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### Questions (217)

 17 Let $A$ and $B$ be $n \times n$ real matrices such that $AB=BA=0$ and $A+B$ is invertible 11 How to solve : $\,8^x=6x$ 8 The number of limit points of the set $\left\{\frac1p+\frac1q:p,q \in \Bbb N\right\}$ is which of the following: 8 If $x \neq 0,y \neq 0,$ then $x^2+xy+y^2$ is … 7 Let $f$ be a non-constant entire function such that $\left \lvert f(z) \right\lvert=1$ for every $z$ with $\left \lvert z \right\lvert=1$.

### Reputation (2,899)

 +3 How to find the area of the following isosceles triangle +20 Finding the number of symmetric, positive definite $10 \times 10$ matrices having… +5 Find the complete integral of $(p+q)(px+qy)=1$. +5 How to find the length of the shortest path?

 11 Prove that $4x-x^4 \leq 3, x \in \Bbb R$ 10 $u_n=\frac {1}{1\cdot n}+\frac {1}{2(n-1)}+\ldots+\frac {1} {n \cdot 1}$,then $\lim u_n=?$ 7 $A$ and $B$ are different matrices satisfying $A^3=B^3$ and $A^2B=B^2A$ 5 Finding the number of symmetric, positive definite $10 \times 10$ matrices having… 5 If $a_1,a_2,\dotsc,a_n>0$, then $\lim\limits_{x \to \infty} \left[\frac {a_1^{1/x}+a_2^{1/x}+\dotsb+a_n^{1/x}}{n}\right]^{nx}=a_1 a_2 \dotsb a_n$

### Tags (68)

 18 linear-algebra × 40 8 determinant × 4 16 inequality × 5 6 eigenvalues-eigenvectors × 6 13 matrices × 16 5 calculus × 11 13 sequences-and-series × 15 5 derivatives × 6 10 real-analysis × 68 4 algebra-precalculus × 17

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