# How do you prove that the function #f(x) = x^2 -3x +5# is continuous at a =2?

##### 1 Answer

Apr 5, 2016

Prove using limit definition of continuity...

#### Explanation:

Any polynomial function is continuous everywhere, but let's prove this particular example using the limit definition of continuity...

A function

In our example:

#f(2) = 2^2-3(2)+5 = 4-6+5 = 3#

#f(2+h) = (2+h)^2-3(2+h)+5#

#= 2^2+4h+h^2-3(2)-3h+5#

#= 4-6+5+h+h^2#

#= 3+h+h^2 -> 3# as#h->0#

So