Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
1201	Simplify	cot(x)	$\cot (x)$
1202	Simplify	(x+h)^4	${(x + h)}^{4}$
1203	Simplify	(x^(1/3))^2	${(x^{\frac{1}{3}})}^{2}$
1204	Solve for x	4x^3-16x=0	$4 x^{3} - 16 x = 0$
1205	Solve for x	x=2 square root of x	$x = 2 \sqrt{x}$
1206	Solve for x	3-x^2=x-17	$3 - x^{2} = x - 17$
1207	Solve for x	3x^2-6x=0	$3 x^{2} - 6 x = 0$
1208	Solve for ?	tan(x)=-1/3	$\tan (x) = - \frac{1}{3}$
1209	Evaluate the Limit	( limit as x approaches 0 of x^3+12x^2-5x)/(5x)	$\frac{lim_{x \to 0} x^{3} + 12 x^{2} - 5 x}{5 x}$
1210	Find the Area Between the Curves	y=81x , y=x^5 , x=0 , x=3	$y = 81 x$ , $y = x^{5}$ , $x = 0$ , $x = 3$
1211	Evaluate the Limit	limit as x approaches 2 of 3	$lim_{x \to 2} 3$
1212	Evaluate the Limit	limit as x approaches -2 of f(x)	$lim_{x \to - 2} f (x)$
1213	Evaluate the Limit	limit as x approaches 2 of 1/((x-2)^2)	$lim_{x \to 2} \frac{1}{{(x - 2)}^{2}}$
1214	Evaluate the Limit	limit as x approaches 0 of (sin(x)^2)/x	$lim_{x \to 0} \frac{\sin^{2} (x)}{x}$
1215	Evaluate the Limit	limit as x approaches -1 of (x^2-1)/(x+1)	$lim_{x \to - 1} \frac{x^{2} - 1}{x + 1}$
1216	Evaluate the Limit	limit as x approaches 0 of xcos(1/x)	$lim_{x \to 0} x \cos (\frac{1}{x})$
1217	Evaluate the Limit	limit as x approaches -2 of (x^2-4)/(x+2)	$lim_{x \to - 2} \frac{x^{2} - 4}{x + 2}$
1218	Evaluate the Limit	limit as x approaches negative infinity of x+ square root of x^2+2x	$lim_{x \to - \infty} x + \sqrt{x^{2} + 2 x}$
1219	Evaluate the Limit	limit as x approaches 0 of csc(x)-cot(x)	$lim_{x \to 0} \csc (x) - \cot (x)$
1220	Evaluate the Limit	limit as x approaches 0 of (1-2x)^(1/x)	$lim_{x \to 0} {(1 - 2 x)}^{\frac{1}{x}}$
1221	Evaluate the Limit	( limit as x approaches 36 of square root of x-6)/(x-36)	$\frac{lim_{x \to 36} \sqrt{x} - 6}{x - 36}$
1222	Evaluate the Limit	( limit as x approaches 25 of square root of x-5)/(x-25)	$\frac{lim_{x \to 25} \sqrt{x} - 5}{x - 25}$
1223	Evaluate the Limit	( limit as x approaches 5 of x^2-25)/(x-5)	$\frac{lim_{x \to 5} x^{2} - 25}{x - 5}$
1224	Evaluate the Limit	( limit as x approaches 6 of x^2-36)/(x-6)	$\frac{lim_{x \to 6} x^{2} - 36}{x - 6}$
1225	Evaluate the Limit	limit as x approaches pi/2 of (cos(x))/(1-sin(x))	$lim_{x \to \frac{π}{2}} \frac{\cos (x)}{1 - \sin (x)}$
1226	Find the Antiderivative	x^4	$x^{4}$
1227	Find the Derivative - d/dx	sixth root of x^7	$\sqrt[6]{x^{7}}$
1228	Find the Derivative - d/d@VAR	f(x)=cos( natural log of x)	$f (x) = \cos (\ln (x))$
1229	Find the Derivative - d/d@VAR	f(X) = square root of 1-2x	$f (X) = \sqrt{1 - 2 x}$
1230	Find the Derivative - d/d@VAR	f(x)=5x^2	$f (x) = 5 x^{2}$
1231	Find the Local Maxima and Minima	f(x)=(2x^2+3)/(4x^2+5)	$f (x) = \frac{2 x^{2} + 3}{4 x^{2} + 5}$
1232	Find the Local Maxima and Minima	f(x)=2x^3-12x^2-72x+2017	$f (x) = 2 x^{3} - 12 x^{2} - 72 x + 2017$
1233	Evaluate the Limit	limit as x approaches 1 of (x^3-1)/(x-1)	$lim_{x \to 1} \frac{x^{3} - 1}{x - 1}$
1234	Find dy/dx	y=( square root of x-4)/( square root of x+4)	$y = \frac{\sqrt{x} - 4}{\sqrt{x} + 4}$
1235	Evaluate the Limit	limit as x approaches 5 of x^2	$lim_{x \to 5} x^{2}$
1236	Evaluate the Limit	limit as x approaches 8 of f(x)	$lim_{x \to 8} f (x)$
1237	Find Where Undefined/Discontinuous	f(x)=tan((pix)/2)	$f (x) = \tan (\frac{π x}{2})$
1238	Evaluate	sec(pi/3)^2	$\sec^{2} (\frac{π}{3})$
1239	Find the Critical Points	3x^(2/3)-2x	$3 x^{\frac{2}{3}} - 2 x$
1240	Find the Critical Points	f(x)=x^3-27x	$f (x) = x^{3} - 27 x$
1241	Evaluate	cot(pi)	$\cot (π)$
1242	Evaluate	tan(-1/3)	$\tan (- \frac{1}{3})$
1243	Evaluate	tan(-4/5)	$\tan (\frac{- 4}{5})$
1244	Evaluate	tan((7pi)/6)	$\tan (\frac{7 π}{6})$
1245	Find Where Increasing/Decreasing Using Derivatives	f(x)=x/(x^2+1)	$f (x) = \frac{x}{x^{2} + 1}$
1246	Find the Inflection Points	f(x)=x^3-12x	$f (x) = x^{3} - 12 x$
1247	Find the Derivative - d/dx	x^2-2	$x^{2} - 2$
1248	Find the Derivative - d/dx	x^5e^x	$x^{5} e^{x}$
1249	Find the Horizontal Tangent Line	f(x)=x/( square root of 2x-1)	$f (x) = \frac{x}{\sqrt{2 x - 1}}$
1250	Evaluate the Limit	limit as x approaches -2 of (2-\|x\|)/(2+x)	$lim_{x \to - 2} \frac{2 - \| x \|}{2 + x}$
1251	Find the Derivative of the Integral	integral of cos(x) with respect to x	$\int \cos (x) d x$
1252	Evaluate the Limit	limit as x approaches -1 of (x^3+1)/(x+1)	$lim_{x \to - 1} \frac{x^{3} + 1}{x + 1}$
1253	Evaluate the Integral	integral from 1 to e of ( natural log of x)/x with respect to x	$\int_{1}^{e} \frac{\ln (x)}{x} d x$
1254	Evaluate the Integral	integral from 0 to 2pi of t^2sin(2t) with respect to t	$\int_{0}^{2 π} t^{2} \sin (2 t) d t$
1255	Evaluate the Integral	integral of (x^2+3x)cos(x) with respect to x	$\int (x^{2} + 3 x) \cos (x) d x$
1256	Evaluate the Integral	integral from 2 to 4 of 3 with respect to x	$\int_{2}^{4} 3 d x$
1257	Evaluate the Integral	integral from 0 to 5 of square root of y+4 with respect to y	$\int_{0}^{5} \sqrt{y + 4} d y$
1258	Evaluate the Integral	integral from 0 to 1 of arctan(x) with respect to x	$\int_{0}^{1} \arctan (x) d x$
1259	Evaluate the Integral	integral from -4 to 4 of square root of 16-x^2 with respect to x	$\int_{- 4}^{4} \sqrt{16 - x^{2}} d x$
1260	Evaluate the Integral	integral of x square root of 2x+1 with respect to x	$\int x \sqrt{2 x + 1} d x$
1261	Evaluate the Integral	integral of x*cos(x) with respect to x	$\int x \cdot \cos (x) d x$
1262	Evaluate the Integral	integral of (e^u)/((6-e^u)^2) with respect to u	$\int \frac{e^{u}}{{(6 - e^{u})}^{2}} d u$
1263	Evaluate the Integral	integral of x^5cos(x^3) with respect to x	$\int x^{5} \cos (x^{3}) d x$
1264	Evaluate the Integral	integral of (17x+5)/(2x^2+7x-4) with respect to x	$\int \frac{17 x + 5}{2 x^{2} + 7 x - 4} d x$
1265	Evaluate the Integral	integral of e^(3x-1) with respect to x	$\int e^{3 x - 1} d x$
1266	Evaluate the Integral	integral of square root of 1-4x^2 with respect to x	$\int \sqrt{1 - 4 x^{2}} d x$
1267	Evaluate the Integral	integral from -1 to 1 of \|x\| with respect to x	$\int_{- 1}^{1} \| x \| d x$
1268	Evaluate the Integral	integral of 8x^7 with respect to x	$\int 8 x^{7} d x$
1269	Evaluate the Integral	integral of 2xcos(x) with respect to x	$\int 2 x \cos (x) d x$
1270	Evaluate the Integral	integral of 2sin(2x) with respect to x	$\int 2 \sin (2 x) d x$
1271	Evaluate the Integral	integral of 3(2t+5)^3 with respect to t	$\int 3 {(2 t + 5)}^{3} d t$
1272	Evaluate the Integral	integral from 0 to pi of (6+sin(x)) with respect to x	$\int_{0}^{π} (6 + \sin (x)) d x$
1273	Evaluate the Integral	integral of x square root of 4-9x^2 with respect to x	$\int x \sqrt{4 - 9 x^{2}} d x$
1274	Evaluate the Integral	integral of x/(1+x^4) with respect to x	$\int \frac{x}{1 + x^{4}} d x$
1275	Evaluate the Integral	integral of x/( square root of x-1) with respect to x	$\int \frac{x}{\sqrt{x - 1}} d x$
1276	Evaluate the Integral	integral of x/( square root of x+9) with respect to x	$\int \frac{x}{\sqrt{x + 9}} d x$
1277	Evaluate the Integral	integral of cos( square root of x) with respect to x	$\int \cos (\sqrt{x}) d x$
1278	Evaluate the Integral	integral of square root of 36-x^2 with respect to x	$\int \sqrt{36 - x^{2}} d x$
1279	Evaluate the Integral	integral of e^(5x)(5) with respect to x	$\int e^{5 x} (5) d x$
1280	Evaluate the Integral	integral of -e^x with respect to x	$\int - e^{x} d x$
1281	Evaluate the Integral	integral of xsec(x)^2 with respect to x	$\int x \sec^{2} (x) d x$
1282	Evaluate the Integral	integral of 1/x with respect to xdx	$\int \frac{1}{x} d x d x$
1283	Evaluate the Integral	integral of x^2cos(2x^3) with respect to x	$\int x^{2} \cos (2 x^{3}) d x$
1284	Evaluate the Integral	integral of tan(x)^4 with respect to x	$\int \tan^{4} (x) d x$
1285	Evaluate the Integral	integral from 1 to 2 of 4x^3 with respect to x	$\int_{1}^{2} 4 x^{3} d x$
1286	Evaluate the Integral	integral of x^4e^(x^5) with respect to x	$\int x^{4} e^{x^{5}} d x$
1287	Evaluate the Integral	integral of 12^x with respect to x	$\int 12^{x} d x$
1288	Evaluate the Integral	integral of sec(t)^2 with respect to t	$\int \sec^{2} (t) d t$
1289	Evaluate the Integral	integral of 4/(x^3) with respect to x	$\int \frac{4}{x^{3}} d x$
1290	Evaluate the Integral	integral of (x^2)/( square root of 16-x^2) with respect to x	$\int \frac{x^{2}}{\sqrt{16 - x^{2}}} d x$
1291	Evaluate the Integral	integral of ((3+e^x)^2)/(e^x) with respect to x	$\int \frac{{(3 + e^{x})}^{2}}{e^{x}} d x$
1292	Evaluate the Integral	integral from 1 to 2 of 1/(1+x^4) with respect to x	$\int_{1}^{2} \frac{1}{1 + x^{4}} d x$
1293	Evaluate the Integral	integral of (x^2)/(3-x^3) with respect to x	$\int \frac{x^{2}}{3 - x^{3}} d x$
1294	Evaluate the Integral	integral of sin(x)cos(x) with respect to x	$\int \sin (x) \cos (x) d x$
1295	Evaluate the Integral	integral of x^5 natural log of x with respect to x	$\int x^{5} \ln (x) d x$
1296	Evaluate the Integral	integral of 1/(4+x^2) with respect to x	$\int \frac{1}{4 + x^{2}} d x$
1297	Find the 2nd Derivative	y=5	$y = 5$
1298	Find the 2nd Derivative	f(x) = square root of x^2+1	$f (x) = \sqrt{x^{2} + 1}$
1299	Find the 2nd Derivative	y=x(x-4)^3	$y = x {(x - 4)}^{3}$
1300	Find the 2nd Derivative	y = square root of x+12	$y = \sqrt{x + 12}$