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3 years ago

NEED HELP ASAP 40 points!! <3 (will mark brainiest) as well :))

Mathematics

1 answer:

Marizza181 [45]3 years ago

3 0

Answer:

12a-2b4 is a binomial

Step-by-step explanation:

one monomial is 12a-2

and the two monomial is b4

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NEED HELP ASAP!! Use the function below to find F(3)

kvv77 [185]

It’s gonna be 1/125.

Since it’s F(3), you need to plug the 3 into the x. Then expand it into 1/5 times 1/5 times 1/5, which gets you 1/125

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3 years ago

For the function f(x) = 1/4e^-x + e^x, prove that the arc length on any interval has the same value as the area under the curve.

faltersainse [42]

Take an arbitrary interval [a, b], where a < b.

Compute the arc length L of y = f(x) over [a, b] :

$L=\displaystyle\int_a^b\sqrt{1+\left(f'(x)\right)^2}\,\mathrm dx$

Now comptue the area A under the curve y = f(x) over [a, b] :

$A=\displaystyle\int_a^bf(x)\,\mathrm dx$

We have

f (x) = 1/4 e ⁻ˣ + e ˣ → f ' (x) = -1/4 e ⁻ˣ + e ˣ

Then

√(1 + (f ' (x))²) = √(1 + (-1/4 e ⁻ˣ + e ˣ)²)

… = √(1 + 1/16 e ⁻²ˣ - 1/2 + e ²ˣ)

… = √(1/16 e ⁻²ˣ + 1/2 + e ²ˣ)

… = 1/4 √(e ⁻²ˣ + 8 + 16e ²ˣ)

… = 1/4 √((e ⁻ˣ + 4 e ˣ)²)

… = 1/4 (e ⁻ˣ + 4 e ˣ)

… = 1/4 e ⁻ˣ + e ˣ

… = f (x)

so both A = L for any choice of interval [a, b].

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3 years ago