Prove 2x^2+5 is continuous at x=3

[gottfried]

Homework Statement

Using the definition of continuity show that f(x) = 2x² + 5 is continuous at x = 3

Homework Equations

The Attempt at a Solution

For all ε>0 there exists δ>0 such that |x-3|<δ implies that |2x² + 5 -23| = |2(x²-9)| = |2(x+3)(x-3)| < |2(x+3)δ|

Could anybody give me advice as to where I should take it from here to show that |2x² + 5 -23|<ε

 

[tiny-tim]

hi gottfried!

if eg you insist that δ < 1, then |x+3| is between 5 and 7

 

[STEMucator]

|2(x+3)(x-3)| = 2|x+3||x-3| < 2δ|x+3|

Now is |x+3| = |x - 3 + 6| ? Also remember to use the triangle inequality.