Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
1301	Evaluate the Integral	integral of 12x^11-11/(x^11) with respect to x	$\int 12 x^{11} - \frac{11}{x^{11}} d x$
1302	Evaluate the Integral	integral of b^2-5b+5 with respect to b	$\int b^{2} - 5 b + 5 d b$
1303	Evaluate the Integral	integral of te^(-5t) with respect to t	$\int t e^{- 5 t} d t$
1304	Evaluate the Integral	integral from 0 to 1 of (x^2+3)e^(-x) with respect to x	$\int_{0}^{1} (x^{2} + 3) e^{- x} d x$
1305	Evaluate the Integral	integral of ((2+e^x)^2)/(e^x) with respect to x	$\int \frac{{(2 + e^{x})}^{2}}{e^{x}} d x$
1306	Evaluate the Integral	integral of (x+1)(3x-2) with respect to x	$\int (x + 1) (3 x - 2) d x$
1307	Evaluate the Integral	integral of (x^2+1)^2 with respect to x	$\int {(x^{2} + 1)}^{2} d x$
1308	Evaluate the Integral	integral of (3x-2)^2 with respect to x	$\int {(3 x - 2)}^{2} d x$
1309	Find the Derivative - d/dx	1/( square root of x^17)	$\frac{1}{\sqrt{x^{17}}}$
1310	Find the Derivative - d/dx	y=16^4 square root of 4x^4+4	$y = 16^{4} \sqrt{4 x^{4} + 4}$
1311	Find the Derivative - d/dy	xy^2	$x y^{2}$
1312	Find the Derivative - d/dy	(1/(y^2)-5/(y^4))(y+7y^3)	$(\frac{1}{y^{2}} - \frac{5}{y^{4}}) (y + 7 y^{3})$
1313	Find the Derivative - d/dx	2x^(3/2)	$2 x^{\frac{3}{2}}$
1314	Find the Derivative - d/dr	k(R^2-r^2)	$k (R^{2} - r^{2})$
1315	Find the Derivative - d/dx	6sin(x)	$6 \sin (x)$
1316	Find the Derivative - d/dx	( square root of x+1/( cube root of x))^2	${(\sqrt{x} + \frac{1}{\sqrt[3]{x}})}^{2}$
1317	Evaluate the Limit	limit as x approaches 8 of cos(1/x)	$lim_{x \to 8} \cos (\frac{1}{x})$
1318	Evaluate the Limit	limit as x approaches 49 of ( square root of x-7)/(x-49)	$lim_{x \to 49} \frac{\sqrt{x} - 7}{x - 49}$
1319	Evaluate the Limit	limit as x approaches 8 of square root of 4x^2+x-2x	$lim_{x \to 8} \sqrt{4 x^{2} + x} - 2 x$
1320	Evaluate the Limit	limit as x approaches infinity of square root of 16x^2+x-4x	$lim_{x \to \infty} \sqrt{16 x^{2} + x} - 4 x$
1321	Evaluate the Limit	limit as x approaches 4 of f(x)	$lim_{x \to 4} f (x)$
1322	Find the Local Maxima and Minima	3x^4-16x^3+2016	$3 x^{4} - 16 x^{3} + 2016$
1323	Find the Local Maxima and Minima	f(x)=e^(1-5x^2)	$f (x) = e^{1 - 5 x^{2}}$
1324	Find the Local Maxima and Minima	3x^2-12x-8	$3 x^{2} - 12 x - 8$
1325	Find the Local Maxima and Minima	f(x)=x^2-2x-3	$f (x) = x^{2} - 2 x - 3$
1326	Find the Local Maxima and Minima	f(x)=x+4/x	$f (x) = x + \frac{4}{x}$
1327	Find the Local Maxima and Minima	f(x)=sin(x)+cos(x)	$f (x) = \sin (x) + \cos (x)$
1328	Find the Derivative - d/d@VAR	f(x)=xe^(-x)	$f (x) = x e^{- x}$
1329	Find the Derivative - d/d@VAR	f(x)=x^8	$f (x) = x^{8}$
1330	Find the Derivative - d/d@VAR	f(x)=1/2x^2	$f (x) = \frac{1}{2} x^{2}$
1331	Find the Derivative - d/d@VAR	f(x)=3x^2-x	$f (x) = 3 x^{2} - x$
1332	Find the Local Maxima and Minima	f(x)=8/(x^2+1)	$f (x) = \frac{8}{x^{2} + 1}$
1333	Evaluate the Limit	( limit as x approaches 5 of x^2-6x+5)/(x-5)	$\frac{lim_{x \to 5} x^{2} - 6 x + 5}{x - 5}$
1334	Evaluate the Limit	( limit as x approaches 8 of natural log of x)/x	$\frac{lim_{x \to 8} \ln (x)}{x}$
1335	Evaluate the Limit	limit as x approaches -3 of (x^2-9)/(x+3)	$lim_{x \to - 3} \frac{x^{2} - 9}{x + 3}$
1336	Evaluate the Limit	limit as x approaches 5 of (x^2-25)/(x-5)	$lim_{x \to 5} \frac{x^{2} - 25}{x - 5}$
1337	Evaluate the Limit	limit as x approaches 0 of (sin(4x))/(sin(6x))	$lim_{x \to 0} \frac{\sin (4 x)}{\sin (6 x)}$
1338	Evaluate the Limit	limit as x approaches 121 of ( square root of x-11)/(x-121)	$lim_{x \to 121} \frac{\sqrt{x} - 11}{x - 121}$
1339	Evaluate the Limit	limit as x approaches 0 of e^x	$lim_{x \to 0} e^{x}$
1340	Evaluate the Limit	limit as x approaches 0 of (sin(2x))/(3x)	$lim_{x \to 0} \frac{\sin (2 x)}{3 x}$
1341	Evaluate the Limit	limit as x approaches 4 of (x-4)/( square root of x-2)	$lim_{x \to 4} \frac{x - 4}{\sqrt{x} - 2}$
1342	Find the Derivative - d/dx	((x+9)x)/(x+1)	$\frac{(x + 9) x}{x + 1}$
1343	Evaluate the Limit	limit as x approaches 1 of (x-1)/(x^2-1)	$lim_{x \to 1} \frac{x - 1}{x^{2} - 1}$
1344	Evaluate the Limit	limit as x approaches 2 of 3x^2-5x+2	$lim_{x \to 2} 3 x^{2} - 5 x + 2$
1345	Find the Area Between the Curves	y=5-x^2 , y=x-1	$y = 5 - x^{2}$ , $y = x - 1$
1346	Evaluate the Limit	( limit as x approaches 0 of 1-cos(x))/x	$\frac{lim_{x \to 0} 1 - \cos (x)}{x}$
1347	Evaluate the Limit	( limit as x approaches 0 of square root of x+9-3)/x	$\frac{lim_{x \to 0} \sqrt{x + 9} - 3}{x}$
1348	Evaluate the Limit	( limit as x approaches 0 of square root of x+2- square root of 2)/x	$\frac{lim_{x \to 0} \sqrt{x + 2} - \sqrt{2}}{x}$
1349	Evaluate the Limit	( limit as x approaches 0 of \|x\|)/x	$\frac{lim_{x \to 0} \| x \|}{x}$
1350	Evaluate the Limit	( limit as h approaches 0 of (3+h)^2-9)/h	$\frac{lim_{h \to 0} {(3 + h)}^{2} - 9}{h}$
1351	Evaluate the Limit	( limit as h approaches 0 of (x+h)^2-x^2)/h	$\frac{lim_{h \to 0} {(x + h)}^{2} - x^{2}}{h}$
1352	Graph	natural log of square root of x	$\ln (\sqrt{x})$
1353	Graph	natural log of 1/x	$\ln (\frac{1}{x})$
1354	Graph	1/( natural log of x)	$\frac{1}{\ln (x)}$
1355	Solve for v	v = square root of 4^2+(-1)^2	$v = \sqrt{4^{2} + {(- 1)}^{2}}$
1356	Simplify	e^( natural log of x)	$e^{\ln (x)}$
1357	Simplify	1/(tan(x))	$\frac{1}{\tan (x)}$
1358	Find the Derivative - d/dx	natural log of x^2+y^2	$\ln (x^{2} + y^{2})$
1359	Find the Derivative - d/dx	2^3*0	$2^{30}$
1360	Find the Derivative - d/dx	1/(x^2+3)	$\frac{1}{x^{2} + 3}$
1361	Find the Derivative - d/dx	1/(x-3)	$\frac{1}{x - 3}$
1362	Find the Derivative - d/dx	1/(4 square root of x+x square root of x)	$\frac{1}{4 \sqrt{x + x \sqrt{x}}}$
1363	Find the Derivative - d/dx	1/(4x)	$\frac{1}{4 x}$
1364	Find the Derivative - d/dx	5 natural log of x	$5 \ln (x)$
1365	Find the Derivative - d/dx	1/(e^x)	$\frac{1}{e^{x}}$
1366	Find the Derivative - d/dx	x-7	$x - 7$
1367	Find the Derivative - d/dx	(x^2)/x	$\frac{x^{2}}{x}$
1368	Find the Derivative - d/dx	(3x-9)/(2x+8)	$\frac{3 x - 9}{2 x + 8}$
1369	Find the Derivative - d/dx	(x^2+1)/(x^2-1)	$\frac{x^{2} + 1}{x^{2} - 1}$
1370	Find the Derivative - d/dx	((x+7)x)/(x+1)	$\frac{(x + 7) x}{x + 1}$
1371	Find the Derivative - d/dx	(x^2)/(e^x)	$\frac{x^{2}}{e^{x}}$
1372	Find the Derivative - d/dx	e^9	$e^{9}$
1373	Find the Derivative - d/dx	y=x(x^2+1)	$y = x (x^{2} + 1)$
1374	Find the Derivative - d/dx	y=((x+2)x)/(x+1)	$y = \frac{(x + 2) x}{x + 1}$
1375	Find the Derivative - d/dx	e^8	$e^{8}$
1376	Find the Derivative - d/dx	9/x-2/(x^3)+1/(x^4)	$\frac{9}{x} - \frac{2}{x^{3}} + \frac{1}{x^{4}}$
1377	Find the Derivative - d/dx	2xe^x	$2 x e^{x}$
1378	Find the Derivative - d/dx	[(x^3+x)(x^3-x)]	$[(x^{3} + x) (x^{3} - x)]$
1379	Find the Derivative - d/dx	e^(-6x)	$e^{- 6 x}$
1380	Find the Derivative - d/dx	(3x+4)^2	${(3 x + 4)}^{2}$
1381	Find the Derivative - d/dx	9x^2	$9 x^{2}$
1382	Find the Derivative - d/dx	log base 5 of xe^x	$\log_{5} (x e^{x})$
1383	Find the Derivative - d/dx	x^-5	$x^{- 5}$
1384	Find the Derivative - d/dx	(4x-4)^2	${(4 x - 4)}^{2}$
1385	Find the Derivative - d/dx	(x^2-6x+2)/(2x)	$\frac{x^{2} - 6 x + 2}{2 x}$
1386	Find the Derivative - d/dx	-2x^3	$- 2 x^{3}$
1387	Find the Derivative - d/dx	(x^4)/4+1/(8x^2)	$\frac{x^{4}}{4} + \frac{1}{8 x^{2}}$
1388	Find the Derivative - d/dx	x/(x^2+3)	$\frac{x}{x^{2} + 3}$
1389	Find the Derivative - d/dx	y=0	$y = 0$
1390	Find the Derivative - d/dx	x^(1/4)	$x^{\frac{1}{4}}$
1391	Find the Derivative - d/dx	(5 square root of x)/8	$\frac{5 \sqrt{x}}{8}$
1392	Find the Derivative - d/dx	tan(4x)	$\tan (4 x)$
1393	Find the Derivative - d/dx	( natural log of x)/x	$\frac{\ln (x)}{x}$
1394	Find the Derivative - d/dx	y=((x+4)x)/(x+1)	$y = \frac{(x + 4) x}{x + 1}$
1395	Find the Derivative - d/dx	2x^2-x-3	$2 x^{2} - x - 3$
1396	Find the Derivative - d/dx	x^2(1-6x)	$x^{2} (1 - 6 x)$
1397	Find the Derivative - d/dx	1/( square root of x^13)	$\frac{1}{\sqrt{x^{13}}}$
1398	Find the Derivative - d/dx	2x-1	$2 x - 1$
1399	Find the Derivative - d/dx	3x^2y	$3 x^{2} y$
1400	Find the Derivative - d/dx	(3x)/(x^2+1)	$\frac{3 x}{x^{2} + 1}$