Algebra of Limits

Q.

Find $\underset{x\to 5}{\text{lim}}$, where f(x) = |x| - 5,

Q.

If $\underset{x\to a}{lim}$[f(x) + g(x)] = 10 and $\underset{x\to a}{lim}$ f(x)=2, then find the value of $\underset{x\to a}{lim}$ g(x), provided the limit

exist

Q.

Evaluate the following limit:
$\underset{x\to \pi }{\text{lim}}(x-\frac{22}{7})$

Q. cosx16. lim

Q.

If $\omega$, ${\omega }^2$ are imaginary cube roots of unity and

$\frac{1}{a+\omega }$ + $\frac{1}{b+\omega }$ + $\frac{1}{c+\omega }$ = 2${\omega }^2$ and $\frac{1}{a+{\omega }^2}$ + $\frac{1}{b+{\omega }^2}$ + $\frac{1}{c+{\omega }^2}$ = 2$\omega$, then $\frac{1}{a+1}$ + $\frac{1}{b+1}$ + $\frac{1}{c+1}$ is equal to:

1. 1

2. -1

3. 2

4. 3

Q. 27. Find lmf(x)where f(x)-lxl-5

Q. If $z_1$ and $z_2$ both satisfy $z+\overline{z}=2|z-1|$ and $arg(z_1-z_2)=\frac{\pi }{4}$, find $Im(z_1+z_2)$.

Q.

$\underset{n\to \infty }{\overset{}{lim}}$ $\sum _{x=1}^{20}$ $cos{}^{2n}(x-10)$ is equal to

1. 0

2. 1

3. 19

4. 20

Q. $\underset{x\to 2}{\lim }\frac{x^2-4}{x+2}$
The limit of the function is

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

Q. 29. Letta, a, . . ., a, be fixed real numbers and define a functiona)x-aa2)...(x- anWhat is limf(x) ? For some a # a1, a2, , an, compute lim f(x).x→ax→ a

Q.

$\underset{x\to 1}{lim}f\left(x\right)=5$, $\underset{x\to 2}{lim}g\left(x\right)=6$ and $\underset{x\to 1}{lim}g\left(x\right)=2$ find the value of $\underset{x\to 1}{lim}$ $\left(\right[g\left(x\right){]}^{f\left(x\right)})$ ___

Q.

If a ≤ 0, the roots of $x^2-2a|x-a|-3a^2=0$ is / are :

1. a

2. 

3. a

4. 

Q. 13. (ax +b)" (cx +d)

Q.

Let $a_1$, $a_2$, ..., $a_n$ be fixed real numbers and define a function f(x) = $(x-a_1)(x-a_2)...(x-a_n)$. What is $\underset{x\to a_1}{\text{lim}}$ f(x)?
For some a $\ne a_1,a_2...a_n$, compute $\underset{x\to a}{\text{lim}}$ f(x).

Q.

$\underset{x\to a}{lim}\left[f\right(x)+g(x\left)\right]=\underset{x\to a}{lim}f\left(x\right)+\underset{x\to a}{lim}g\left(x\right)$
is valid if $\underset{x\to a}{lim}f\left(x\right)$ does not exists?

1. True

2. False

Q.

If $\underset{x\to a}{lim}f\left(x\right)=l$ and $\underset{x\to a}{lim}g\left(x\right)=m$, then $\underset{x\to a}{lim}{\left(f\right(x\left)\right)}^{g\left(x\right)}=l^m$

1. True

2. False

Q. 19. lim a secarx->0

Q. 30. If f(x)-0, x0-1, x>(0For what value (s) of a does lim fo) exists?

Q.

If z be a complex number satisfying $z^2$ + z + 1 = 0. Find the value of $\left|z\right|$.

__

Q. f(x)-2xa_1π , evaluate limi f (x)31. If the function fx) satisfies lim

Q. $\underset{x\to \infty }{lim}\frac{co{s}^{2}x}{x}=$

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

Q. Sinar+bx20. lima, b, a + b#0

Q.

$\underset{x\to 1}{lim}f\left(x\right)=5$, $\underset{x\to 2}{lim}g\left(x\right)=6$ and $\underset{x\to 1}{lim}g\left(x\right)=2$ find the value of $\underset{x\to 1}{lim}$ $\left(\right[g\left(x\right){]}^{f\left(x\right)})$

Q. x< 032. )xm Osrl. For what integers m and n does both lim f(x)x→0nx +m, and lim f (x) exist?x→1

Q.

Evaluate the following limit:
$\underset{x\to 4}{\text{lim}}\frac{4x+3}{x-2}$

Q.

$\underset{x\to \infty }{lim}\frac{{\cos }^{2}x}{x}=$

1. $0$

2. $1$

3. $-1$

4. $\infty$

Q. 3. lim㎡

Q. Find the general solution:
$cos4x=cos2x$

Q.

If $\underset{x\to a}{lim}$[f(x) + g(x)] = 10 and $\underset{x\to a}{lim}$ f(x)=2, then find the value of $\underset{x\to a}{lim}$ g(x), provided the limit

___

Q. sin (T-x)15, lim