Question

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

Answer #1

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

use
the epsilon-delta definition to prove that
limit (x,y) goes to (-1,-4) -3x+y=-1

By using delta- epsilon show that the two definitions of the
limit are equivalent
Def1: lim┬(x→x_0 )〖f(x)=f(x_0)〗. If for any ϵ>0,there exist
a δ>0 such that 0<|x-x_0 |<δ implies |f(x)-L|<ϵ
Def2: If for any sequence {x_n }→x_0 we have f(x_n)→L

Prove that lim x^2 = c^2 as x approaches c by appealing directly
to the definition of a limit.

Assumptions:
The formal definition of the limit of a function is as follows:
Let ƒ : D →R with x0 being an
accumulation point of D. Then ƒ has a limit L at
x0 if for each ∈ > 0 there is a δ > 0
that if 0 < |x – x0| < δ and
x ∈ D, then |ƒ(x) – L| <
∈.
Let L = 4P + Q. when P = 6 and Q = 24
Define...

Prove directly from the definition of the limit
(b) lim (n−2)/(n+12)=1
c) lim n√8 = 1. (Hint: recall the formula for x^n − 1).

show that any polynomial is continuous on R using the
epsilon-delta definition of continuity (not the limit
definition)

What mathematicians were instrumental in developing the
epsilon-delta definition of a limit? In your own words, explain
what a limit is. What practical application do limits have, if any?
If you don’t think there are any practical applications, why do you
think so?

Use
the formal definition of derivative to prove f(x) = 10|x| is not
differentiable at a=0.

Finding Limits: Use L’Hopital’s rule to evaluate the limit .
SHOW WORK .
8. lim┬(x→-1)〖(x-8x^2)/(12x^2+5x)〗
9. lim┬(x→0)〖sin5x/(2x^2 )〗

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