### Questions (190)

 9 $f(x) \equiv 1$ mod $(x-1)$ and $f(x) \equiv 0$ mod $(x-3)$ then is there any $f(x)$? 7 $G$ is a group of order $60$. Will $G$ always contain a subgroup of order $6$? 7 $\int _0^\infty f(x)$ exists and $f(x)$ is differentiable then $\lim _{x \to \infty} f '(x)$ exists. Counter example of this statement. 7 If $\frac {a_{(n+1)} }{a_n} < \frac {n^2}{(n+1)^2}$ and if $a_n > 0$ for all n . $\sum a_n$ converges or not 7 If $f(x) =\frac{1}{3} ( \frac {5}{f(x+2)}+f(x+1))$ then $\underset{x \to \infty}{\lim}f(x) = ?$

### Reputation (2,846)

 +10 If $X$ and $Y$ are compact subsets of $\mathbb R^n$, then $X+Y$ is compact. +10 Is the set $\{AB-BA\colon A,B\text{ are } n\times n\text{ matrices}\}$ a subspace of all square matrices of order $n$? +18 The following set will be $G_\delta$ set. +10 the composite function $G(z) = g(2z−2+i)$ is analytic in the half plane $x>1$

 3 if $\int_{0}^{1}|f_n(x)-f(x)|dx\to 0$ then $f_n\to f$ uniformly on $[0,1]$: True/false 3 Sylvester's criteria and Negative definite Matrices. 2 Is “$S$ = {$x ∈ l_2$ | $x = (x_n)$, $x_n = 0$ for inﬁnitely many $n$} in $l_2$ ” Nowhere Dense? 1 Two methods are giving two different answers to the this differential equation : $\frac{dy}{dx}=\frac{1}{2} \frac{d(\sin ^{-1}(f(x))}{dx}$ 1 Finding Maximum area of the isosceles triangle

### Tags (120)

 3 real-analysis × 46 2 metric-spaces × 14 3 general-topology × 41 1 algebra-precalculus × 14 3 linear-algebra × 23 1 derivatives × 7 3 matrices × 10 1 ordinary-differential-equations × 6 3 quadratic-forms × 6 1 analytic-geometry × 4

### Bookmarks (36)

 11 The relationship between the eigenvalues of matrices $XY$ and $YX$ 10 find total number of maximal ideals in $\mathbb{Q}[x]/\langle x^4-1\rangle$. 9 Eigenvalues of $AB$ and $BA$ where $A$ and $B$ are square matrices 7 If $f(x) =\frac{1}{3} ( \frac {5}{f(x+2)}+f(x+1))$ then $\underset{x \to \infty}{\lim}f(x) = ?$ 7 $\int _0^\infty f(x)$ exists and $f(x)$ is differentiable then $\lim _{x \to \infty} f '(x)$ exists. Counter example of this statement.

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