Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
1401	Find the Domain	f(x)=1/(x+2)	$f (x) = \frac{1}{x + 2}$
1402	Find the Domain	f(x)=1/(x^2-4)	$f (x) = \frac{1}{x^{2} - 4}$
1403	Find the Domain	y = log base 3 of x	$y = \log_{3} (x)$
1404	Split Using Partial Fraction Decomposition	(3x^2-7x-2)/(x^3-x)	$\frac{3 x^{2} - 7 x - 2}{x^{3} - x}$
1405	Split Using Partial Fraction Decomposition	(pi/2)/2	$\frac{\frac{π}{2}}{2}$
1406	Split Using Partial Fraction Decomposition	(11x-2)/(x^2-x-12)	$\frac{11 x - 2}{x^{2} - x - 12}$
1407	Find the Domain	x=-2	$x = - 2$
1408	Find the Domain	g(x)=(3x)/(2x^2-4x)	$g (x) = \frac{3 x}{2 x^{2} - 4 x}$
1409	Find the Domain	g(x)=(x+5)/(x^2-36)	$g (x) = \frac{x + 5}{x^{2} - 36}$
1410	Find the Domain	h(x)=(2x)/(x^2-1)	$h (x) = \frac{2 x}{x^{2} - 1}$
1411	Find the Domain	h(x)=10/(x^2-2x)	$h (x) = \frac{10}{x^{2} - 2 x}$
1412	Find the Domain	f(x) = natural log of x-x^2	$f (x) = \ln (x - x^{2})$
1413	Find the Domain	square root of x^2-25	$\sqrt{x^{2} - 25}$
1414	Find the Domain	e^x	$e^{x}$
1415	Find the Domain	(3x)/(x^2-4)	$\frac{3 x}{x^{2} - 4}$
1416	Find the Domain	(3x-1)/((x+3)(x-1))	$\frac{3 x - 1}{(x + 3) (x - 1)}$
1417	Find the Domain	(3x(x-1))/(2x^2-5x-3)	$\frac{3 x (x - 1)}{2 x^{2} - 5 x - 3}$
1418	Find the Domain	( square root of x-2)/( square root of x+4)	$\frac{\sqrt{x - 2}}{\sqrt{x + 4}}$
1419	Find the Domain	(x+4)/(x^2-9)	$\frac{x + 4}{x^{2} - 9}$
1420	Divide Using Long Polynomial Division	(4x+7)/(3x-2)	$\frac{4 x + 7}{3 x - 2}$
1421	Simplify	square root of a^2+2ab+b^2	$\sqrt{a^{2} + 2 a b + b^{2}}$
1422	Simplify	square root of 1-(x^2)^2	$\sqrt{1 - {(x^{2})}^{2}}$
1423	Simplify	square root of s square root of s^4	$\sqrt{s \sqrt{s^{4}}}$
1424	Divide Using Synthetic Division	(x^2-6x-6x^3+x^4)/(6+x)	$\frac{x^{2} - 6 x - 6 x^{3} + x^{4}}{6 + x}$
1425	Divide Using Synthetic Division	(16x^3+80x^2+x+5)/(x+5)	$\frac{16 x^{3} + 80 x^{2} + x + 5}{x + 5}$
1426	Divide Using Synthetic Division	(12x^4+5x^3+3x^2-5)/(x+1)	$\frac{12 x^{4} + 5 x^{3} + 3 x^{2} - 5}{x + 1}$
1427	Divide Using Synthetic Division	(3x^2+4x-12)/(x+5)	$\frac{3 x^{2} + 4 x - 12}{x + 5}$
1428	Divide Using Long Polynomial Division	(x^3-9)/(x^2+1)	$\frac{x^{3} - 9}{x^{2} + 1}$
1429	Divide Using Synthetic Division	(2x^3-2x^2+x-1)/(x-3)	$\frac{2 x^{3} - 2 x^{2} + x - 1}{x - 3}$
1430	Divide Using Synthetic Division	(-6x^3+2x^2+5x-10)/(x-2)	$\frac{- 6 x^{3} + 2 x^{2} + 5 x - 10}{x - 2}$
1431	Divide Using Synthetic Division	(6x^5-5x^4+x-4)/(x+1/2)	$\frac{6 x^{5} - 5 x^{4} + x - 4}{x + \frac{1}{2}}$
1432	Simplify	square root of 4x^2+25	$\sqrt{4 x^{2} + 25}$
1433	Simplify	square root of 3i	$\sqrt{3 i}$
1434	Simplify	square root of 1+(x^3-1/(4x^3))^2	$\sqrt{1 + {(x^{3} - \frac{1}{4 x^{3}})}^{2}}$
1435	Simplify	square root of (32a^4)/(b^2)	$\sqrt{\frac{32 a^{4}}{b^{2}}}$
1436	Simplify	square root of (tan(x)^2+1)/(cot(x)^2+1)	$\sqrt{\frac{\tan^{2} (x) + 1}{\cot^{2} (x) + 1}}$
1437	Simplify	(x^2+12x+12)/(x^3-4x)	$\frac{x^{2} + 12 x + 12}{x^{3} - 4 x}$
1438	Simplify	( fourth root of 16x)^3	${(\sqrt[4]{16 x})}^{3}$
1439	Simplify	square root of (25y^3)/(x^2)	$\sqrt{\frac{25 y^{3}}{x^{2}}}$
1440	Simplify	(1/3+( square root of 7)/6*i)^2	${(\frac{1}{3} + \frac{\sqrt{7}}{6} \cdot i)}^{2}$
1441	Simplify	((x+1)^3(x-2)+3(x+1)^2)/((x+1)^4)	$\frac{{(x + 1)}^{3} (x - 2) + 3 {(x + 1)}^{2}}{{(x + 1)}^{4}}$
1442	Simplify	( square root of 3+ square root of 15i)( square root of 3- square root of 15i)	$(\sqrt{3} + \sqrt{15 i}) (\sqrt{3} - \sqrt{15 i})$
1443	Simplify	(2 square root of 3m+3 square root of 5n)(2 square root of 3m-3 square root of 5n)	$(2 \sqrt{3 m} + 3 \sqrt{5 n}) (2 \sqrt{3 m} - 3 \sqrt{5 n})$
1444	Solve for x	x^3-3x>0	$x^{3} - 3 x > 0$
1445	Find the Exact Value	tan(arcsin(6/7))	$\tan (\arcsin (\frac{6}{7}))$
1446	Find the Exact Value	tan(pi/4-2)	$\tan (\frac{π}{4} - 2)$
1447	Find the Exact Value	tan(arccos(-2/3))	$\tan (\arccos (- \frac{2}{3}))$
1448	Find the Exact Value	tan(-150)	$\tan (- 150)$
1449	Find the Exact Value	sin(arctan(7))	$\sin (\arctan (7))$
1450	Find the Exact Value	tan((11pi)/6+pi/4)	$\tan (\frac{11 π}{6} + \frac{π}{4})$
1451	Find the Exact Value	tan(11/6*pi)	$\tan (\frac{11}{6} \cdot π)$
1452	Find the Exact Value	tan(15/8)	$\tan (\frac{15}{8})$
1453	Find the Exact Value	tan(-(17pi)/6)	$\tan (- \frac{17 π}{6})$
1454	Find the Exact Value	sin((17pi)/12)cos(pi/4)	$\sin (\frac{17 π}{12}) \cos (\frac{π}{4})$
1455	Find the Exact Value	sin(-15)	$\sin (- 15)$
1456	Find the Exact Value	sin(67.5)	$\sin (67.5)$
1457	Expand the Trigonometric Expression	1/x	$\frac{1}{x}$
1458	Find the Exact Value	tan(-60)	$\tan (- 60)$
1459	Find the Exact Value	tan(960)	$\tan (960)$
1460	Expand the Trigonometric Expression	(x+h)^2	${(x + h)}^{2}$
1461	Expand the Trigonometric Expression	sin(arccos(2x))	$\sin (\arccos (2 x))$
1462	Find the Exact Value	arcsin(0.635)	$\arcsin (0.635)$
1463	Find the Exact Value	tan(pi/4)^2	$\tan^{2} (\frac{π}{4})$
1464	Verify the Identity	sin(3pi-x)=sin(x)	$\sin (3 π - x) = \sin (x)$
1465	Verify the Identity	tan(3pi+x)=tan(x)	$\tan (3 π + x) = \tan (x)$
1466	Find the Exact Value	arcsin(-0.12)	$\arcsin (- 0.12)$
1467	Find the Exact Value	arccos(2)	$\arccos (2)$
1468	Find the Exact Value	arccos(cos((11pi)/4))	$\arccos (\cos (\frac{11 π}{4}))$
1469	Find the Exact Value	cot(51)	$\cot (51)$
1470	Find the Exact Value	csc((31pi)/6)	$\csc (\frac{31 π}{6})$
1471	Find the Exact Value	cot((-7pi)/4)	$\cot (\frac{- 7 π}{4})$
1472	Find the Exact Value	csc(-135)	$\csc (- 135)$
1473	Find the Exact Value	csc(-45)	$\csc (- 45)$
1474	Find the Exact Value	csc(-30)	$\csc (- 30)$
1475	Find the Exact Value	sin(-1/3*pi)	$\sin (- \frac{1}{3} \cdot π)$
1476	Find the Exact Value	sin(-11/6*pi)	$\sin (- \frac{11}{6} \cdot π)$
1477	Find the Exact Value	sec(arctan(5/12))	$\sec (\arctan (\frac{5}{12}))$
1478	Find the Exact Value	sec(arcsec(1/2))	$\sec (arcsec (\frac{1}{2}))$
1479	Find the Exact Value	sec(-300)	$\sec (- 300)$
1480	Find the Exact Value	arcsin(0.76)	$\arcsin (0.76)$
1481	Find the Exact Value	arcsin(1.2)	$\arcsin (1.2)$
1482	Find the Exact Value	arctan(5)	$\arctan (5)$
1483	Find the Exact Value	cos((20pi)/9)	$\cos (\frac{20 π}{9})$
1484	Find the Exact Value	cos(7/3*pi)	$\cos (\frac{7}{3} \cdot π)$
1485	Find the Exact Value	cos(arctan(5/4))	$\cos (\arctan (\frac{5}{4}))$
1486	Find the Exact Value	cos(arcsin(4/9))	$\cos (\arcsin (\frac{4}{9}))$
1487	Find the Exact Value	cos(arctan(5/12))	$\cos (\arctan (\frac{5}{12}))$
1488	Find the Exact Value	cos(-270)	$\cos (- 270)$
1489	Find the Exact Value	cos(285)-cos(165)	$\cos (285) - \cos (165)$
1490	Find the Exact Value	cos(8.1)	$\cos (8.1)$
1491	Verify the Identity	(cot(x))/(sec(x))=csc(x)-sin(x)	$\frac{\cot (x)}{\sec (x)} = \csc (x) - \sin (x)$
1492	Find the Reference Angle	-300	$- 300$
1493	Find the Reference Angle	43	$43$
1494	Verify the Identity	1/(tan(x))+tan(x)=sec(x)csc(x)	$\frac{1}{\tan (x)} + \tan (x) = \sec (x) \csc (x)$
1495	Verify the Identity	(cot(x)^2)/(csc(x)+1)=(1-sin(x))/(sin(x))	$\frac{\cot^{2} (x)}{\csc (x) + 1} = \frac{1 - \sin (x)}{\sin (x)}$
1496	Find the Complement	cos(75)	$\cos (75)$
1497	Find Amplitude, Period, and Phase Shift	y=3cos(x+1)	$y = 3 \cos (x + 1)$
1498	Find Amplitude, Period, and Phase Shift	y=-3cos(1/4)x	$y = - 3 \cos (\frac{1}{4}) x$
1499	Find Amplitude, Period, and Phase Shift	y=3sin(2/3x)	$y = 3 \sin (\frac{2}{3} x)$
1500	Find Amplitude, Period, and Phase Shift	y=3sin(x-1)	$y = 3 \sin (x - 1)$