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!“Everything must be made as simple as possible. But not simpler.” ― Albert Einstein

# 208 Questions

 12 How to solve : $\,8^x=6x$ 12 Let $A$ and $B$ be $n \times n$ real matrices such that $AB=BA=0$ and $A+B$ is invertible 8 If $x \neq 0,y \neq 0,$ then $x^2+xy+y^2$ is … 6 Finding the number of symmetric,positive definite $10 \times 10$ matrices having… 6 Find the limit of $x_n = \prod_{j=2}^{n} \left(1 - \frac{2}{j(j+1)}\right)^2$

# 2,682 Reputation

 +10 Complex number ( equation) Find the number of solutions of $z^3+\overline{z}=0$ … +5 Let G be a group of order 60.Pick out the true statements: +10 If $\,x-\frac 1 x=k, \, k$ being any integer,then $\,\,x^5-\frac {1}{x^5}=?$ +5 If $n$ is a positive integer such that the sum of all positive integers $a$…

 10 $u_n=\frac {1}{1\cdot n}+\frac {1}{2(n-1)}+\ldots+\frac {1} {n \cdot 1}$,then $\lim u_n=?$ 10 Prove that $4x-x^4 \leq 3, x \in \Bbb R$ 7 $A$ and $B$ are different matrices satisfying $A^3=B^3$ and $A^2B=B^2A$ 4 Find all functions $f \colon \Bbb R \rightarrow \Bbb R$ that satisfy… 3 How to show the following infinite series is convergent

# 64 Tags

 16 linear-algebra × 40 7 real-analysis × 68 15 inequality × 5 4 algebra-precalculus × 16 13 sequences-and-series × 14 4 eigenvalues-eigenvectors × 6 11 matrices × 16 3 puzzle × 4 8 determinant × 3 2 calculus × 11

# 7 Accounts

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