Anyone know how to prove these? (Function & Limits) #1

[harieche]

Hello everyone,

I have been doing a past paper and there are some questions that I cannot prove. Can anyone help me please?

Here is my first question:
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1. Prove that the function : f(x) = x⁴+2e^2x,

(is continuous at the point x = 2 by using the definition of continuity. You can use, without need to prove, that f(x) is differentiable at x=2.)
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[stapel]

1. Prove that the function : f(x) = x⁴+2e^2x,

(is continuous at the point x = 2 by using the definition of continuity. You can use, without need to prove, that f(x) is differentiable at x=2.)

What is your book's "definition of continuity"? How far have you gotten in applying this information?

Please show all of your work and reasoning so far. Thank you!