Question

can someone help me prove continuity on this problem (2x+3)/(x-2) on the interval (2,infinity)

Answer 1

Polynomials are continuous at all points.
Rational functions are continuous at all point on their domain
(2,infinity) is in the domain of (2x+3)/(x-2)

Answer 2

yeah i wrote that down but the teach said it was wrong since i didnt show the 3 step method

Answer 3

Ah!
1) show that the function is continuous
2) show that limit of the function exists
and 3) that f(L) = lim x->L f(x)

Answer 4

yeah that i get stuck on the limit part

Answer 5

yea, just show that the function is equal to it limit at that point

Answer 6

?

Answer 7

f(x) = (2x+3)/(x-2)
so f(3) = 9
the limit of f(x) as x approaches 3 is 9
f(3) = lim x->3 f(x)

Answer 8

it continuous on (2, infinity) because
1) the function is continuous on (2, infinity)
2) The function had a value at all point( 2, infinity )
and 3) the value of the function at all point equal it limit at all those points

Answer 9

[2, infinity ) is not continuous because the function is undefined at 2, has not limit at 2, and cannot equal the limit at 2( because it does not have one )

Answer 10

ok i get what you did thanks a lot man

Answer 11

rock on.