how would i go about solving this? (1 Viewer)

[chilli 412]

is there a way to solve this without having to draw a graph?

 

[cossine]

is there a way to solve this without having to draw a graph?
View attachment 36199

Definition: A function is continuous at x=a if lim x->a f(x) = f(a)

So we want lim(x->1) a-x^2 = lim(x->1) (x-a)^2

=> lim (x->1) a-x^2 - (x-a)^2 = 0

=> a-1 - (1-a)^2 = 0
=> a-1 -1 -a^2 +2a = 0
=> a^2 -3a +2 = 0
=> (a-2)(a-1) = 0

=> a = 2