Question

limit as x --> ininity

of (5-e^x)/5+ 3e^x

Answer 1

nevermind i got that, can someone help me with this

Find the values of a and b that make f continuous everywhere.

f(x) =


x2 − 4
x − 2
if x < 2
ax2 − bx + 3 if 2 ≤ x < 3
4x − a + b if x ≥ 3

Answer 2

You want to travel to orpen gate and you are at Kruger national park how many kilometres would it be

Answer 3

If you mean f(x) =
(x^2-4)/(x-2) if x<2
then since x<2, (x^2-4)/(x-2) = x+2
So,

f(x) =
x+2 if x < 2
ax^2-bx+3 if 2 <= x < 3
4x-a+b if x >= 3

So, as x->2-, f(x)->4
That means we must have

4a-2b+3 = 4 at x=2
9a-3b+3 = 12-a+b at x=3

a = 7/2
b = 13/2

f(x) =
x+2 if x < 2
7/2 x^2 - 13/2 x + 3 if 2 <= x < 3
4x - 3 if 3 <= x

see the graphs and their intersections at 2,3 at

http://www.wolframalpha.com/input/?i=plot+y%3Dx%2B2%2Cy%3D7%2F2+x^2+-+13%2F2+x+%2B+3%2Cy%3D4x%2B3