Graphical Interpretation of Continuity

Q. The function f(x)=tan x is discontinuous at x = .

1. \N
2. $\frac{\pi }{4}$
3. $\frac{\pi }{2}$
4. $\pi$

Q. If f(x) is a function whose domain is symmetric about the origin, then f(x) + f(–x) is

1. One-one
2. Even
3. Odd
4. Both even and odd

Q. If \vert x+(1/x)\vert>2 , then x is (A) R-\{0\} (B) R-\{-1, 0, 1\} (C) R-\{1\} (D) R-\{-1, 1

Q.

Evaluate the following limits in
$\underset{x\to \frac{\pi }{2}}{\text{lim}}\frac{\text{tan 2x}}{x-\frac{\pi }{2}}$

Q.

$Letf\left(x\right)=\frac{x-\left[x\right]}{1+x-\left[x\right]},xϵR,\left[\right]dentoesthegreatestintegerfunction.Then,therangeoffis$

1. 

2. [0, 1]

3. 

4. (0, 1)

Q. WHICH OF THE FOLLOWINF FUNCTIONS HAVE FINITE NO OF POINTS OF DISCONTINUITY ON REAL SET

Q. Graph of y= \lbrack x\rbrack + \sqrt{x-\lbrack x\rbrack

Q.

Draw the curve $\frac{2^x}{2^{\left[x\right]}}$. Where [.] denotes greatest integer function

1. 

2. 

3. 

4. 

Q. In the interval $(-\frac{\pi }{4},\frac{\pi }{4})$, the function $f\left(x\right)=tanx$ is .

1. continuous
2. discontinuous
3. undefined

Q. The domain of definition of the function f(x) = log |x| is

(a) R
(b) (−∞, 0)
(c) (0, ∞)
(d) R − {0}

Q. The range of f(x) = cos [x], for π/2 < x < π/2 is

(a) {−1, 1, 0}
(b) {cos 1, cos 2, 1}
(c) {cos 1, −cos 1, 1}
(d) [−1, 1]

Q. 18. Graph of {sinx

Q.

Find the value of $\underset{x\to 0}{lim}120.\frac{tanx-x-x^3}{x^3}$

Q.

Find the number of discontinuities of the given function between x = 0 and x =2.

___

Q. Let f(x) = x - |x| then f(x) is,

1. Continuous ⩝×∈ R

2. discontinuous at x = 0

3. Always increasing

4. a constant

Q. Domain of the function f(x)=log(x^2-3)(log4^x) is

Q. State whether each of the following statements are true or false. If the statements is false, re-write the given statements correctly:

(i) If P = {m, n} and Q = {n, m}, then P × Q = {(m, n), (n, m)}
(ii) If A and B are non-empty sets, then A × B is a non-empty set of ordered pairs (x, y) such that x ∈ B and y ∈ A.
(iii) If A = {1, 2}, B = {3, 4}, then A × (B ∩ ϕ) = ϕ.

Q. Let f : R $\to$ R be a function. Define g:R $\to$ by g(x) = |f(x)| for all x. Then g is

1. Onto if f is onto
2. One-one if f is one-one
3. Continuous if f is continuous
4. None of these

Q.

Among which of these points is $f\left(x\right)=\tan x$ discontinuous?

1. 0

2. $\frac{-\pi }{4}$

3. $\frac{\pi }{4}$

4. $\frac{\pi }{2}$

Q. The figure formed by the lines ax ± by ± c = 0 is
(a) a rectangle
(b) a square
(c) a rhombus
(d) none of these

Q. ∫_0^L1/ax+b)\operatorname dx=

Q. \lim_{x→0} (5x + 3)(6x + 2)

Q.

An experiment consists of rolling a die and then tossing a coin once if the number on the die is even. If the number on the die is odd, the coin is tossed twice. Write the sample space for this experiment.

Q.

Find the number of discontinuities of the given function between x = 0 and x =2.

Q. The number of solution(s) of \vert\log\vert x\vert\vert+\vert x\vert=2 is equal to (1) 0 (2) 6 (3) 5 (4) 4

Q.

The function $f\left(x\right)=\tan x$ where $x\in (\frac{-\pi }{4},\frac{\pi }{4})$.

1. is continuous

2. is discontinuous

3. is increasing

4. is decreasing

Q.

Find the number of discontinuities of the given function between x = 0 and x =2.

___