Question

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

Answer #1

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).

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

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

Estimate the lim as f(x) approaches -infinity by graphing
f(x)=sqrt{x^{2}+x+9}+x
(b) Use a table of values of f(x) to guess the
value of the limit. (Round your answer to one decimal place.)
(c) Prove that your guess is correct by evaluating
lim x→−∞ f(x).

Prove that lim n^k*x^n=0 as n approaches +infinity. Where
-1<x<1 and k is in N.

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

Prove that if (xn) is a sequence of real numbers,
then lim sup|xn| = 0 as n approaches infinity. if and
only if the limit of (xN) exists and xn
approaches 0.

1. if limit X approaches to 2 from the negative side then
evaluate the equation X-10/X-2
2. If limit X approaches to 3 from the positive site then
evaluate the equation X-11/X-3
3.Evaluate the following equation if limit X approaches to
infinity -11X^2+4X-4/8X-8
4. Evaluate the following equation if lim X approaches to
negative infinity -3X^2-9X+9/9X-6

Using the definition of convergence of a sequence, prove that the
sequence converges to the proposed limit.
lim (as n goes to infinity) 1/(n^2) = 0

prove directly by definition that [1, \infty) is not
compact.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 23 minutes ago

asked 24 minutes ago

asked 27 minutes ago

asked 39 minutes ago

asked 53 minutes ago

asked 57 minutes ago

asked 57 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago