PLS HELP: Give a value of A so that the function f(x)= {x-x^2, x=2 is continuous. Usually I check to see if the f(x) exists and then go from there, but the A is in that equation!

Question

PLS HELP: Give a value of A so that the function
f(x)= {x-x^2,    x<2
         {x^2 - Ax,  x>=2
is continuous.
Usually I check to see if the f(x) exists and then go from there, but the A is in that equation!

anonymous · Answer

Continuous means lim$$\lim_{x \rightarrow a}f(x)=f(a)$$

So we just plug in 2.

2-2^2=2^2-2A

-2=4-2A

2A=6

A=3

anonymous · Answer

wow, you're good!

anonymous · Answer

that really helped me understand it- thanks a ton!

anonymous · Answer

so you made the left hand side equal to the right hand side as both must agree, as well as f(x) for the it to be continuous?

anonymous · Answer

Right, the limits from both sides must be equal, so I just plugged 2 in (remember that if you plug a number into a function, it'll give you the limit, provided that you get something normal...i.e. not divided by 0, etc.).

anonymous · Answer

ok, gotcha!

myininaya · Answer

gj goblue