Evaluate a limx rightarrow 1 x23x3x2 b limx rightarrow 2 x23

Evaluate (a) lim_x rightarrow 1 x^2+3x+3/x-2 (b) lim_x rightarrow 2 x^2+3x+3/x-2

a) lim x--> 1 ( x^2 + 3x + 3) / (x - 2)

plugging in the value x = 1

(1^2 + 3 + 3 ) / (1 - 2)

7 / -1

= -7

b) lim x--> 2 ( x^2 + 3x + 3 ) / ( x- 2)

plugging in the value x = 2

( 2^2 + 3*2 + 3) / ( 2-2 )

13 / 0

since dividing by zero leads to undefined

hence, the limit diverges that is does not exists