Graph r 3 sin 2 theta Evaluate limx rightarrow 1 x3 x2 3x

Graph r = 3 sin 2 theta Evaluate: lim_x rightarrow 1 x^3 - x^2 + 3x - 3/x^2 + x - 2 Evaluate: lim_x rightarrow 2 3x^5 - 2x^2 + 1/x^2 + 1

lim x>1 x^3 -x^2 +3x -3/x^2 +x-2

if we directly keep x=1 then we get 0/0 form

we can write x^3 -x^2 +3x-3 = (x-1) (x^2 +3)

and x^2 +x-2 =(x-1) (x+2)

so now the

lim x->1 (x-1) (x^2 +3) /(x-1)(x+2) = (x^2 +3) /(x+2) = (1+3)/(1+2) =4/3

3).

lim x->2 (3x^5 -2x^2 +1) /(x^2 +1) = (3.2^5 -2.2^2 +1)/(2^2+1) = (3.32 -8 +1)/(5) = 89/5