User Fatma Keskin

1 vote

1025th term of the sequence $ 1,2,2,4,4,4,4,8,8,8,8,8,8,8,8, ... $

answered Jul 23, 2019 at 8:33

1 vote

Evaluating $\lim_{x\to0} \frac{\cos x - \cos 3x}{\sin 3x^2 - \sin x^2}$

answered Nov 6, 2020 at 16:19

1 vote

Limit of: $\lim_{x\to0}\frac{1-\sqrt[3]{\cos{x}}}{1-\cos{\sqrt[3]{x}}}$

answered Nov 8, 2020 at 19:45

1 vote

Finding a general term for the sequence

answered Feb 1, 2021 at 9:41

1 vote

There is a number divisible by all integers from 1 to 200, except for two consecutive numbers. What are the two?

answered Feb 2, 2021 at 13:17

1 vote

Accepted

Find the x-coordinate of the stationary points of the curve and determine the nature of these stationary points.

answered Feb 3, 2021 at 14:10

1 vote

Prove that $\prod_{k=2}^{99}\frac{k^{3}-1}{k^{3}+1}$ is greater than $\frac{2}{3}$.

answered Feb 12, 2021 at 20:52

1 vote

Interesting integral $\int_0^{2\pi}\tan(\cos(x))dx=0$

answered Feb 24, 2021 at 14:43

1 vote

Prove: $\int_{0}^{1} \frac{e^x}{x^{2}+1}dx\le e -1 $

answered Mar 1, 2021 at 11:22

0 votes

Computing integral $\int_0^1 |x-a| \, {\rm d} x$

answered Mar 10, 2021 at 16:34

0 votes

Computing $\lim_{x\to-\frac\pi2}\frac{e^{\tan x}}{\cos^2x}$

answered Feb 26, 2021 at 17:22

0 votes

Other ways to evaluate $\lim_{x \to 0} \frac 1x \left [ \sqrt[3]{\frac{1 - \sqrt{1 - x}}{\sqrt{1 + x} - 1}} - 1\right ]$?

answered Mar 1, 2021 at 0:16

0 votes

$\int_0^{\pi} \frac{x \sin x}{2 + \cos x}dx$

answered Feb 24, 2021 at 1:14

0 votes

Find general solution in radians of $\cos x + \cos 3x + \cos 5x = 0$

answered Feb 3, 2021 at 23:22

0 votes

Differentiate $\sin^{-1}\left(\frac {\sin x + \cos x}{\sqrt{2}}\right)$ with respect to $x$

answered Feb 7, 2021 at 16:54

0 votes

Show the following function is differentiable

answered Feb 7, 2021 at 18:34

0 votes

$\ln{2n+1\over n+1}<{1\over n+1}+{1\over n+2}+\cdots +{1\over 2n}<\ln 2$

answered Feb 10, 2021 at 8:37

0 votes

How to find the $\lim _{x\to 0}\left(2-e^{\arcsin^{2}\left(\sqrt{x}\right)}\right)^{\frac{3}{x}}$

answered Feb 10, 2021 at 14:47

0 votes

If both $x+10$ and $x-79$ are perfect squares, what is $x$?

answered Feb 2, 2021 at 18:24

0 votes

General solution of $\cos (2\arctan x) = \frac{{1 - x^2 }}{{1 + x^2 }}?$

answered Feb 2, 2021 at 20:41

0 votes

The number of integers 'a' ($1\leq a\leq 200$) such that a^a is a perfect square are:$ A). 105$ $ B) 103$ $C)107$ $D)109?$

answered Feb 1, 2021 at 12:01

0 votes

Limit $\lim_\limits{x\to0}{\tan{x}-\sin{x}\over x^3}$

answered Nov 8, 2020 at 21:26

0 votes

Show something using the Mean Value Theorem

answered Dec 6, 2020 at 19:05

0 votes

Proving using mean value theorem

answered Dec 17, 2020 at 0:08

0 votes

Prove $f^\ {''}(c)=0$

answered Jan 2, 2021 at 23:10

0 votes

How can evaluate $\lim_{x\to0}\frac{\sin(3x^2)}{\tan(x)\sin(x)}$

answered Jan 5, 2021 at 19:15

0 votes

Why does $\lim\limits_{\theta\to\infty}n\sin\frac {\theta}n=\theta$

answered Nov 6, 2020 at 22:08

0 votes

Solving $\lim\limits_{x\to0} \frac{x - \sin(x)}{x^2}$ without L'Hospital's Rule.

answered Nov 7, 2020 at 10:15

0 votes

What is the intuition for why row reduction can show linear dependence

answered Sep 1, 2020 at 10:25

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29 Answers

1025th term of the sequence $ 1,2,2,4,4,4,4,8,8,8,8,8,8,8,8, ... $

Evaluating $\lim_{x\to0} \frac{\cos x - \cos 3x}{\sin 3x^2 - \sin x^2}$

Limit of: $\lim_{x\to0}\frac{1-\sqrt[3]{\cos{x}}}{1-\cos{\sqrt[3]{x}}}$

Finding a general term for the sequence

There is a number divisible by all integers from 1 to 200, except for two consecutive numbers. What are the two?

Find the x-coordinate of the stationary points of the curve and determine the nature of these stationary points.

Prove that $\prod_{k=2}^{99}\frac{k^{3}-1}{k^{3}+1}$ is greater than $\frac{2}{3}$.

Interesting integral $\int_0^{2\pi}\tan(\cos(x))dx=0$

Prove: $\int_{0}^{1} \frac{e^x}{x^{2}+1}dx\le e -1 $

Computing integral $\int_0^1 |x-a| \, {\rm d} x$

Computing $\lim_{x\to-\frac\pi2}\frac{e^{\tan x}}{\cos^2x}$

Other ways to evaluate $\lim_{x \to 0} \frac 1x \left [ \sqrt[3]{\frac{1 - \sqrt{1 - x}}{\sqrt{1 + x} - 1}} - 1\right ]$?

$\int_0^{\pi} \frac{x \sin x}{2 + \cos x}dx$

Find general solution in radians of $\cos x + \cos 3x + \cos 5x = 0$

Differentiate $\sin^{-1}\left(\frac {\sin x + \cos x}{\sqrt{2}}\right)$ with respect to $x$

Show the following function is differentiable

$\ln{2n+1\over n+1}<{1\over n+1}+{1\over n+2}+\cdots +{1\over 2n}<\ln 2$

How to find the $\lim _{x\to 0}\left(2-e^{\arcsin^{2}\left(\sqrt{x}\right)}\right)^{\frac{3}{x}}$

If both $x+10$ and $x-79$ are perfect squares, what is $x$?

General solution of $\cos (2\arctan x) = \frac{{1 - x^2 }}{{1 + x^2 }}?$

The number of integers 'a' ($1\leq a\leq 200$) such that a^a is a perfect square are:$ A). 105$ $ B) 103$ $C)107$ $D)109?$

Limit $\lim_\limits{x\to0}{\tan{x}-\sin{x}\over x^3}$

Show something using the Mean Value Theorem

Proving using mean value theorem

Prove $f^\ {''}(c)=0$

How can evaluate $\lim_{x\to0}\frac{\sin(3x^2)}{\tan(x)\sin(x)}$

Why does $\lim\limits_{\theta\to\infty}n\sin\frac {\theta}n=\theta$

Solving $\lim\limits_{x\to0} \frac{x - \sin(x)}{x^2}$ without L'Hospital's Rule.

What is the intuition for why row reduction can show linear dependence