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Ilovemath's user avatar
Ilovemath
  • Member for 2 years, 8 months
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10 votes
Accepted

Improper integral $\int_0^{\infty} \frac{1}{(x+1)(\pi^2+\ln^2(x))}dx$

5 votes
Accepted

Find limit $\lim_{n \to \infty} \sum_{k=1}^{n} \frac{k^4}{k^5+n^5}$.

5 votes
Accepted

Smallest positive integer that when divided by 23 has 20 as remainder and 34 remainder when divided by 41.

4 votes
Accepted

Find $a$, $b$ if $3 + 4i = \frac{3+ai}{5+bi}$.

4 votes
Accepted

If $x^4 + ax^3 + 3x^2 +bx +1\geq0$, $\forall x\in \mathbb{R}$, find maximum of $a^2+b^2$

3 votes

Find an equation of the tangent line to the circle $(x-3)^2+(y-5)^2=5$ at $P(4,7).$

3 votes
Accepted

If $9z + 2/z$ is a real number, find the value of $zz^*$

3 votes

Ratio of terms in sequences satisfying $a_{n}+a_{n+1}=a_{n+2}$ - always tends to the golden ratio

2 votes

Value of $\sum_{n=0}^{1947}\frac{1}{2^n+\sqrt{2^{1947}}}$ $?$

2 votes

What happens to $w=\frac{x^2y^3}{z^4}$ , if $x,y,z$ increase by $\%1$ , $\%2$ , $\%3$ respectively?

2 votes

Find the number of ways the commander can be chosen

2 votes
Accepted

Find conditions on $p,q$ such that $p+q-1<pq-p-q+2$?

2 votes

How to find the maximum value of $\frac{2\sin\theta\cos\theta}{(1+\cos\theta)(1+\sin\theta)}$?

2 votes
Accepted

Use trigonometry in a triangle that is not right angled.

2 votes

If $11z^{10}+10iz^9+10iz-11 = 0$. Then possible value of $\mid z \mid,$ is

2 votes

Proving divisibility by $9$ for $10^n + 3 \times 4^{n+2} + 5$.

2 votes
Accepted

Evaluate $\int\frac{3\cot3x-\cot x}{\tan x-3\tan3x}\,dx$

2 votes

Sum of series with changing ratio

1 vote

What does (plane) + (lambda*plane) refer to?

1 vote
Accepted

Find area of triangle given orthocenter and centroid

1 vote

Why is this approach wrong?

1 vote

Log rules with $\ln(a^{b^c})$

1 vote

Why $ \lim_{x\rightarrow\infty}\frac{\cos(x)-x}{x+2} $ doesn't work with L'Hopital?

1 vote

Let $L$ be the line of intersection between two planes

1 vote

Find the length of DQ and the angle QDB on the triangle

1 vote
Accepted

Let $f(x)=ax^3+bx^2+cx+5$. If $|f(x)|\le|e^x-e^2|$ for all $x\ge0$ and if the maximum value of $|12a+4b+c|$ is $m$, then find $[m]$

0 votes
Accepted

Maximum value of $p$

0 votes

Prove $\int_0^{\infty}\frac{\ln(1+x^2)}{x^2(1+x^2)}dx=\pi\ln\big(\frac 2 e\big)$

0 votes

Need help graphing an absolute value function

0 votes

Proving a function is increasing in $n$.