# calculus

1. ### Calculus Quiz Problems

Determine the area of the region enclosed by the graphs of f(x) = x^2 + x +5, g(x) = 3x +13, and the vertical line x = 0 I got 26.67 but he gave me zero points for it so idk. Set up (but do not evaluate) an integral that will give the area of the surface generated when y= x^3/8 is revolved...
2. ### Help with functions on intervals in TI Nspire CX CAS

Hello everyone. I have the TI-nspire CX CAS and I need some help plugging in numbers. I was wondering how to solve the function "0=x(sin(x))-(cos(x)" on the interval [0,4]. I need to find the precise points, not a graphical analysis. I can't seem to find any button that allows me to specify an...
3. ### Find the slope of the tangent line on f at x=1

So I'm studying for my first calculus exam, and this problem has me stumped for hours now. I've used the formula of lim h-->0 f(x+h)-f(x) / h It becomes so complicated and confusing as I try to multiply by the conjugate to remove the radicals in the numerator, it just never simplifies to a...
4. ### Understanding what is meant by the Taylor Series polynomial problem listed

I need help understanding the wording of this problem. I think it wants me to write a Taylor Series polynomial for the arctanx....then im not really sure even where to go after that. With writing the polynomial...what does all the p(j) f(j) stuff getting at? Give the unique polynomail p of...
5. ### Calculus Old Quiz Problems Help

1. Let R be the region bounded by the graphs of y= sinx and y = 1 - sinx on (pi/6, 5pi/6) Use the washer or disk method to set up (but do not evaluate) an integral that will determine the volume of the solid obtained by revolving R about the line y=3 2. Use calculus determine volume of the...

I would like to know whether I am correct in my thinking below. You can add two vectors using basic arithmetic only when either two cases occur: (1) the vectors are parallel to each other (2) the vectors direction are opposite of each other (in which case, you could multiply one of the...
7. ### Surface Area of a Regular Tetrahedron

How to find the surface area of a regular tetrahedron using calculus? The surface area should be √3 a^2. I tried to do the same approach that MarkFL did for the volume but I could not figure out how to do it with the area!
8. ### Regular Tetrahedron

How to find the volume of a regular tetrahedron using calculus? V = ∫ dV = ∫∫∫ dx dy dz This is what I did first I was thinking to take a cross-sectional equilateral triangle and integrate it from 0 to h, but I could not figure out how to do that. Instead I integrated each variable as...
9. ### Volume of Hexagonal Pyramid - Using Integration from (0-h)

The Question: By using Riemann’s sum, synthesise a mathematical model for finding the exact volume of any ‘tepee’ tent of side s and height h. Here's what I have so far However, I am currently unsure if I am heading in the right direction, and am stuck at what comes next. Any help would be...
10. ### Need help with this

How can i possibly approach this? Thanks in advance.
11. ### Need help with polar form

For example let's take - 1 + sqrt(3) i I want t change the above expression into polar form. I know how to change it to polar form in the form of r*cis(thetha) I know how to get r and thetha, but my issue lies with getting the exact thetha value (meaning I want the answer in a fraction...
12. ### Help with a Derivative question that involves Sin

Hey i have this question given to me by teacher that i just cant wrap my head around i know the derivative of sin(x) is cos(x) but the way its done confuses me here's the question: The self induced e.m.f (measured in volts, V) in an inductor can be found by using: e= L V, where L is the...
13. ### How to solve this integral using substitution?

$$int{(x-(\sqrt{x}-5)^2)^2} dx$$ I find the answer using expansion. How to solve it using substitution?
14. ### DE help

how to solve (1+x^2)y'+y^2+1=0? what I come up with is arctany=-arctanx-C then how can i proceed?
15. ### Intermediate Value Theorem

Let f: [0, +oo] of all real numbers be differentiable with f(0)=A>0 and f'(x)<= 0 for all x>0 (a) show that there exists some c of (0, +oo) such that f(c)=c (b) show that there is only one such c (Note: These facts are obviously intuitively, as you can see be drawing a graph showing the curve...
16. ### Deriv of an Integral

Let F(x) = integral from x^2 to x^3 of sin (t^2) dt. What is F'(x)? (This problem cannot be addressed by trying to work the integral.)
17. ### Illumination Optimization Problem

Optics tells us that for any light illuminating with strength s, and for any point located distance d away from the light source, the intensity of illumination at the point is s/d^2. Now let two light sources be placed one unit apart. The first one illuminates with strength a, the second with...
18. ### Help with and improper integral!

I need help to figure out how can i resolve this improper integral, i don't know what to do with the absolute value: ∞ ∫e^(-lyl) <--- Where lyl is the absolute value of "y", and evaluated from -∞ to ∞ -∞ There is also a photo attached of the integral. Thanks!
19. ### Want help in solving this Diferrential equation by variable separable method!

How can I solve this euqation by variable separable ? I know after separating variable it will be solved by partial fraction by I stuck at the values of A and B on the side of y! dy/dx = (y3 + 2y) / (x2 ​+ 3x )
20. ### Why is that we use the boundaries from -1 to 1 instead of 0 to 1?

The given curve is rotated about the y-axis. Find the area of the resulting surface. $\sqrt[3]{x^2}+\sqrt[3]{y^2}=1 , 0\leq y \leq1$ We set up the surface area integral: \int_{-1}^{1} 2\pi x ds I understand how to find the arc-length(ds) and set up the integral but why...