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$lim_{p \to 0} \frac{1}{2 p} ((1 + p) e^{- \frac{y}{1 + p}} - (1 - p) e^{- \frac{y}{1 - p}}) = e^{- y} + y e^{- y}$
I have already tried L'Hopital's Rule, but it gave me something that I couldn't simplify. The problem seems to be the $\frac{1}{2 p}$ term never seems to go away. I know the exponential function can be represented as: $e^{x} = lim_{n \to \infty} (1 + \frac{x}{n})^{n}$ , but it doesn't seem immediately obvious how that would apply in this situation.

Loldi9s 2022-09-02

Use the graph of $f (x) = 3^{x - 8} - 10$ to give the range of f(x).
a) y $\leq$ -10
b) y < 10
c) y > -10
d) y $\geq$ -10
e) y < -10
f) None ofthe above.

Kent Beduya2022-09-01

slawejagdw 2022-09-01

Find the value of x. (use 3.14 as an approximation for $π$ )
A=28.26
D=4x

zibazeleor 2022-09-01

Let B=(8,12,16,18) and C=(3,8,11,12,15).
B _ C=(8,12)
Which symbol inserted in the blank will make the above statement correct?
A. $\cup$
B. $⧸ \in$
C. $\cap$
D. $\in$

Archita Gahoi2022-08-31

Consider the function f(x) = x + x ∈ . If α is the length of interval of decrease and β be the length of interval of increase, then 3(α + β) is equal to

chrisysakh 2022-08-31

What is the value of $lim_{x \to 0} ((1 + \tan x) / (1 + \sin x))^{c o s e c x}$ ?

suffisantfn 2022-08-31

What is the derivative of $4 e^{2 x}$ ?
Do you use the product rule to multiply it out, or can youjust apply power rule to get: $8 x e^{2 x}$ ?

Teisha Springer2022-08-30

f(x) =
x2 − 8x
x − 8
and g(x) = x

yakige8425 2022-08-30

A bacteria that grows according to the function 𝑓(𝑡) = 500𝑒^0.05𝑡
, where 𝑡 is measured in minutes.
a) How many bacteria are present in the population after 4 hours?
b) When does the population reach 100 million bacteria?

epifizamvg 2022-08-29

Let D = {14,17,19}, E = {14,16,17,18} and F= {13,15,16,17,19}. List the elements in the set $D \cup E$

Corinne Woods 2022-08-29

Every finite integral domain is isomorphic to Zp
Prove or disprove

Felix Fitzgerald 2022-08-22

Simplify as much as possible.
$u^{2} \sqrt{24 u w^{2}} - 6 w \sqrt{6 u^{5}}$
Assume that all variables represent positive real numbers.

Felix Fitzgerald 2022-08-22

What mistake have I committed in doing these steps to find the limit: $lim_{x \to 0} \frac{\cos x - 1}{x^{2}}$ ?

MOHAMMED ABDUL RAZAK2022-08-21

Y'+y^2=25 solve for general solution
Find the order of the differential equation
Find whether the differential equation is linear or not linear

Loldi9s 2022-08-21

Differentiate
$x^{2} \ln (1 + x^{2})$
I simplified it till -
$2 x^{2} \ln (x)$
Then I differentiate -
$2 x^{2} (\frac{1}{x} (\frac{d}{d x} x) + \ln x (4 x)$
$\frac{2 x^{2}}{x} + 4 x \ln x$
Where have I gone wrong ? Because the answer I am trying to achieve is
$\frac{2 x^{3}}{1 + x^{2}} + 2 x \ln (1 + x^{2})$

Macy Villanueva 2022-08-20

I have the following limit:
$lim_{x \to + \infty} \frac{\log (e^{2 x + 1} + x)}{x} = 2$
I know for sure that
$lim_{x \to + \infty} \frac{\log x}{x} = 0$
Because x grows a lot faster than $\log x$ . Then why wouldn't the first limit be equal to 0 as well?

cronaficsiiilm 2022-08-20

Prove that: $\ln (e^{x + y} + 1)$
is a convex function.
I have tried to used $F \circ G$ , while
$F = \ln (t + 1)$ and $G = e^{x + y}$
G is convex but I need to prove that F is convex and growing, which I do not get.

slawejagdw 2022-08-20

Prove that lim x tends to $0 x^{4} \frac{\cos 2}{x} = 0$

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