### Questions (18)

 8 $\lim\limits_{x\to 0} \frac{\tan x - \sin x}{x^3}$? 2 What is the dimension of the given vector space? 2 Is $\langle\mathbb R^*,*\rangle$ a group ($\mathbb R^* =\mathbb R\setminus\{0\}$), where $*$ is defined as $a*b = |a| b$? 1 How to use Charpit's Method? 1 How is a polynomial ring in uncountably many unknowns with coefficients over a commutative ring R defined?

### Reputation (305)

 +10 How to use Charpit's Method? +20 What is the dimension of the given vector space? +10 How is a polynomial ring in uncountably many unknowns with coefficients over a commutative ring R defined? +10 $x^2f''(x)+xf'(x)+y=x^2+1$, $x>0$, $f(0)=f'(0)=0$. Find $f(x)$.

### Tags (29)

 0 calculus × 3 0 vectors × 2 0 abstract-algebra × 2 0 probability-distributions 0 group-theory × 2 0 proof-verification 0 limits × 2 0 real-analysis 0 polynomials × 2 0 ring-theory

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