Factorization

Q. The value of $\underset{x\to 5}{\lim }\frac{x^3-125}{x^2-7x+10}$ is

Q. Evaluate the following:

$\left|\begin{array}{ccc}x& 1& 1\\ 1& x& 1\\ 1& 1& x\end{array}\right|$

Q. Evaluate the following integrals:

$\underset{-4}{\overset{4}{\int }}\left|x+2\right|dx$

Q. $\int \frac{x+1}{x^2+4x+5}dx$

Q.

The value of $\underset{x\to 2}{lim}\frac{x^3-4x^2+4x}{x^2-4}$

Q. The value of $\underset{x\to 2}{\lim }\frac{x^2-4}{\sqrt{3x-2}-\sqrt{x+2}}$ is

Q. The value of $\underset{x\to 0}{\lim }\frac{\sqrt{1+x^2}-\sqrt{1-x^2}}{x}$ is

Q. Evaluate the following integrals:
$\underset{-6}{\overset{6}{\int }}\left|x+2\right|dx$

Q. The value of $\underset{x\to 2}{\lim }\frac{x^2-4}{\sqrt{3x-2}-\sqrt{x+2}}$ is

Q. Q. Evaluate : ${\int }_{}^{}\frac{6x+7}{\sqrt{x-5)(x-4)}}dx$

Q. $\int \frac{1}{\sqrt{x}}\left(1+\frac{1}{x}\right)dx$

Q. $\int \left(2x+3\right)\sqrt{4x^2+5x+6}dx$

Q. $y\sqrt{1+x^2}+x\sqrt{1+y^2}\frac{dy}{dx}=0$

Q. 5x + 7y = − 2
4x + 6y = − 3

Q. x − 2y = 4
−3x + 5y = −7

Q. $\int \frac{x+3}{{\left(x+1\right)}^4}dx$

Q. Evaluate the following integrals:
$\underset{1}{\overset{4}{\int }}\left\{\left|x-1\right|+\left|x-2\right|+\left|x-4\right|\right\}dx$

Q. Find x, y, a and b if

Q. $\int \frac{x}{{\left(x-1\right)}^2\left(x+2\right)}dx$

Q. $\int \frac{x^2+x-1}{{\left(x+1\right)}^2\left(x+2\right)}dx$

Q. $\int \frac{1}{\sqrt{x+a}+\sqrt{x+b}}dx$

Q. The value of $\underset{x\to 0}{\lim }\frac{\sqrt{1+x^2}-\sqrt{1-x^2}}{x}$ is

Q. $\underset{0}{\overset{2}{\int }}\sqrt{4-x^2}dx$

Q. $\int \frac{x+2}{\sqrt{x^2+2x-1}}dx$

Q. $\int \sqrt{\frac{a+x}{x}}dx$

Q. 5x + 7y = − 2
4x + 6y = − 3

Q. $\int \sqrt{1+x-2x^2}dx$

Q. $\underset{0}{\overset{1}{\int }}\frac{1}{\sqrt{1+x}-\sqrt{x}}dx$

Q. $\int \sqrt{4x^2-5}dx$

Q. $\int {\left(x+1\right)}^2{e}^{x}dx$