Question

Compute the following limits and show all your work:

(a) A = lim x→∞ [3x^2 −4/x^2 +10lnx]

(b) B = lim x→2+ [(x-2)^2ln(x-1)]

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Answer #1

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Compute the following limits and show all your work: (a) 5pts A
= limx→∞· 4x^2 −3/x^2 +11 lnx ¸ . (b) 5pts B = lim x→3+ (x−3)^3
ln(x−2) . Hint for (b): Taking the natural logarithm of “both
sides” will help

please show all work Evaluate each of the following limits, for
after lim the part with x-> and then a number is below the lim
and then after is the fraction part
1) lim x->3 (x^2-2x-3/x^2-5x+6)
2) limx->2 (x-2/square root(2x)-2)
3) lim x->inf (3x^5-7x^3/-5x^5+x^3-9)

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 )〗

a.) Find the following limit.
lim x→−∞ x^3 - sqrt(4x^6-3x)/7x^3+x
b.) Sketch the graph of a function f(x) that has all of the
following features:
f ' (x) > 0 on the intervals (−∞, −4) ∪ (3,∞).
f ' (x) < 0 on the intervals (−4, −1) ∪ (−1, 3).
f '' (x) > 0 on the intervals (−∞, −4) ∪ (−4, −2) ∪ (−1,
4).
f '' (x) < 0 on the intervals (−2, −1) ∪ (4,∞).
x-intercepts when...

hi guys , using this definition for limits in higher dimensions
:
lim (x,y)→(a,b) f(x, y) = L
if 1. ∃r > 0 s.th. f(x, y) is defined when 0 < || (x, y) −
(a, b) || < r
and 2. given ε > 0 we can find δ > 0 s.th. 0 < || (x,
y) − (a, b) || < δ =⇒ | f(x, y) − L | < ε
how do i show that this is...

Find the derivatives of m(x)=2ln((x^(3)e^(x))/(x^(2)-4)^(1/2))
and h(x)=(e^(3x))/(1-e^(-3x))

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.

****SHOW ALL WORK****
1. Solve for x: -8 ≤ 3x - 5
2 a. Re-write in equivalent exponential form: log2 64 = 6 b.
Find x to four decimal places: log x = 3.0832
3. Perform: [ 6 2 ] [ 1 1 ]
[ 2 4 ] - [ 1 -1 ] =
4. Calculate the following: a. Jane wants to create a password
for one of her Internet accounts using some portion of her street
name, which is...

1. Evaluate the limit
lim x→0 sin4x /7x
2. In which limits below can we use L'Hospital's Rule? select
all that apply.
lim x→∞ e^−x /x
lim x→0 1−e^x /sin(2x)
lim x→0 x+tanx /sinx
lim x→−∞ e^−x /x

Solve the following equations:
1) 4e^(2x)+5=17
2) e^(2x)-e^x-12=0
3) 2ln(x+1)=18
4) log(3x+2)-Log(4)=log(x+4)

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