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user8277998
  • Member for 6 years, 2 months
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7 votes
Accepted

Find limit of trigonometric function

7 votes

How to calculate $\lim_{x\to0} \frac{\ln(1+x)+\ln(1-x)}{x^2}$?

7 votes

Find the limit of $\lim_{x\to0}{\frac{\ln(1+e^x)-\ln2}{x}}$ without L'Hospital's rule

5 votes
Accepted

Evaluate: $\int \frac {\sec (x)}{\sec (x)+\tan (x)} dx$

5 votes

Suppose $x$ and $y$ are real numbers and $x^2+9y^2-4x+6y+4=0$. Then find the maximum value of $\left(\frac{4x-9y}{2}\right)$

5 votes
Accepted

How do I solve $\lim\limits_{x\to\infty} \ \frac{\ln \ x}{x} = 0$?

5 votes

Is $\frac{200!}{(10!)^{20} \cdot 19!}$ an integer or not?

5 votes
Accepted

Why is $\sqrt[3]{18+5\sqrt{13}} + \sqrt[3]{18-5\sqrt{13}} = 3$?

5 votes

Solving $\int\limits_{-\infty}^\infty \frac{1}{x^8+1}dx$ through Glasser's Master Theorem

4 votes

Calculating the limit $\lim\limits_{x \to 0^+} \frac{\sqrt{\sin x}-\sin\sqrt{ x}}{x\sqrt{x}}$

4 votes

How to calculate this hard integral $\int_0^{\infty} \frac{\arctan(x)\sqrt{\sqrt{1+x^2}-1}}{x\sqrt{1+x^2}}\,dx$?

3 votes

Integrate $\int \frac{\sin x \cos x}{\sin^4x + \cos^4x} \,dx$

3 votes

Find real solutions in $x$,$y$ for the system $\sqrt{x-y}+\sqrt{x+y}=a$ and $\sqrt{x^2+y^2}-\sqrt{x^2-y^2}=a^2.$

3 votes
Accepted

Closed form of $I(t) = \int_0^{\pi/2}\frac{\cos xdx}{\sqrt{\sin^2 x+ t\cos^2 x}}$

2 votes

How to compute $\lim_{x\to 0}\frac{\sin(x^2+x)-x}{x^2}$ without L'Hospital's Rule or series?

2 votes
Accepted

How does the first equation transform to the second one?

2 votes

Area of ellipse which is not in standard form

2 votes
Accepted

Factorising 4th degree polynomial

2 votes
Accepted

Inner product on a complex field defined by norms

2 votes
Accepted

How to proof: $\cos(10°)*\cos(30°)*\cos(50°)*\cos(70°)=\frac{3}{16}$

2 votes
Accepted

Calculate $\lim_{x \to 0} (\cot^3(x)·x·(\ln(1+3x)-3x))$

2 votes

Find the limit of $\lim\limits_{x\to0^+}\frac{1}{e} \frac{e- e^ \frac{\ln (1+x)}{x}}{x}$ as $x$

1 vote

How to solve $\int \cot^3 x\,dx$?

1 vote

What is $\int \frac{ \sqrt{(a^2 - x^2)}}{x^2}$?

1 vote

How to find major & minor axes of the ellipse $10x^2+14xy+10y^2-7=0$?

1 vote

How can I calculate $\lim\limits_{x\rightarrow 0} \frac{(1+x)^{\frac{1}{x}}-e}{x}$?

1 vote
Accepted

Prove that $\lim_{x \to y} \frac{x^k-y^k}{x-y} = k*y^{k-1}$ for $y\in\mathbb R$ and $k\in\mathbb N$

1 vote

How to calculate limit of sequence : $a_n=\frac{1^k+2^k+3^k+...+n^k}{n^{k+1}}$?

1 vote

Limit of $\lim_{n\to\infty}n\cdot \sqrt[n]{\sin\left(\frac{1}{1}\right)\cdot \sin\left(\frac{1}{2}\right)\cdots\sin\left(\frac{1}{n}\right)}$

1 vote

A tough limit problem involving $1/(\sin x - \sin a)$ and its generalization