# Search results

1. ### I need series-us help: Sum_(n=0)^inf(.7^n + .8^n) = 25/3

Sum_(n=0)^inf(.7^n + .8^n) = 25/3 I had to look up the answer but I can't find how to get it myself. The book only gives me a/(1-r) but there isnt a consistent ratio between the terms. Sent from my LGLS755 using Tapatalk
2. ### lim [x->2^+] [8/(x^2 - 4) - x/(x - 2)]: tried multiplying common denom's, then....

I evaluated the limit by multiplying common denominators then distributed terms so I have polynomials on top and bottom. Then derived each separately and got -6x/6x=-1 but the limit is actually -3/2. What's up with that? . . . . .\displaystyle \lim_{x \rightarrow 2^+}\, \left(\dfrac{8}{x^2\...
3. ### Definite Integral: int[1,3][(x+1)/(x(x^2+1))]dx (I don't get correct value)

Ok so I evaluated the indefinite integral and got the right answer but when I plugged in the bounds, I got the wrong answer. Calculate the definite integral: . . . . .\displaystyle \int_1^3\, f(x)\, dx\, =\, F(x)\, =\, \int_1^3\, \dfrac{x\, +\, 1}{x\, (x^2\, +\, 1)}\, dx Computed by Maxima...
4. ### The god equation

What's the big deal with e^(ipi)+1=0? Like it's the 5 most common constants in math, shouldn't we expect the 5 most common ones to show up together? The fact that it has addition, multiplication, and exponentiation is impressive though. Sent from my LGLS755 using Tapatalk

Ok so from y=e^(-x^2) to x=b is being revolved around the y axis and the resulting solid is 3/2 cubic units. I set up the shell method: 2pi int_0^b (x(e^(-x^2)))dx = 3/2 u=-x^2 du=-2xdx u at b = -b^3 u at 0 = 0 -pi int_0^(-b^2) (e^u) du = 3/2 -pi [e^(-b^2) - 1] = 3/2 e^(-b^2) - 1 = (-3/2pi)...
6. ### I don't remember how i did this: "Find fluid force on vertical side of tank where..."

I don't remember how i did this: "Find fluid force on vertical side of tank where..." Find the fluid force on the vertical side of the tank, where the dimensions are given in feet. Assume that the tank is full of water. (The weight-density of water is 62.4 pounds per cubic foot.) So F = (w)...
7. ### Find b s.t. y=b divides area between y=25-x^2, y=0 into 2 equal halves

1. LarCalcET6 7.1.069. Find b such that the line y = b divides the region bounded by the graphs of y = 25 - x2 and y = 0 into two regions of equal area. I got: . . . . .\displaystyle \int_0^5\, (25\, -\, x^2)\, dx\, =\, \dfrac{250}{3} Then tried to find: . . . . .\displaystyle \int_0^b\...
8. ### Probably right for the wrong reason: complete square for -x^2 - 12x

1. LarCalcET6 5.8.037. Find or evaluate the integral by completing the square: . . . . .\displaystyle \int\, \dfrac{1}{\sqrt{\strut -x^2\, -\, 12x\,}}\, dx So when I did complete the square I did -x^2 -12x = -(x^2 + 12x) = -(x^2 +12x +36) - 36 = -36 - (x + 6)^2 I didn't know what to do...
9. ### Find diameter of hole with quarter volume of whole shape.

The region bound by y=(1/8)x^2 and the y axis is rotated about the line y=8 A hole is drilled that takes up 1/4th the volume of the original volume, find the diameter to 3 decimal places. 2pi Int_0^8(8x - (x^3)/8)dx ... =256pi Dividing by 4 yields 64pi 64pi = 2pi Int_0^z(8x - (x^3)/8)dx 32 =...