Left Hand Limit

Q.

Graph of f(x) is given. Find the value of left hand limit as x approaches 3.

1. does not exist

2. 2

3. -2

4. 0

Q.

The range of the function y=cotx is

1. [-1, -1]

2. (-1, 1)

3. R

4. R⁺

Q. Graph of f(x) is given below. The value of left hand limit as x approaches 3 is .

1. 2
2. -2
3. \N
4. non-existent

Q. For each $x\in R$, let $\left[x\right]$ be the greatest integer less than or equal to $x$. Then $\underset{x\to 0{}^{-}}{lim}\frac{x\left(\right[x]+|x|)\sin \left[x\right]}{|x|}$ is equal to :

1. $0$
2. $1$
3. $\sin 1$
4. $-\sin 1$

Q. $Iff\left(x\right)=\{\begin{array}{cc}{x}^2-3,& 2<x<3\\ 2x+5,& 3<x<4\end{array}$, the equation whose roots are $\underset{x\to 3-}{lim}f\left(x\right)$ and $\underset{x\to 3+}{lim}f\left(x\right)is$

1. $x^2-12x+36=0$
2. $x^2-26x+66=0$
3. $x^2-17x+66=0$
4. $x^2-22x+121=0$

Q. $Iff\left(x\right)=\{\begin{array}{cc}{x}^2-3,& 2<x<3\\ 2x+5,& 3<x<4\end{array}$, the equation whose roots are $\underset{x\to 3-}{lim}f\left(x\right)$ and $\underset{x\to 3+}{lim}f\left(x\right)is$

1. x² - 12x + 36 = 0
2. x² - 26x + 66 = 0
3. x² - 17x + 66 = 0
4. x² - 22x + 121 = 0

Q. For each $x\in R$, let $\left[x\right]$ be the greatest integer less than or equal to $x$. Then $\underset{x\to 0{}^{-}}{lim}\frac{x\left(\right[x]+|x|)\sin \left[x\right]}{|x|}$ is equal to :

1. $\sin 1$
2. $0$
3. $-\sin 1$
4. $1$

Q.

Which of the following functions is depicted below?

1. x² – 2

2. x² – 4

3. x² + 4

4. x²

Q.

The graph of 5x + 3 < 28 is

1. 

2. 

3. 

4. 

Q.

The value of $\underset{x\to 1}{lim}\left[sinsi{n}^{-1}x\right]$ is

1. 1

2. does not exist

3. π/2

4. 0

Q. Find the derivative of the following fuctions (it is to be understood that $a,b,c,d,p,q,r$ and $s$ are fixed non-zero constants and $m$ and $n$ are integers) : $\frac{x}{{\sin }^{2}x}$

Q. The range of every odd polynomial is equal to ? 1- {0} 2- R 3- (0, infnity)