Calculus problem help I have this problem as one of my homework problems, but this one is a little tricky, and I'm stuck. Any tips on how to set-up/solve? A bag of sand originally weighing 144 lb was lifted at a constant rate. As it rose, sand also leaked out at a con- stant rate. The sand was half gone by the time the bag had been lifted to 18 ft. How much work was done lifting the sand this far?
Calculus Finding dy/dx for y = integral [dt/(1+t^2)] b = 0, a = tanx There's t, x, and y? How am I supposed to find dy/dx? Help please.
Which integration method to use for this? I have to find the volume between x = -1; x = 1 The two functions are: y= x^2 y= 2-(x^2) I don't know if I'm supposed to use the disk method or washer method.
Math Can you simplify this? The following is inside of the SQRT symbol: 1+(x^2+2x+1-(4/(4x+4)^2)^2) Now obviously I have to the square root of that...but I'm stuck.... I can simply the expression of "x" into: (x+1)^2-(2/(4x+4))^2 Thus what's really inside the SQRT is 1+ (that above expression --- squared) Im stuck right now...and I need help. Any tips? Note: This is to find the arc length for a calc problem. I found the f '(x), which is the expression of x mentioned first, then i "simplified" it by factoring. And if you're wondering, the original f(x) was: (x^3)/3+x^2+x+(1/(4x+4))
How to write sigma/summation notation for the following: -(1/5)+(2/5)-(3/5)+(4/5)-(5/5) I know "k" starts at 1 and 5 is above the Sigma. I also know that the function is k/5, but i don't know how the alternating minus and plus signs...i don't know how that affects the overall notation. So I know roughly it should look like this: 5 [Capital Sigma] k/5 k=1 I'm missing the last piece. Can someone help me?