निम्नलिखित के मान है :
(i) ` lim_( x to 0) ((x^(2)+1)/(x +100))` (ii) ` lim_(xto 2)((x^(3)-4x^(2)+4x)/(x^(2)-4))`
(iii) `lim_(x to 2) ((x^(2)-4)/(x^(3)-4x^(2)+4x))` (iv) ` lim_(x to 2)((x^(3)-2x^(2))/(x^(2)-5x+6))`

Options

A. `1, 0, -1, -4`
B. `2/101, 0, oo, 0`
C. `1/100, 0, oo, -4`
D. इनमे से कोई नहीं

Answer

C

Explanation

(i) `lim_(x to 0) ((x^(2)+1)/(x+100))`
` = ((0)^(2)+1)/(0+100)=(1)/100`
(ii) ` lim_( x to 2)((x^(3)-4x^(2)+4x)/(x^(2)-4))`
` = lim_( x to 2) ((x^(2)-4x+4)/(x^(2)-2^(2)))` ltbrge ` lim _( xto2) (x(x-2)^(2))/((x-2)(x+2))=lim_(x to2)(x(x-2))/(x+2)` ltbrge ` (2(2-2))/(2+2)=(2xx0)/4=0`
(iii) ` lim_( xto2) ((x^(2)-4)/(x^(3)-4x^(2)+4x))`
`= lim _( x to 2) ((x)^(2)-(2)^(2))/(x(x^(2)- 4x +4))`
` =lim_( xto2) ((x-2)(x+2))/(x(x-2)^(2)) = lim_(x to 2) (x+2)/(x(x-2))`
` = (2 +2)/(2(2-2))=4/(2xx0)=4/0=oo`
(iv) ` lim_( x to2) ((x^(3)-2x^(2))/(x^(2)-5x+6))`
` =lim_(x to 2) (x^(2) (x-2))/((x-2)(x-3))=lim_(xto2)(x^(2))/(x-3)`
` (2)^(2)/(2-3)=4/(-1)=-4`