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How do I find the following integral:
$\int_{0}^{1} x \sqrt{1 - x^{2}} d x$

Aryanna Fisher 2022-11-05

Given the equation $p = \frac{2 x}{y}$ , find $\frac{d y}{d t}$

klesstilne1 2022-11-05

How to do is bring the $sup$ onto the RHS, ie. to get
$G (θ x + (1 - θ) y) \geq θ G (x) + (1 - θ) G (y) .$

Hanna Webster 2022-11-05

Is the utility function $u (x) = x_{1} x_{2} + γ x_{2}$ concave or quasi-concave?

Yaretzi Mcconnell 2022-11-05

$f (x) = 2^{x}$
$g (x) = x^{2} + 3 x - 3$
For what positive integer values of x is f(x)>g(x)?
A) x<6 and x>1
B) x<2 and x>5
C) x<5 and x>2
D) x<1 and x>6

Rigoberto Drake 2022-11-05

Integrate $\int_{0}^{\infty} \frac{\sqrt{x}}{x^{2} + 1} d x$

Laila Murphy 2022-11-05

Do $lim_{x ↓ 0} f (x)$ and $lim_{x ↑ 1} f (x)$ exist if $f$ is concave over $[0, 1]$ ?

Jonas Huff 2022-11-05

Solve for x
$\log_{4} (x - 3) = 1 - \log_{4} (x - 6)$

Joglxym 2022-11-04

Use the properties of logarithms to write the logarithm in terms of $\log_{3} 5$ and $\log_{3} 7$
$\log_{3} \frac{45}{49}$

Brooke Richard 2022-11-04

Solve:
$\frac{d y}{d x} + 5 = 20, y (0) = 2$

Mark Rosales 2022-11-04

Solve each logarithmic equation.Express irrational solutions in exact form and as a decimal rounded to three decimal places.
$\log (2 x + 1) = 1 + \log (x - 2)$

Clara Dennis 2022-11-04

Im need in graphing this log function: y=log1/4∣∣x2−5x+6∣∣
I found the intervals: (−∞,2), (2,3), (3,∞)
Should I just give x values and find y to graph this or is there another way?

apopiw83 2022-11-04

Given the vector space, $C (- \infty, \infty)$ as the set of all continuous functions that are always continuous, is the set of all exponential functions, $U = {a^{x} ∣ a \geq 1}$ , a subspace of the given vector space?As far as I'm aware, proving a subspace of a given vector space only requires you to prove closure under addition and scalar multiplication, but I'm kind of at a loss as to how to do this with exponential functions (I'm sure it's way simpler than I'm making it).My argument so far is that the set U is a subset of the set of all differentiable functions, which itself is a subset of $C (- \infty, \infty)$ , but I doubt that argument would hold up on my test, given how we've tested for subspaces in class (with closure).

Owen Mathis 2022-11-04

Find the derivative $y_{x}^{'}$ (edit: $y_{x}^{'} = \frac{d y}{d x}$ ) from the equation
$y^{3} + x^{2} = x e^{y^{2}} - y \sin x$

Madison Costa 2022-11-04

Find x in the following logarithmic functions:
$a) \log_{10} x = 2 b) \log_{10} x = - 3 c) \log_{10} x = \frac{1}{2}$

Annie French 2022-11-04

Let $φ$ be a closed concave function, and $M = max_{x \in R^{d}} φ (x)$ . Let $D_{r} := {φ \geq r}$ be the level set. Then given $r \leq s \leq M$ ,
$λ_{d} (D_{s}) \geq (\frac{M - s}{M - r})^{d} λ_{d} (D_{r})$
where $λ_{d}$ is the Lebesgue measure on $R^{d}$ .

Lesly Arias2022-11-03

(Once you have their money, never give it back.) An apartment complex on Ferenginar with 250 units currently has 199 occupants. The current rent for a unit is 1592 slips of Gold-Pressed Latinum. The owner of the complex knows from experience that he loses one occupant every time he raises the rent by 4 slips of Latinum. Since "profit is its own reward", the owner wants to maximize his profit so he asks for our help, even though he knows that "free advice is seldom cheap".

What should be our recommendation for the optimal rent?

Lesly Arias2022-11-03

(Once you have their money, never give it back.) An apartment complex on Ferenginar with 250 units currently has 199 occupants. The current rent for a unit is 1592 slips of Gold-Pressed Latinum. The owner of the complex knows from experience that he loses one occupant every time he raises the rent by 4 slips of Latinum. Since "profit is its own reward", the owner wants to maximize his profit so he asks for our help, even though he knows that "free advice is seldom cheap".

What should be our recommendation for the optimal rent?

Aditya Bhandari2022-11-03

If f(x) = x ^ 2 and g(x) = x - 3 find the composite functions f o g and gof.

Barrett Osborn 2022-11-03

Clarification about the Antiderivative of $x^{- 1 / 3}$ .
In some textbook the antiderivative of $x^{- 1 / 3}$ is written as
$\int x^{- 1 / 3} d x = \frac{3}{2} x^{2 / 3} + C,$
where C is a constant. But should not the following function also be considered as an antiderivative of $x^{- 1 / 3}$ ?
$F (x) = {\begin{cases} \frac{3}{2} x^{2 / 3} + C_{0}, if x >0 \\ \frac{3}{2} x^{2 / 3} + C_{1}, if x <0 \end{cases}$
When $C_{0} \neq C_{1}$ , F(x) cannot be written as $\frac{3}{2} x^{2 / 3} + C$ .
Edit: I would like to clarify: which one of the following should be the correct answer to $\int x^{- 1 / 3} d x$ :
- $\frac{3}{2} x^{2 / 3} + C$
- or ${\begin{cases} \frac{3}{2} x^{2 / 3} + C_{0}, if x >0 \\ \frac{3}{2} x^{2 / 3} + C_{1}, if x <0 \end{cases} ?$

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