calculus

  1. Z

    Partial Derivative Equation as solutions

    I have to solve PDE as ODE, but my lecturer didn't give me enough help and tutorial, to solve these problems. I searched YouTube and other websites to find a clue how to solve them but I find no clue. Please help! The problems are: i have to solve PDE as ODE where u = u(x,y) u_y + u = e^{xy}...
  2. N

    Optimal distribution?

    Suppose we have a young female population of 1 and the probability young females survive and reach older age (lets say >50) is 'k'. While young, females have a fertile potential of b1. While old, females have a fertile potential of b2. Thus lifetime fertile potential for females is 1*b1 +...
  3. A

    Can someone please help me find the limit to this math problem?

    Does anyone know how to find the limit of this problem? Your help would be much appreciated!
  4. S

    Calculus word problem [am I solving this problem right so far?]

    Please check the image attached to see the problem and the work I completed. Thank you in advance!
  5. M

    U-subsitution

    Can someone please explain the u-substitution? I don't see a tan(x/2) anywhere in the integral expression.
  6. O

    Derivative of ln(-x)

    Can someone please explain to me why the derivative of ln(-x) is 1/x? Thanks!
  7. L

    An integral inequality

    I spent a day trying to prove this inequality, but I didn't finish it. Hopefully someone will prove it. f(x) and g(x) are monotonically increasing or decreasing simultaneously on [a,b].
  8. O

    Generating inverse

    Can someone help me find the inverse of $y = 7 + 5x^3 + x^7$? The fact that there is more than one variable to a unique power makes the inverse a little less obvious than usual.
  9. O

    Limit calculation

    In the image below, how am I applying the limit laws wrong? I know the correct solution is 5, but I get -1! The problem I am facing is something related to my usage of the product rule for limits.
  10. O

    Calculating derivative using formal definition tricky

    Can someone guide me in terms of finishing off the derivative computation that I have started below? Help is greatly appreciated!
  11. O

    Calculate derivative using formal definition

    I'm really hoping someone can help me calculate the derivative (using the formal definition) for the following function: Here is my attempted solutions but I know it is wrong: Can someone tell me what I am doing incorrectly?
  12. O

    Using formal definition of a limit

    Can someone help me complete the derivative computation below? I'm a bit stuck.
  13. J

    Series Convergence

    What are the values of k that make the series convergent?
  14. O

    Calculating limit of rational function

    For the question in the image, can someone please explain to me why we should interpret $\sqrt{x^2}$ as $|x|$?
  15. D

    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...
  16. M

    Minimum volume of empty space in container with water

    Volume of a container is $\frac{4 \pi}{3}$. Water can flow in and out of container.The volume of water in container is given by: $g(t), 0 \leq t \leq 4$, where $t$ is time in hours and $g(t)$ is measured in $m^3$. The rate of change of the volume of water in the container is: $g'(t)= 0.9 - 2.5...
  17. L

    How to solve improper integral ln(x) / (x^2 + 1)

    Hello, guys, I just want you to help me of finding the integral of \int_{0}^{1}\dfrac{\ln(x)}{x^2 + 1}\mathrm{d}x. I just know that is improper.
  18. L

    Calculus 3

    Curve \mathcal{K} is defined as an intersection of surfaces z^2 = 2x^2 + y^2 and z = x + 1. The curve's projection on plane z = 0 is positive oriented. Parametrise the curve \mathcal{K}. Find the Frenet-Serret basis of the curve \mathcal{K} at point A(2, 1, 3). Find the...
  19. K

    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...