Question

prove the statement using the epsilon delta definition of a limit

lim x-->2 (x^2-2x+7)=1

Answer #1

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

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

prove
limit 2x^2-x-5=1as x approaches 2 using epislon/delta

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 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)

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

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)

A graphing calculator is recommended.
For the limit
lim x → 2 (x3 −
2x + 5) = 9
illustrate the definition by finding the largest possible values
of δ that correspond to ε = 0.2 and ε =
0.1. (Round your answers to four decimal places.)

1. Evaluate the limit using L'Hospital's rule if necessary
lim x→∞ (1+ 12 / x)^x/1
2. In which limits below can we use L'Hospital's Rule?
lim x→π/5 sin(5x) /5x−π
lim x→−∞ e^−x / x
lim x→0 2x/ cotx
lim x→0 sin(3x) / 3x
I Need help with both questions please! thank you so much.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 11 minutes ago

asked 12 minutes ago

asked 16 minutes ago

asked 25 minutes ago

asked 25 minutes ago

asked 37 minutes ago

asked 37 minutes ago

asked 48 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago