset{x\to 0}{\mathop{\lim }}\,f(x)={{y}_{0}}$
• B) $\underset{x\to +\infty }{\mathop{\lim }}\,f(x)=0$
• C) $\underset{x\to +\infty }{\mathop{\lim }}\,f(x)=\infty$
• D) $\underset{x\to +\infty }{\mathop{\lim }}\,f(x)={{y}_{0}}$

If f(x) = x^5 + 6, then which of the following is Not true about it.

• A) Its anti – derivative is x^6/6 + 6x + 10.
• B) Its anti – derivative is x^6/6 + 6x + 6.
• C) Its anti – derivative is x^6/6 + 6x.
• D) Its anti – derivative is x^6/6 + 12x

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

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

For the area under the curve f(x) = 2x from x = 0 to x = 8 with mid points approximations for n = 2, what will be the values of xk* ?

• A) 4 and 6
• B) 1 and 5
• C) 3 and 7
• D) 2 and 6

The symbol $\int {}$ was introduced by___________and is called integral sign.

• A) Leibnitz
• B) Newton
• C) Lagrange
• D) Cauchy

An Inflection Point is a point where a curve changes from

• A) a. Concave up to concave down
• B) d. None of these
• C) c. Both a and b
• D) b. Concave down to concave up

Increase in number of rectangles under any continuous function gives …………. approximation to area.

• A) no change in
• B) None of these
• C) Poor
• D) better

$${\text{The integral }}\int {{{\sec }^2}(2{x^2})\,.4x\,dx\,} {\text{will be equal to ?}}$$

• A) $$\tan (2{x^2}) + c$$
• B) $${\text{se}}{{\text{c}}^2}(2x) + c$$
• C) $$\tan (2x) + c$$
• D) $$\sec (2{x^2}).\tan (2{x^2}) + c$$

summation of (n+i);where (i varies from 1 to 1) =………..

• A) 0
• B) 1
• C) n+1
• D) n

To get better approximation to actual area under a continuous curve over a closed interval, we have to increase ………

• A) Total area
• B) Size of the interval
• C) Width of the subintervals
• D) Number of subintervals

If f(x)=1 / (x^2) and the interval is [-1,1] , then Rolle’s theorem can be applied.

• A) True
• B) False
• C)
• D)

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

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

• A) 10
• B) 18
• C) 8
• D) 24

$${\text{The integral }}\int {\cot (2x)\,dx\,} {\text{will be equal to ?}}$$

• A) $$\frac{1}{2}\ln \left| {\sec (2x)} \right| + c$$
• B) $${\text{ln}}\left| {\sin (2x)} \right| + c$$
• C) $$\frac{1}{2}\ln \left| {\sin (2x)} \right| + c$$
• D) $$\ln \left| {{\text{sec}}(2x)} \right| + c$$

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

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

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

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

Given f(x)= 1/(x-1) on the interval (0,3) , then ‘f ’ has no relative maxima or relative minima due to………

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

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) 76
• C) 26
• D) 38

\[{\text{What}}\,{\text{does}}\,{\text{the}}\,{\text{indefinite}}\,{\text{integral }}\int_{}^{} {f(x)} dx\,{\text{represent?}}\]

• A) \[{\text{Area}}\,{\text{under}}\,{\text{the}}\,{\text{curve}}\]
• B) \[{\text{Families}}\,{\text{of}}\,{\text{antiderivative}}\,{\text{of}}\,{\text{the}}\,{\text{function }}f(x)\]
• C) \[{\text{None}}\,{\text{of}}\,{\text{these}}\]
• D) \[{\text{Curvature}}\,{\text{of}}\,{\text{the}}\,{\text{curve}}\]

Summation of ‘kx’ where k goes from 1 to 5 equals

• A) 15k
• B) 55
• C) None of these
• D) 15x