How can I find the number of positive real roots in the equation $$x^6 - x - 1 =0$$ This question is given in my analysis book and I have no idea how to s...

I have a problem that asks Evaluate to five decimal places using the taylor series for the definite integral. $$\int_{1}^{2} \frac{e^x}{x} dx$$ I don'...

While doing research in electrical engineering, I derived the following integral representation of the Bessel function of the first kind: $$J_n(x)=\frac{e...

I believe I am misinterpreting the Taylor Remainder theorem somehow. The Taylor Remainder theorem is (taken from Briggs 3rd ed Calculus: Early Transcenden...

I am trying to find out how to solve $ax^2 - by^2 + cx - dy + e = 0$ to get integer solutions, failing this the rational solutions. Thanks!

I figured out how to calculate the area under the curve from the Right endpoint and Left endpoints, but I can't figure out how to calculate it using ...

In trying to write a nice proof of the derivatives of $\sin(x)$ and $\cos(x)$, I encountered a serious problem, namely that I have never seen a proper def...

Does someone have a solution for the following equation where the carrying capacity varies linearly with time (and only time): $$\frac{\mathrm dN}{\mathrm...

I'm trying to solve the third Project Euler problem and I'd like a little help understanding a mathematical concept underlying my tentative solu...

I need to find an expression that satisfies the qualifying conditions for a quintic polynomial. $f(0)=3$ and $f(-2)=f(\frac{1}{2})=f(1)=0$. With this info...