Homework Statement
Sorry I don't know how to use symbols on this site so bear with me:
the question is does the following series converge: sum of sin(1/n^2) where n goes from 1 to infinity
Homework Equations
Limit comparison test, maybe others
The Attempt at a Solution
Okay I think I got...
Okay this problem might be over my head. I've only just learned first order linear differential equations and solving them by separation of variables.
Is there any easier way to do this?
Homework Statement
Find the solution to (x+1)y' +2y -(x+1)^(5/2)=0
Homework Equations
Definiton of antiderivative
The Attempt at a Solution
I have been trying to manipulate this equation in every possible way so that I can get x on one side and y on the other. Ever attempt has...
Sorry one more question, how would you deal with finding the derivative if there was another function being multiplied by the integral?
For example, d(x^5 * integral of f(x) from x to x^2-x)/dx?
Do you use the product rule here or is there some other trick?
Homework Statement
I'm trying to solve a problem where you are asked to find the derivative of an integral where both limits of integrations contain variables
Homework Equations
Definition of integrals, derivatives
The Attempt at a Solution
For problems where you have an...
Homework Statement
The problem:
Find the derivative of
x2 multiplied by the integral of dt/(t-2t2) from x to -x2+2x
i.e, the function is x^2 times integral of [1/(t-2t^2)]dt from a to b with a being x and b being -x^2+2x
Homework Equations
Derivative and integral definitions
The Attempt...
Sorry i was given dy/dx and was asked to solve for y, i just replaced with with f(x) and dy/dx with f'(x). The solution was to separate the variables, I forgot all about it.
Homework Statement
f'(x)= x+1-yx-y
Solve for f(x)
Homework Equations
definitions of integrals and derivatives
The Attempt at a Solution
Okay, so I integrated both sides.
This gives f(x) = x^2/2 + x -integral(yx) - integral(y) +c
The problem I'm having is how do you...
Homework Statement
Graph x^(1/3) +x^(4/3)
Homework Equations
Limits, derivatives, etc.
The Attempt at a Solution
Hi guys, I was attempting this problem and then verifying it using a function grapher online. I noticed that all of the function graphers do not plot the function...
Oh is is actually this easy?
In that case, I would think since the numerator will always be positive regardless of which side the limit approaches from, and the denominator will switch signs depending on which side it approaches from, then the limit from the left will be -infinity and will be...
Homework Statement
Calculate the limit as x-->pi/4 of [tan(x-pi/4)+1]/x-pi/4
Homework Equations
lim h-->0 of [f(x+h)-f(x)]/h = f'(x)
lim x--->a [f(x)-f(a)]/(x-a) = f'(x)
The Attempt at a Solution
I've attempted to turn this equation into the form f(x)-f(a)/x-a by letting...
Homework Statement
Find derivative of x^(2/3) from first principles (i.e limit definition)
Homework Equations
lim h-->0 (f(x+h)-f(x)/h)
The Attempt at a Solution
[(x+h)^(2/3)-x^(2/3)]/h
I've tried multiplying the top and bottom by the conjugate, but I end up with the same...