$\frac{x^2-7x+10}{x^2-5x-14}\times \frac{x^3+8}{x^3-8}\times \frac{x^2+2x+4}{x^2-2x+4}\times \frac{x-7}{x-5}=?$

Q. Multiply the following and write your answer in lowest terms: $\frac{x^2-3x-10}{x^2-x-20}\times \frac{x^2-2x+4}{x^3+8}$

Q. Which of the following are quadratic equations?

(i) x² + 6x − 4 = 0
(ii) $\sqrt{3}{x}^2-2x+\frac{1}{2}=0$
(iii) $x^2+\frac{1}{x^2}=5$
(iv) $x-\frac{3}{x}=x^2$
(v) $2x^2-\sqrt{3x}+9=0$
(vi) $x^2-2x-\sqrt{x}-5=0$
(vii) 3x² − 5x + 9 = x² − 7x + 3
(viii) $x+\frac{1}{x}=1$
(ix) x² − 3x = 0
(x) ${\left(x+\frac{1}{x}\right)}^2=3\left(x+\frac{1}{x}\right)+4$
(xi) (2x + 1) (3x + 2) = 6(x − 1) (x − 2)
(xii) $x+\frac{1}{x}=x^2,x\ne 0$
(xiii) 16x² − 3 = (2x + 5) (5x − 3)
(xiv) (x + 2)³ = x³ − 4
(xv) x(x + 1) + 8 = (x + 2) (x − 2)

Q. Find the limits :
$i.$ $\underset{x\to 1}{lim}\left[\frac{x^2+1}{x+100}\right]$
$ii.$ $\underset{x\to 2}{lim}\left[\frac{x^3-4x^2+4x}{x^2-4}\right]$
$iii.$ $\underset{x\to 2}{lim}\left[\frac{x^2-4}{x^3-4x^2+4x}\right]$
$iv.$ $\underset{x\to 2}{lim}\left[\frac{x^3-2x^2}{x^2-5x+6}\right]$
$v.$ $\underset{x\to 1}{lim}[\frac{x-2}{x^2-x}-\frac{1}{x^3-3x^2+2x}]$

Q. $\int (x+x^2+x^3+x^4)$ dx is equal to