I have to check whether a graph is planar. The given type is $$ e ≤ 3v − 6 .$$ From Wikipedia: Note that these theorems provide necessary conditions for planarity that are not sufficient cond...

Feb 24, 2016 · Calculate E (X^3) and E (X^4) for X~N (0,1). I am having difficulty understanding how to calculate the expectation of those two. I intially would think you just calculate the $\int x^3e^\frac { …

Sep 7, 2016 · Given a random variable X ∼ N(0,σ2) X ∼ N (0, σ 2), how can we prove that E[X4] = 3σ4 E [X 4] = 3 σ 4? I am having trouble even starting with the proof.

Feb 3, 2016 · I have to evaluate the integral $\int_ {0}^ {\infty}t^3e^ {-3t}dt$ using complex analysis techniques (the laplace transform). Can you check my steps, please? $$\int_ {0}^ {\infty}t^3e^ {-3t}dt …

I need to find the value of $\displaystyle \int _0^ {2\pi}\sin^2 \left (\frac {-\pi} {6}+3e^ {it} \right)dt$. I figured I could use contour integration and the Cauchy-Goursat theorem to do so.

Aug 14, 2015 · A nice and quick way to visualize integration by parts (it could be a time-saver!): $$\matrix {&\text {differentiate}&&& &\text {integrate}&\\ &x^3&&&&e^x ...

Oct 4, 2013 · Geometric series: $$1+e^ {-x}+e^ {-2x}+\ldots=\sum_ {n=0}^\infty\left (e^ {-x}\right)^n=\frac1 {1-e^ {-x}}=\frac {e^x} {e^x-1}$$ as long as $\;e^ {-x}<1\iff e^x>1\iff ...

Mar 23, 2021 · I was going to do it the normal way such that it equals to $\cos (3e^ {\frac {i\pi} {3}})+i\sin (3e^ {\frac {i\pi} {3}})$, but its not working since I can't exponentially multiply it.

Nov 7, 2021 · Find the general solution to $xy' = 2y + x^3e^x$ Ask Question Asked 4 years, 2 months ago Modified 4 years, 2 months ago

Feb 21, 2023 · Evaluate: $\int\frac {3e^ {2x}-2e^x} {e^ {2x}+2e^x-8}dx$ Ask Question Asked 2 years, 10 months ago Modified 1 year, 2 months ago