Detailed Explanations for Calculus 2 Equations

What is the average value of a function $f (x) = 3 x^{2} - 2$ on the interval [0,2]?

Summer Bradford 2022-06-16

How do you find the volume of the region enclosed by the curves y=x, y=-x, and x=1 rotated about y=-1?

anginih86 2022-06-16

What is the average value of a function $y = 7 \sin x$ on the interval $[0, π]$ ?

Dwllane4 2022-06-16

The following claim seems true for me:

For any continuous function over reals $f (\vec{x})$ , if $f (\vec{x}) = c$ has no zero, then either $f (\vec{x}) > c$ for all $\vec{x}$ or $f (\vec{x}) < c$ for all $\vec{x}$ .

However, my calculus is a bit rusty, and I am wondering from which this claim follows? (For univariate functions, this follows from the intermediate value theorem?)

Boilanubjaini8f 2022-06-16

Just as the topic ask how to evaluate
$\sum_{k = 1}^{\infty} \frac{(18) [(k - 1)!]^{2}}{(2 k)!} .$

Carolyn Beck 2022-06-16

How would you compute the following series? I'm interested in some easy approaches that would allow me to work it out.
$\sum_{n = 1}^{\infty} \frac{4^{n} n!}{(2 n)!}$

Feinsn 2022-06-16

Find $lim_{n \to \infty} \sum_{p = 0}^{k n} f (\frac{1}{n + p})$

George Bray 2022-06-16

Can someone help me in proving the following:
$\frac{π}{2} = \sum_{l = 0}^{\infty} \frac{(- 1)^{l}}{2 l + 1} (P_{2 l} (x) + sgn (x) \cdot P_{2 l + 1} (x)),$

Roland Manning 2022-06-16

Does there exist an explicit expression for
$\sum_{k = 0}^{\infty} \frac{{(- 1)}^{k} e^{- λ {(2 k + 1)}^{2}}}{{(2 k + 1)}^{3}},$
where $λ$ is a positive scalar?

Dindo Yapyapan2022-06-16

(x + 3y)dx - xdy =0

Jasmin Pineda 2022-06-15

Find:
$lim_{n \to \infty} [n + n^{2} \log (\frac{n}{n + 1})] = \frac{1}{2}$

Eden Solomon 2022-06-15

Find $\frac{1 \cdot 2}{3!} + \frac{2 \cdot 2^{2}}{4!} + \frac{3 \cdot 2^{3}}{5!} + \frac{4 \cdot 2^{4}}{6!} + \dots$ up to n terms?

Bailee Short 2022-06-15

let $f$ defined and continuous function in $[a, b]$ with $[a, b] \subseteq f ([a, b])$ .Prove that $f (x) = x$ admits at least one solution in $[a, b]$

I am not sure how to deal with this theorem so I have no idea where to start. if someone could walk me through the process that would be great.

Gabriella Sellers 2022-06-15

Is there a $p$ -adic analogue to the intermediate value theorem? I know there is a notion of convex sets in the $p$ -adic context but can we hope for an intermediate value theorem in this context?

Feinsn 2022-06-15

How to use $3 \tan^{2} x = - 3 + 3 \sec^{2} x$ to integrate $3 \tan^{2} x$ ?

dourtuntellorvl 2022-06-15

If i have 2 functions f and g, both with the domain [a,b] interval. Where both are continuous. Also, f(a)>g(a) and f(b)<g(b), how would i use intermediate value theorem to show there exists a c in [a,b] for the fucntion h(x)=f-g such that f(c)=g(c)

Yahir Crane 2022-06-14

How do you find the average value of the function for $f (x) = 2 - \frac{1}{2} x, 0 \leq x \leq 4$ ?

crossoverman9b 2022-06-14

What is the arc length of $f (x) = e^{3 x} + x^{2} e^{x}$ on $x \in [1, 2]$ ?

Jamiya Weber 2022-06-14

How do you find the length of a curve defined parametrically?

Gybrisysmemiau7 2022-06-14

I need help please with the following question. (Do I need to use radians in dealing with the sin part?))
(a) Use the Intermediate Value Theorem to show that the equation $x + \sin (x) = 1$ , has at least one solution in the interval [0,1].
(b) Find an approximation of the solution with an error of at most 0.05.

When you are dealing with any Calculus 2 homework, it is vital to have a look at the various questions and answers that will help you see whether you are correct in your approach to finding solutions. Even if you are dealing with analytical aspects of Calculus 2, it will be helpful as you are looking at provided equations and learn how the answers relate to original questions and problems specified.

Do not be afraid to take a look at the basic integration and related application if Calculus 2 does not sound clear or start with the Calculus 1 first.

Calculus 2

Calculus 2 Equations: Expert Solutions and More