# GaMbiT

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# 24 Questions

 3 Interesting Number Game 2 Using Monte Carlo method to estimate the value of $\int_0^1\int_0^1e^{xy} \ dx \ dy$ 2 Find the radius of convergence of the power series $J_{o}(x)= \sum_{n=0}^{\infty}\frac{(-1)^nx^{2n}}{2^{2n}(n!)^2}$ 2 Let $H$ be the subgroup of all rotations in $D_n$ and let $\phi$ be an automorphism of $D_n$. Prove $\phi(H) = H$. 1 Find the first-variational curve which corresponds to the functional $\int_{-1}^1 t^2 \dot{x}^2 dt$ when $x(-1) = -1$ and $x(1) = 1$.

# 120 Reputation

 +5 Find the first-variational curve which corresponds to the functional $\int_{-1}^1 t^2 \dot{x}^2 dt$ when $x(-1) = -1$ and $x(1) = 1$. +10 Does the chain rule apply in inverse function derivatives? +8 Solve for $\textbf{x}(t)$ from the system of differential equations $\textbf{x}' (t) = A \textbf{x}(t)$. +5 Find max rate of change of $f(x,y) = \sin(xy)$ at the point $(1,0)$ and in the direction in which it occurs.

 1 Does the chain rule apply in inverse function derivatives?

# 32 Tags

 1 derivatives 0 monte-carlo × 2 0 calculus × 6 0 limits × 2 0 elementary-number-theory × 5 0 multivariable-calculus × 2 0 differential-equations × 3 0 linear-algebra × 2 0 calculus-of-variations × 3 0 divisibility × 2

# 3 Accounts

 Mathematics 120 rep 8 TeX - LaTeX 6 rep 1 Cryptography 1 rep