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a) Rewrite as an exponential equation.
$\ln 8 = y$
b) Rewrite as a logarithmic equation
$e^{x} = 2$

Mariyah Bell 2022-10-28

A proof of why y=mx grows faster than $y = \ln x$ for all $m \neq 0$
How do I prove that the linear function y=mx grows faster than the logarithmic function?

Chloe Arnold 2022-10-28

I was doing a integral, the last part is
$\int_{0}^{\frac{π}{2}} x^{3} \csc x d x$

Brianna Schmidt 2022-10-28

Let $A ⊊ R^{n}$ ( A is compact). Consider $f : R^{n} \to R_{+}^{n} \cup {0}$ is continuous map. Suppose that for all $a \in A$ , $α \mapsto f (α)$ is concave positive function.

Evelyn Freeman 2022-10-28

Is there any function $f : R^{+} \to R^{+}$ satisfying the following conditions?:
the sequence $f (n)$ is convergent;
$\log f$ is eventually monotone (i.e., it is monotone from a number on);
$\log f$ is not eventually convex or concave.
If yes, is there a (big) class of such functions (with various properties)?

shiya43 2022-10-28

How to prove that there exist a concave function and $γ \in [0, 1]$ and some other numbers which satisfy an inequality

Emmy Swanson 2022-10-28

How can a quasi-convex function be concave?

omgespit9q 2022-10-28

Find the domain of the logarithmic function: $f (x) = \ln (x^{2} - x - 2)$

Juan Leonard 2022-10-28

How do I determine that this series $\sum_{n = 1}^{\infty} \log (1 + \frac{x}{n^{3}})$ converges pointwise for $- 1 < x < 1$ ?

omgespit9q 2022-10-27

How to transform a straight line into a curve. Linear to convex/concave function.
$f (x) = m x + b$

Oscar Burton 2022-10-27

How can I explain that this integral diverges?
$\int_{0}^{\infty} \frac{d x}{x \sin x}$

Madilyn Quinn 2022-10-27

Apply the inverse properties of logarithmic and exponential functions to simplify the expression.
$- 8 + e^{\ln (x^{5})}$

Tessa Peters 2022-10-27

We have been taught that linear functions, usually expressed in the form y=mx+b, when given a input of 0,1,2,3, etc..., you can get from one output to the next by adding some constant (in this case, 1).
$\begin{array}{cl} Input & Output \\ 0 & 1 \\ 1 & 2 \\ 2 & 3 \end{array}$
But with exponential functions (which are usually expressed in the form $y = a \cdot b^{x}$ ), instead of adding a constant, you multiply by a constant. (In this case, 2)
$\begin{array}{cl} Input & Output \\ 0 & 1 \\ 1 & 2 \\ 2 & 4 \\ 3 & 8 \end{array}$
We can keep going, can't we?
$\begin{array}{cl} Input & Output \\ 0 & 1 \\ 1 & 2 \\ 2 & 4 \\ 3 & 16 \\ 4 & 256 \end{array}$

Emilio Calhoun 2022-10-27

Show that
$\int_{\ln \frac{3}{2}}^{\ln 2} \frac{e^{x} + e^{- x}}{e^{x} - e^{- x}} d x = \ln \frac{9}{5}$
How would you integrate this logarithmic function in order to obtain $\ln (\frac{9}{5})$

Lilah Hurst 2022-10-26

Is the following function concave?
$f (x) := min_{b \in B} D (x, b)$

Krish Logan 2022-10-26

Let $f$ be a concave function (and differentiable). Show that
$\frac{f (y) - f (x)}{y - x} \geq f^{'} (y)$
where $y > x$ .

Keyla Koch 2022-10-26

In general, two concave functions intersect at at most two points. True or False?

robbbiehu 2022-10-26

For a concave function $f (x) \geq 0$ , N is a positive integer, then
$\frac{1}{N + 1} \sum_{n = 0}^{N} \frac{f (n)}{f (N)}$
increases in $N$ .Let f:R2→R be a continuos concave function which is continuously differentiable in the first variable. Is it true that

Seth Burghard2022-10-25

A piece of wire 10 m long is cut into two pieces. one piece is bent into a square and the other is bent into a circle
How should the wire be cut so that the total area enclosed is (a) a maximum? (b) A minimum?

Eliza Gregory 2022-10-25

Let $h$ be a convex decreasing function and $g$ a convex function. Is it true that $h (g (x))$ is a quasi-concave function?

The majority of Calculus 1 questions and answers that you will find below should be sufficient for understanding the basic rules that are necessary for problem-solving purposes. Take a look at the original answers, seek math assignment help, and compare them to what you have for your assignment.

If you need any other kind of help for your Calculus 1 tasks, combine several solutions or look at the problem that seems similar to your original assignment. If Math is not your subject per se, start with the most basic problems and proceed with the complex ones.

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