# calculus

1. ### Classic bath tub differential problem

[LEFT] Hi guys can anyone help with this problem I found this problem in my applied math textbook? A tank has diameter 5m and a hole of diameter 0.1m at the base. When the hole is uncovered the depth of the water is 2m. (assume this follows Torricelli's law and g=9.81m/s2) form a...
2. ### need someone to solve this question

2yy' +3 = y^2 + 3x with initial value y(0) = 8
3. ### I need some help with this bernoulli's equation that is given in my assignment

solve y′−6y/x=y^5/x^13 i have tried again and again but my answer is still wrong. can someone show me the steps to solving this question? solve y′−6y/x=y^5/x^13 i have tried again and again but my answer is still wrong. can someone show me the steps to solving this question?
4. ### Need help finding the maximum of an equation

Hi, I need someone to help me point to the right direction in solving the following problem: Find the maximum of y = -4x3 - 27x2 + 5x +45 in the range -6 <= x <= 5 I believe this is a cubic equation and I would like to solve this problem without derivative if possible, if so, could you point...
5. ### Integral of (cosx+sinx)^2dx

I did this but not sure if it is correct: ∫(cosx+sinx)^2dx= ∫(cos^2x+2cosxsinx+sin^2x)= ∫(2cosxsinx)= 2∫cosxsinx= 2sinx-cosx+C <--------End
6. ### Simplifying derivative part 2

Hi, I'm significantly confused about the steps that brought line 1 to line 2 of the expression below: Can someone please provide the in-between steps? Reallly appreciate it.
7. ### Simplifying derivative

Hi, So I've been analyzing the following steps in this algebraic expression for quite some time now: Could someone please provide the in-between steps for how the first line led to the second line? Really appreciate help.
8. ### Finding derivative example

Hi, I hope someone can help. I'm trying to find the derivative at x = 4 for the following equation: For some reason, I get the wrong solution when I don't factor out the expression before finding the derivative: The actual solution for f^1(4) is apparently 12: Help would be very much...
9. ### Integral of 1/(1-x)

Yeah so basically we all know that the integral of 1/(1-x) is -ln(1-x)+c, but if I factor out -1 from the denominator before integration I seem to get -ln(x-1)+c. Can someone explain where the mistake is?
10. ### Volume of a Wine Glass

Design a wine glass that may have a flat base, solid stem and curved shape defined by the function y = Square root of x. The glass must hold 100mL. set the dimensions of the glass and confirm that it will hold 100ml. Use calculus to calculate the volume of the glass itself if it has to be...
11. ### Finding the volume of an ellipse watermelon

An ellipse watermelon has a major axis 28cm and minor axis 25cm. The equation of the ellipse is y = 12.5 - 12.5x/145 Find the volume using calculusJust wondering if anyone can help me out on this question! I'm not quite sure how to answer it as I keep getting an abnormally large number.Thanks!
12. ### Guidance regarding integration

Before learning Integration in calculus we should know Trignometry and inverse Trignometry forumulas . If a student is through with formulas can he solve Integration Problem fast.
13. ### a point of inflection

Question, I am learning how to sketch gradient function using the given features of the function y = f(x). The question in the book asked to sketch the gradient function of y=f(x) I was able to sketch it ( y=f'(x)), but the question got me thinking that if a y=f(x) has a point of inflection at...
14. ### The dimensions of the largest-volume rectangular box

What are the dimensions of the largest-volume rectangular box, with a square base and an open top , that can be made from 10 000 cm^2 of materials ?
15. ### Liquid Pressure and Fluid Force

I am so lost right now, can you explain the formula and the step by step solution
16. ### rregarding studying

how to read textbook of math while studying
17. ### Equations of a line through a point, intersects z axis, and parallel to a plane

A question on my review guide asks for me to find the parametric equations of the line through the point (3,6,4) that intersects the z-axis and is parallel to the plane x − 3y + 5z = 6 . The answer should be (x = 3t + 3, y = 6t + 6 z = 3t + 4) Any help is appreciated!
18. ### Conformal Mapping Complex Analysis

Hello everyone, I am really struggling on these 3 questions. I have attached both the question and the answer. I am reviewing for my final exam, so could someone please just explain to me the detailed process to arrive at the answer, as I am really just trying to understand the concepts for...
19. ### Related Rates with Spheres

Here's the question I have: The radius of a sphere is increasing at a constant rate of 2cm/sec. At the instant when the volume of the sphere is increasing at 32pi cm^3/sec, the surface area of the sphere is A) 8pi B) 32pi/3 C) 16pi D) 64pi E) 256pi/3 So far I have dr/dt=2, and when dv/dt=32...
20. ### What I have to do first, to take the derivative of this function?

Given f(x) = x^2 - 2x and g(x) = 3*(f(x)), What is the derivative of g(x)? I want to know, if I have to multiply 3 by f(x) and then use the Power Rule, or if I need to substitute the f(x) and the use the Produc Rule? Please dont give the solution!