Factorization Method Form to Remove Indeterminate Form

Q.

$\underset{n\to 0}{lim}\frac{n!}{(n+1)!-n!}\text{is equal to:}$

1. 0

2. 1

3. does not exist

4. ∞

Q. ABC is an isosceles triangle inscribed in a circle of radius r. If AB = AC and h is the altitude from A to BC.The triangle ABC has perimeter $P=2[\sqrt{(2hr-h^2)}+\sqrt{2hr}]$ and A be the area of the triangle .Find $\underset{h\to 0}{lim}\frac{A}{P^3}$

1. 
2. 
3. 
4. 

Q. The value of $\underset{x\to 8}{lim}\frac{2x^2-17x+8}{8-x}$ is

1. $15$
2. None of the above
3. $-15$
4. $-1$

Q.

$\text{The values of constants a and b so that}\underset{x\to \infty }{lim}(\frac{x^2+1}{x+1}-ax-b)=\frac{1}{2},are$

1. 

2. 

3. 

4. 

Q.

Find the value of $\underset{x\to 0}{lim}\frac{\sqrt{a+x}-\sqrt{a}}{x}$

1. 

2. 

3. 

4. 

Q. The value of $\underset{x\to 0}{\lim }\frac{\tan x-\sin x}{{\sin }^{3}x}$ is

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

Q. $\underset{x\to \frac{\pi }{4}}{lim}\frac{{\cot }^{3}x-\tan x}{\cos (x+\frac{\pi }{4})}$ is:

1. $4\sqrt{2}$
2. $4$
3. $8\sqrt{2}$
4. $8$

Q. Let $f\left(x\right)=5-|x-2|$ and $g\left(x\right)=|x+1|,x\in R.$ If $f\left(x\right)$ attains maximum value at $\alpha$ and $g\left(x\right)$ attains minimum value at $\beta ,$ then $\underset{x\to -\alpha \beta }{lim}\frac{(x-1)(x^2-5x+6)}{x^2-6x+8}$ is equal to:

1. $\frac{-1}{2}$
2. $\frac{3}{2}$
3. $\frac{1}{2}$
4. $\frac{-3}{2}$

Q. If $L=\underset{x\to -2}{lim}\frac{3x^2+kx+k-7}{2x^2+x-6}$ exists and is finite, where $k$ is a real number, then the values of $k$ and $L$ are

1. $k=5,L=-1$
2. $k=5,L=1$
3. $k\in R,L=\frac{3}{2}$
4. $k=-5,L=1$

Q. $\underset{n\to \infty }{lim}({\sin }^4\theta +\frac{1}{4}{\sin }^{4}2\theta +.......+\frac{1}{4^n}{\sin }^4(2^n\theta \left)\right)$ is equal to

1. ${\sin }^2\theta$
2. ${\sin }^4\theta$
3. ${\cos }^2\theta$
4. ${\cos }^4\theta$