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Using antiderivatives to find velocity given acceleration with a domain
If the acceleration is:
$a = 9 - 0.9 t$ if $0 \leq t \leq 10$
$a = 0$ if $t > 10$
Which function of a do I use to find the velocity? On my attempt, I had two separate antiderivatives (one for each domain), but it did not get me the correct answer.

Kapalci 2022-06-22

Let a and b be positive reals. Show that
$lim_{n \to \infty} {(\frac{a^{\frac{1}{n}} + b^{\frac{1}{n}}}{2})}^{n} = \sqrt{a b}$

protestommb 2022-06-22

How to find instantaneous rate of change for $f (x) = \frac{3}{x}$ when x=2?

Summer Bradford 2022-06-22

Why can't you find all antiderivatives by integrating a power series?
if $f (x) = \sum_{n = 0}^{\infty} \frac{f^{(n)} (0)}{n!} x^{n}$ why can't you do the following to find a general solution
$F (x) \equiv \int f (x) d x$
$F (x) = \int (\sum_{n = 0}^{\infty} \frac{f^{(n)} (0)}{n!} x^{n}) d x = \sum_{n = 0}^{\infty} \frac{f^{(n)} (0)}{n!} (\int x^{n} d x) = \sum_{n = 0}^{\infty} \frac{f^{(n)} (0)}{n!} (\frac{x^{n + 1}}{n + 1}) = \sum_{n = 0}^{\infty} \frac{f^{(n)} (0)}{(n + 1)!} x^{n + 1}$
I was wondering about this because I tried this approach to finding the antiderivative $\int e^{x^{2}} d x$

Boilanubjaini8f 2022-06-22

How do you find the instantaneous slope of $y = \frac{1}{x}$ at x=4?

Mara Cook 2022-06-22

I have a concrete example thou:
$lim_{x \to 0^{+}} x {(1 + \frac{4}{x^{2}})}^{\frac{1}{2}}$

Gøvîñd Kûmär Sàmirêddy2022-06-21

Peyton Velez 2022-06-21

Suppose I have the limit:
$lim_{t \to 0^{+}} \int_{0}^{\sqrt{\sqrt{t} + 4}} \sqrt{1 + \frac{t}{4 \sqrt{x}}} d x$

Zion Wheeler 2022-06-21

Explanation how it can be that $f^{'} (x) = g (x)$ but wolfram alpha says $\int g (x) \neq f (x)$ ?
I've just started learning about antiderivatives/primitive functions/indefinite integrals, and I have the functions
$f (x) = 3 \ln ((\frac{x + 2}{3})^{2} + 1)$
$g (x) = \frac{2 \frac{x + 2}{3}}{(\frac{x + 2}{3})^{2} + 1}$
I came to the conclusion that $f^{'} (x) = g (x)$ so that $\int g (x) = f (x)$ and I wanted to check with wolfram alpha, but wolfram says that $\int g (x) \neq f (x)$ even though it says $f^{'} (x) = g (x)$ .
It seems to me that this violates the definition of antiderivative?

mravinjakag 2022-06-21

Antiderivative of $\sin (\frac{1}{x})$
I have to find the values of parameter a so the function
$f : R \to R, f (x) = {\begin{cases} \sin \frac{1}{x} & for x \in R ∖ {0} \\ a & for x = 0 . \end{cases}$
has an antiderivative on $R$ . I know that $lim_{x \to 0} \sin \frac{1}{x}$ does not exist in $x = 0$ . I have found that the answer is $a = 0$ but i can't explain it.

Tristian Velazquez 2022-06-21

Compute $I_{n} = lim_{n \to \infty} \sqrt{n} \int_{0}^{\frac{π}{2}} \sin^{n} x d x$

Emmy Knox 2022-06-21

If I have a list of data points and i would like to build some sort of model based on this data which is the most appropriate? And then of the choice selected, how do i select among the most many different methods of either approximation or interpolation.

juanberrio8a 2022-06-21

The problem is the integral of
$\int \frac{- 8 x}{x^{4} - a^{4}} d x$

Sonia Gay 2022-06-21

How to find instantaneous rate of change for $f (x) = x^{3}$ when x=2?

Gaaljh 2022-06-21

Finding f with the given information, antiderivatives?
Find f.
$f^{″} (t) = 3 / \sqrt{t}$
$f (4) = 12$
$f^{'} (4) = 5$
I'm not quite sure how I am supposed to find f with this information.

misurrosne 2022-06-21

How do you find the instantaneous rate of change of the function $y = 5 x - x^{2}$ when x=-2?

Trizzie Kyrene Alves2022-06-21

find the equation of the tangent line to y^3=x^2 if that is parallel to the line y=4x-1

Garrett Black 2022-06-20

Finding the limit for recurrence relation $x_{n + 1} = \sqrt{x_{n} + \frac{1}{4}} - \frac{1}{2}$

Sattelhofsk 2022-06-20

I have this complex limit which is rather difficult to solve.
$lim_{z ⟶ 3 i} \frac{z^{2} + 9}{z - 3 i}$

sedeln5w 2022-06-20

Antiderivative of a function
Prove or disprove that
$f (x) = {\begin{cases} \sin (\frac{1}{x}) & for x \neq 0 \\ \frac{1}{2} & for x = 0 \end{cases}$
has an antiderivative in $R$ .
This function satisfies the Darboux's property, but how to say definitely that admits an antiderivative?

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