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3 years ago

Find the horizontal and vertical asymptotes of the curve. y = 9ex ex − 2

Mathematics

1 answer:

JulsSmile [24]3 years ago

4 0

There are no vertical or horizontal asymptotes. the graph is a parabola

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EXAMPLE 5 If F(x, y, z) = 4y2i + (8xy + 4e4z)j + 16ye4zk, find a function f such that ∇f = F. SOLUTION If there is such a functi

Valentin [98]

If there is such a scalar function f, then

$\dfrac{\partial f}{\partial x}=4y^2$

$\dfrac{\partial f}{\partial y}=8xy+4e^{4z}$

$\dfrac{\partial f}{\partial z}=16ye^{4z}$

Integrate both sides of the first equation with respect to x :

$f(x,y,z)=4xy^2+g(y,z)$

Differentiate both sides with respect to y :

$\dfrac{\partial f}{\partial y}=8xy+4e^{4z}=8xy+\dfrac{\partial g}{\partial y}$

$\implies\dfrac{\partial g}{\partial y}=4e^{4z}$

Integrate both sides with respect to y :

$g(y,z)=4ye^{4z}+h(z)$

Plug this into the equation above with f , then differentiate both sides with respect to z :

$f(x,y,z)=4xy^2+4ye^{4z}+h(z)$

$\dfrac{\partial f}{\partial z}=16ye^{4z}=16ye^{4z}+\dfrac{\mathrm dh}{\mathrm dz}$

$\implies\dfrac{\mathrm dh}{\mathrm dz}=0$

Integrate both sides with respect to z :

$h(z)=C$

So we end up with

$\boxed{f(x,y,z)=4xy^2+4ye^{4z}+C}$

7 0

2 years ago

While reviewing his budget, Andre calculated his variable and total expenses for last month: variable expenses: $2,863.09 total

Elenna [48]

Answer:

Fixed expenses = 1767.07

Step-by-step explanation:

Andre calculated his variable and total expenses for last month.

His variable expenses is $2,863.09

His total expenses is $4,630.16

Now, Total expenses = Variable expenses + Fixed expenses

So, Fixed expenses = Total expenses - Variable expenses

⇒ F = T - V

⇒ F = 4630.16 - 2863.09

⇒ F = 1767.07

So, this the equation to represent Andre's fixed income. (Answer)

7 0

2 years ago

Read 2 more answers

Which expression is equivalent to -2(1 - 4n)?

padilas [110]

Answer:

-2+8n

Step-by-step explanation:

we can distribute the -2 inside the parentheses to find an equivalent expression.

-2(1-4n)

(-2)(1)+(-2)(-4n)

-2+8n

there's your answer!

7 0

2 years ago

Help pls quickly. It is very long for me to type sorry :(

Olin [163]

Answer:

s. o. r. r. y. f. o. r. w. h. a. t

6 0

2 years ago

Read 2 more answers

I need help asappp!!!

arlik [135]

Answer:

the first blank is corresponding and the second blank is 105.

Step-by-step explanation:

Hope This Helps!!

(brainliest please if possible)

4 0

2 years ago