Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
47301	Find the Antiderivative	4cos(4x)	$4 \cos (4 x)$
47302	Find the Antiderivative	cube root of 1+t^2	$\sqrt[3]{1 + t^{2}}$
47303	Find the Antiderivative	10x^2	$10 x^{2}$
47304	Find the Antiderivative	(cos(x))e^(sin(x))	$(\cos (x)) e^{\sin (x)}$
47305	Find the Antiderivative	(2-t) square root of t	$(2 - t) \sqrt{t}$
47306	Find the Antiderivative	(du)/u	$\frac{d u}{u}$
47307	Find the Antiderivative	square root of x	$\sqrt[2]{x}$
47308	Find the Antiderivative	2/x-x+ square root of 2	$\frac{2}{x} - x + \sqrt{2}$
47309	Find the Antiderivative	2sin(e^(x/4))+1	$2 \sin (e^{\frac{x}{4}}) + 1$
47310	Find the Antiderivative	1/(x^(1/4))	$\frac{1}{x^{\frac{1}{4}}}$
47311	Find the Antiderivative	tan(theta)^3	$\tan^{3} (θ)$
47312	Find the Antiderivative	x^(-7/3)	$x^{- \frac{7}{3}}$
47313	Find the Antiderivative	(y^2)/16	$\frac{y^{2}}{16}$
47314	Find the Antiderivative	2e^(-t)	$2 e^{- t}$
47315	Find the Antiderivative	\|2x-1\|	$\| 2 x - 1 \|$
47316	Find the Antiderivative	(2( natural log of x)^4)/x	$\frac{2 \ln^{4} (x)}{x}$
47317	Find the Roots (Zeros)	6x^2-54x+108	$6 x^{2} - 54 x + 108$
47318	Find the Roots (Zeros)	x^3-31x+30	$x^{3} - 31 x + 30$
47319	Find the Roots (Zeros)	1-2cos(x)	$1 - 2 \cos (x)$
47320	Find the Roots (Zeros)	x^3-4x^2-7x+10	$x^{3} - 4 x^{2} - 7 x + 10$
47321	Find the Roots (Zeros)	3x^2-6x-7	$3 x^{2} - 6 x - 7$
47322	Find the Roots (Zeros)	6x^2+6x-120	$6 x^{2} + 6 x - 120$
47323	Find the Roots (Zeros)	12x^2-84x+104	$12 x^{2} - 84 x + 104$
47324	Find the Roots (Zeros)	4x^3-2x square root of 5-6x	$4 x^{3} - 2 x \sqrt{5} - 6 x$
47325	Find the Roots (Zeros)	3x^2+3	$3 x^{2} + 3$
47326	Find the Roots (Zeros)	3t^2-36t+96	$3 t^{2} - 36 t + 96$
47327	Find the Roots (Zeros)	x^4+29x^2+100	$x^{4} + 29 x^{2} + 100$
47328	Find the Roots (Zeros)	x^2-2x-6	$x^{2} - 2 x - 6$
47329	Find the Roots (Zeros)	x^4-16x^3+50x^2+152x+85	$x^{4} - 16 x^{3} + 50 x^{2} + 152 x + 85$
47330	Find the Roots (Zeros)	x^3-3x^2-x-12	$x^{3} - 3 x^{2} - x - 12$
47331	Find the Roots (Zeros)	x^2+81	$x^{2} + 81$
47332	Find the Roots (Zeros)	x^3-6x^2+3x+10	$x^{3} - 6 x^{2} + 3 x + 10$
47333	Find the Roots (Zeros)	3x^2-7x-6	$3 x^{2} - 7 x - 6$
47334	Find the Roots (Zeros)	x^3-3x^2+3x-1	$x^{3} - 3 x^{2} + 3 x - 1$
47335	Find the Roots (Zeros)	x^2-8x+17	$x^{2} - 8 x + 17$
47336	Find the Roots (Zeros)	12x^2-92x+120	$12 x^{2} - 92 x + 120$
47337	Find the Roots (Zeros)	2x^4+27x^3+33x^2+6x-2	$2 x^{4} + 27 x^{3} + 33 x^{2} + 6 x - 2$
47338	Find the Roots (Zeros)	3x^2+14x-5	$3 x^{2} + 14 x - 5$
47339	Find the Roots (Zeros)	x^2+4x-8	$x^{2} + 4 x - 8$
47340	Find the Roots (Zeros)	3x^2-75	$3 x^{2} - 75$
47341	Find the Roots (Zeros)	6x^2-6x-120	$6 x^{2} - 6 x - 120$
47342	Find the Roots (Zeros)	x^3-21x+20	$x^{3} - 21 x + 20$
47343	Find the Roots (Zeros)	12x^2-252x+902	$12 x^{2} - 252 x + 902$
47344	Find the Roots (Zeros)	x^3-216	$x^{3} - 216$
47345	Find the Roots (Zeros)	6x^2-12x-18	$6 x^{2} - 12 x - 18$
47346	Find the Roots (Zeros)	-3x^3+50x^2-225x+250	$- 3 x^{3} + 50 x^{2} - 225 x + 250$
47347	Find the Roots (Zeros)	64x^3-400x	$64 x^{3} - 400 x$
47348	Find the Roots (Zeros)	x^3-10x^2+27x-18	$x^{3} - 10 x^{2} + 27 x - 18$
47349	Find the Roots (Zeros)	3x^2-8x+5	$3 x^{2} - 8 x + 5$
47350	Find the Roots (Zeros)	1-1/(3t^(2/3))	$1 - \frac{1}{3 t^{\frac{2}{3}}}$
47351	Find the Roots (Zeros)	x^2-3x-1	$x^{2} - 3 x - 1$
47352	Find the Roots (Zeros)	x^5-3x-1	$x^{5} - 3 x - 1$
47353	Find the Roots (Zeros)	(x^3-15x^2+68x-96)÷(x-3)	$(x^{3} - 15 x^{2} + 68 x - 96) \div (x - 3)$
47354	Find the Roots (Zeros)	e^(sin(x))cos(x)	$e^{\sin (x)} \cos (x)$
47355	Find the Roots (Zeros)	x^2-8x-20	$x^{2} - 8 x - 20$
47356	Find the Antiderivative	e^xcos(x)	$e^{x} \cos (x)$
47357	Find the Antiderivative	1/(tan(x))	$\frac{1}{\tan (x)}$
47358	Find the Antiderivative	5sec(x)^2	$5 \sec^{2} (x)$
47359	Find the Antiderivative	x-cos(x)	$x - \cos (x)$
47360	Find the Antiderivative	3e^(3x)sin(e^(3x))	$3 e^{3 x} \sin (e^{3 x})$
47361	Find the Average Value of the Function	f(x) = cube root of x ; [1,8]	$f (x) = \sqrt[3]{x}$ ; $[1, 8]$
47362	Find the Average Value of the Function	f(t)=e^(sin(t))cos(t) , [0,pi/2]	$f (t) = e^{\sin (t)} \cos (t)$ , $[0, \frac{π}{2}]$
47363	Find the Tangent Line at the Point	f(x)=1/(x^5) , (1,1)	$f (x) = \frac{1}{x^{5}}$ , $(1, 1)$
47364	Find the Tangent Line at the Point	f(x)=(12x)/(x^2-4) ; (4,4)	$f (x) = \frac{12 x}{x^{2} - 4}$ ; $(4, 4)$
47365	Find the Tangent Line at the Point	y=3x^3-3x , (1,0)	$y = 3 x^{3} - 3 x$ , $(1, 0)$
47366	Find the Tangent Line at the Point	y=7xe^x , (0,0)	$y = 7 x e^{x}$ , $(0, 0)$
47367	Find the Tangent Line at the Point	y=sin(9x)+sin(9x)^2 , (0,0)	$y = \sin (9 x) + \sin^{2} (9 x)$ , $(0, 0)$
47368	Find the Tangent Line at the Point	(1+2x)^12 , (0,1)	${(1 + 2 x)}^{12}$ , $(0, 1)$
47369	Find the Tangent Line at the Point	y=x^3-2x+2 , (2,6)	$y = x^{3} - 2 x + 2$ , $(2, 6)$
47370	Find the Tangent Line at the Point	h(t)=2t^3 , (2,16)	$h (t) = 2 t^{3}$ , $(2, 16)$
47371	Find the Tangent Line at the Point	y=12 square root of x , (4,24)	$y = 12 \sqrt{x}$ , $(4, 24)$
47372	Find the Tangent Line at the Point	f(x)=x^2-5 , (-5,20)	$f (x) = x^{2} - 5$ , $(- 5, 20)$
47373	Find the Tangent Line at the Point	3(x^2+y^2)^2=100(x^2-y^2) , (4,2)	$3 {(x^{2} + y^{2})}^{2} = 100 (x^{2} - y^{2})$ , $(4, 2)$
47374	Find the Tangent Line at the Point	f(x)=tan(x) , (pi/4,1)	$f (x) = \tan (x)$ , $(\frac{π}{4}, 1)$
47375	Find the Tangent Line at the Point	x^2+2xy-y^2+x=27 , (4,7)	$x^{2} + 2 x y - y^{2} + x = 27$ , $(4, 7)$
47376	Find the Tangent Line at the Point	6e^xcos(x) , (0,6)	$6 e^{x} \cos (x)$ , $(0, 6)$
47377	Find the Tangent Line at the Point	h(t)=-t^3 , (-2,8)	$h (t) = - t^{3}$ , $(- 2, 8)$
47378	Find the Tangent Line at the Point	natural log of x^2-9x+1 , (9,0)	$\ln (x^{2} - 9 x + 1)$ , $(9, 0)$
47379	Find the Tangent Line at the Point	natural log of x^2-8 , (3,0)	$\ln (x^{2} - 8)$ , $(3, 0)$
47380	Find the Tangent Line at the Point	y=4e^x+x , (0,4)	$y = 4 e^{x} + x$ , $(0, 4)$
47381	Find the Tangent Line at the Point	7e^x+x , (0,7)	$7 e^{x} + x$ , $(0, 7)$
47382	Find the Tangent Line at the Point	36(x^2+y^2)^2=625xy^2 ; (4,3)	$36 {(x^{2} + y^{2})}^{2} = 625 x y^{2}$ ; $(4, 3)$
47383	Find the Tangent Line at the Point	f(x)=((x+2)/(x-2))^2 ; (6,4)	$f (x) = {(\frac{x + 2}{x - 2})}^{2}$ ; $(6, 4)$
47384	Find the Tangent Line at the Point	4(x^2+y^2)^2=289xy^2 ; (4,1)	$4 {(x^{2} + y^{2})}^{2} = 289 x y^{2}$ ; $(4, 1)$
47385	Find the Tangent Line at the Point	3e^xcos(x) , (0,3)	$3 e^{x} \cos (x)$ , $(0, 3)$
47386	Find the Tangent Line at the Point	y=( square root of x)/(x+6) , (4,0.2)	$y = \frac{\sqrt{x}}{x + 6}$ , $(4, 0.2)$
47387	Find the Tangent Line at the Point	x^2y^2=100 (2,-5)	$x^{2} y^{2} = 100$ $(2, - 5)$
47388	Find the Tangent Line at the Point	y=(1+3x)^11 , (0,1)	$y = {(1 + 3 x)}^{11}$ , $(0, 1)$
47389	Find the Tangent Line at the Point	cos(4y)=x , (0,pi/8)	$\cos (4 y) = x$ , $(0, \frac{π}{8})$
47390	Find the Tangent Line at the Point	f(x)=tan(x) , ((3pi)/4,-1)	$f (x) = \tan (x)$ , $(\frac{3 π}{4}, - 1)$
47391	Find the Tangent Line at the Point	y=1/(x^3) , (2,1/8)	$y = \frac{1}{x^{3}}$ , $(2, \frac{1}{8})$
47392	Find the Tangent Line at the Point	y=x^3-2x+2 (3,23)	$y = x^{3} - 2 x + 2$ $(3, 23)$
47393	Find the Tangent Line at the Point	h(t)=-t^3 , (-1,1)	$h (t) = - t^{3}$ , $(- 1, 1)$
47394	Find the Tangent Line at the Point	y=arctan(1/4x) ; (4,pi/4)	$y = \arctan (\frac{1}{4} x)$ ; $(4, \frac{π}{4})$
47395	Find the x and y Intercepts	x+108/(x^2)	$x + \frac{108}{x^{2}}$
47396	Find the x and y Intercepts	(x-6)/(x^2-36)	$\frac{x - 6}{x^{2} - 36}$
47397	Find the x and y Intercepts	18x(x-1)^3	$18 x {(x - 1)}^{3}$
47398	Find the x and y Intercepts	19x(x-1)^3	$19 x {(x - 1)}^{3}$
47399	Find the x and y Intercepts	(x+1)/(x^2-4x-5)	$\frac{x + 1}{x^{2} - 4 x - 5}$
47400	Find the Volume	y^2=x , x=2y	$y^{2} = x$ , $x = 2 y$