Register

ISI2015-MMA-66

• recategorized by
468 views
0 votes
0 votes

The smallest positive number $K$ for which the inequality $\mid \sin ^2 x – \sin ^2 y \mid \leq K \mid x-y \mid$ holds for all $x$ and $y$ is

  1. $2$
  2. $1$
  3. $\frac{\pi}{2}$
  4. there is no smallest positive value of $K$; any $K>0$ will make the inequality hold.
• recategorized by
User Avatar

Please log in or register to answer this question.

Voting & Accepting an answer helps improve the community
← PreviousNext →
← Previous in categoryNext in category →

Related questions

2 votes
2 votes
2 answers
1
Arjun asked Sep 23, 2019
543 views
ISI2015-MMA-50
Let ... $V_3<V_2<V_1$ $V_3<V_1<V_2$ $V_1<V_2<V_3$ $V_2<V_3<V_1$
Let$$\begin{array}{} V_1 & = & \frac{7^2+8^2+15^2+23^2}{4} – \left( \frac{7+8+15+23}{4} \right) ^2, \\ V_2 & = & \frac{6^2+8^2+15^2+24^2}{4} – \left( \frac{6+8+15+24...
User Avatar
0 votes
0 votes
1 answer
2
Arjun asked Sep 23, 2019
395 views
ISI2015-MMA-65
Let $n$ be a positive real number and $p$ be a positive integer. Which of the following inequalities is true? $n^p > \frac{(n+1)^{p+1} – n^{p+1}}{p+1}$ $n^p < \frac{(n+1)^{p+1} – n^{p+1}}{p+1}$ $(n+1)^p < \frac{(n+1)^{p+1} – n^{p+1}}{p+1}$ none of the above
Let $n$ be a positive real number and $p$ be a positive integer. Which of the following inequalities is true?$n^p \frac{(n+1)^{p+1} – n^{p+1}}{p+1}$$n^p < \frac{(n+1)^...
User Avatar
1 votes
1 votes
2 answers
3
Arjun asked Sep 23, 2019
618 views
ISI2015-MMA-27
Let $\cos ^6 \theta = a_6 \cos 6 \theta + a_5 \cos 5 \theta + a_4 \cos 4 \theta + a_3 \cos 3 \theta + a_2 \cos 2 \theta + a_1 \cos \theta +a_0$. Then $a_0$ is $0$ $1/32$ $15/32$ $10/32$
Let $\cos ^6 \theta = a_6 \cos 6 \theta + a_5 \cos 5 \theta + a_4 \cos 4 \theta + a_3 \cos 3 \theta + a_2 \cos 2 \theta + a_1 \cos \theta +a_0$. Then $a_0$ is$0$$1/32$$...
User Avatar
0 votes
0 votes
1 answer
4
Arjun asked Sep 23, 2019
594 views
ISI2015-MMA-34
If $f(x) = \dfrac{\sqrt{3}\sin x}{2+\cos x}$, then the range of $f(x)$ is the interval $[-1, \sqrt{3}/2]$ the interval $[- \sqrt{3}/2, 1]$ the interval $[-1, 1]$ none of the above
If $f(x) = \dfrac{\sqrt{3}\sin x}{2+\cos x}$, then the range of $f(x)$ isthe interval $[-1, \sqrt{3}/2]$the interval $[- \sqrt{3}/2, 1]$the interval $[-1, 1]$none of the ...
User Avatar
Link Copied!