# calc

1. ### Just need a little bit of help with these Calc questions-- integrals and volume

1) At a processing plant, over the course of an 8-hour day, workers move material into a pile, which is removed at a constant rate by a conveyor belt. The workers move material into the pile at rate 200e−0.5t units/hr while the conveyor belt removes the material at 50 units/hr. (a) Find the net...
2. ### Integrals and Derivatives

(a) Integral from pi/6 to pi/4 of tan(x)e^(sec(x))sec(x)dx (b) integral from x=0 to ln(2) of (e^2x)/(1+e^x)dx (c) antiderivative of 1/(a+b sqrt(x))dx (d) antiderivative of (ln(x))^2 x
3. ### Pre Calc

Decompose v into two vectors v1 and v2, where v1 is parallel to w and v2 is orthogonal to work. V=i-4j , W=2i+j
4. ### Differential Calc

I'm having trouble getting started on the following problems. Any help to get me started would be appreciated. Find the slope and the equation of the tangent line to the graph of each function at the given value of x. g(x) = -x^5 + 4x^2 - 2x + 2 ; x = 2 The total cost to produce x...
5. ### [CALC 1]: Find a set of real numbers a, b, and c for which this piecewise-defined....

Find a set of real numbers a, b, and c for which this piecewise-defined function is (everywhere) differentiable: f(x)= tan-1x, x≤ 0 f(x)= ax2 + bx + c, 0 < x < 2 f(x)= x3- 1/4x2 + 5, x ≥ 2 so i plugged in x for the numbers and got: tan-1(0)= 0 a(0)2 + b(0) + c = 0 a(2)2 + b(2) + c= 4a+2b+0...
6. ### Calc III HW Help

I have to rewrite as a single integral and evaluate Any help would appreciated!! I'm close, but I don't have the right answer
7. ### Calc II Using Integrals to Find Work

I have a problem that I'm not sure how to figure out. It reads, "A tank in the shape of an inverted right circular cone has a height of 9 meters and a radius of 9 meters. It is filled with 5 meters of hot chocolate. Find the work required to empty the tank by pumping the hot chocolate over the...
8. ### Vector calc problem

Hi, I'm new here. I've been struggling with this problem for some time now and I'd really appreciate some help. It's from the book "Div, Grad, Curl and all that" by Schey. See attached image. In the text they define the curl as the limit of the (circulation)/(enclosed area) as the area...
9. ### Calc project

So I have this calc project that i need help with. Its ok if we receive help as long as we understand the problem so i decided to join this forum for help so here it is. You are a competitive bicyclist.During a race, you bike at a constant velocity of k meters per second. A car is waiting for...
10. ### Need a little help with calc homework online.

So, I've been trying to figure this out but I've already used up 3/5 tries for one answer and 2/5 on the other. I'll put the problems as they appear on the website. Consider the curve of the form y(t) = ksin(bt2). (a) Given that the first critical point of y(t) for positive t occurs at t = 1...

I am reviewing for a midterm and i am stuck on the problem that follows. Evaluate f(-3), f(0), f(2), for the piecewise defined function. Then sketch the graph of the function. f(x)= -1 if x</= 1 f(x)= 7-2(x) if x > 1 I plugged it all in and came up with up f(-3)=-1 f(0)= -1 f(2) = 7-2(2) =...
12. ### Pre Calc Help, Find all solutions in the form a+bi

Hey guys, so I got to my final question on my assignment and it is shown below. I am completely aware (Or I thought I was) of how to solve this problem, however this is through an online program and it has denied every form of my answer I have given. So maybe I have done something wrong so just...
13. ### Seek power series solutions of the given differential equation about the given point

I have been able to make the series and take the derivatives and substitute in . I also got x^n in all the series but I am having trouble making them like starting points so I can add them together. Please help
14. ### help with calc question

I have a question asking, Given two vectors U and V such that vec U * vec V = |vec U| |vec V|, explain what you know about the two vectors. I know the dot product equation is vec U * vec V = |vec U||vec V|cos theta. I know the cross product equation is vec U x vec V =...
15. ### Finding result of calc with upto 14 digits exponent

I want to know if I have 123 (base) ^ (raised to power) 14 digits exponent number, how can i do it? Currently mathematica is supporting only 9 digits in raised to power but i need calculation for raise to power 14. Is there any method or trick available to calculte such big calculation? If...
16. ### Finding the point of inflexion with no calc?

I'm stumped in this non calculator question. F(x) =e^cos(x) -π/2 to π/2 Show there is a point if inflexion between 0 and π/2, and find its coordinates. I got f''(x) = (sin^2(x)-cos(x))e^cos(x) but can't work it to a solution without a calculator... Help would be greatly appreciated/
17. ### Vector Calc - Divergence Theorem

If F(x,y,z) is continuous and |F(x,y,z)| ≤ 1/((x2 + y2 + z2)(3/2) +1) for all (x,y,z), show that R3∫∫∫del dot F dV = 0 My thought was to use a ball of radius r centered at the origin and apply the divergence theorem to it. So, let F = <x2, y2, z> and del dot F = 2x + 2y + 2z. I'm not really...
18. ### Vector Calc - Surface Area

Show that the surface area of the part of the sphere x^2+y^2+z^2=1 lying above the rectangle [-a,a]x[-a,a], where 2a2<1, in the xy-plane is: SA = 2 -a ∫a sin-1(a/sqrt(1-x^2))dx I tried setting it up so F = x2 + y2 + z2 = 1, and ∂z/∂x = -Fx/Fy so that SA = ∫∫ sqrt((-2x/2x)2 + (-2y/2z)2) dA, but...
19. ### Vector Calc - Prove/Disprove

Prove or disprove that if del dot F = 0 and del x F = 0 then F is a constant vector field. I know that F is a conservative vector field if del x F = 0, but beyond that, I'm really not sure how to approach this problem.
20. ### Application of extrema calc 3

A manufacturer makes two models of an item, standard and deluxe, which cost $40 dollars and$60 dollars to make, respectively, and which will be priced at $(40+x) and$(60+y). At these prices the manufacturer expects to sell 500(20+y-x) of the standard items and 500(10-2y+x) of the deluxe...