Question

f(x) =

x^2 +2x if x >= 3

-x+18 if x< 3.

What is the epsilon delta proof to show f is continuous at
x=3?

Answer #1

Use
an epsilon-delta argument to show f(x) = 2x^2 - 1 is continuous at
every a ∈ ℝ.

prove the statement using the epsilon delta definition of a
limit
lim x-->2 (x^2-2x+7)=1

let f(x) = 3x3 - 2 and let epsilon>0 be given Find
a delta so that |x -1 |<=delta implies |f(x) -1|<=epsilon

Show that f: R -> R, f(x) = x^2 + 2x is not uniformly
continuous on R.

Prove that if f(x) is a continuous function and f(x) is not zero
then g(x) = 1/f(x) is a continuous function.
Use the epsilon-delta definition of continuity and please
overexplain and check your work before answering.

Prove that the function f(x,y) is differentiable at (0,0) by
using epsilon-delta method.
(1) f(x,y) = x+y+xy
(2) f(x,y) = sin(xy)

1. Let f(x)=x^2−4x+3/x^2+2X-3 Calculate lim x→1 f(x)
by first finding a continuous function which is equal to ff
everywhere except x=1 .
2. Use the chain rule to find the derivative of the following
function 5(−2x^3−9x^8)^12

Use the formal definition of limit (epsilon-delta definition) to
prove that lim x--> 3 (x^2 + 5x) = 24.

find critical numbers of
f(x)=2x^3 + x^2 - 2x
please show all work :)

Find derivatives (Please show work!)
1. f(x)=ln(5x^3)
2. f(x)=(ln^3)x
3. f(x)=e^(5x2+2)
4. f(x)=xe^2x
5. f(x)=xlnx

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