Question

Calculate the limit if n approaches Infinity:

lim [(5cosn+3sinn+lnn^7)/n - 1/(7^n) - (100^n)/n! ]

Answer #1

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

1. if lim
x->infinity+ (5+2X)/(9-6X)=??
2. what is the value for the same equation if lim x approaches
to negative infinity???
3. if lim x approaches to positive infinity then evaluate the
equation (4X+7)/(5X^2-3X+10)
4. What would be the value of the above mentioned equation is
lim x approaches to negative infinity

If lim Xn as n->infinity = L and lim Yn as n->infinity =
M, and L<M then there exists N in naturals such that Xn<Yn
for all n>=N

Let f be defined on the (0,infinity). Prove that the limit as x
approaches infinity of F(x) =L if and only if the limit as x
approaches 0 from the right of f(1/x) = L. Does this hold if we
replace L with either infinity or negative infinity?

Prove that a sequence (un such that n>=1)
absolutely converges if the limit as n approaches infinity of
n2un=L>0

Prove that (n + 1)! < nn whenever n > 3.
Conclude that lim as n approaches infinity of n!/nn
=0

for the following series
state whether the divergence test applies
either state that lim n-> infinity does not exist, or find
n-> infinity approaches
If test does not apply, state why
147. n=tan (n)

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

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).

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).

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