Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
60001	Find the Concavity	f(x)=2x^3-6x	$f (x) = 2 x^{3} - 6 x$
60002	Find the Concavity	f(x)=5x^3-15x	$f (x) = 5 x^{3} - 15 x$
60003	Find the Area Between the Curves	y=x^2 , y=18-x^2	$y = x^{2}$ , $y = 18 - x^{2}$
60004	Find the Area Between the Curves	y=x^2-37 , y=11-2x	$y = x^{2} - 37$ , $y = 11 - 2 x$
60005	Find the Area Between the Curves	x=-2 , x=2 , y=11x , y=x^2-12	$x = - 2$ , $x = 2$ , $y = 11 x$ , $y = x^{2} - 12$
60006	Find the Area Between the Curves	x=-5 , x=1 , y=4x , y=x^2-5	$x = - 5$ , $x = 1$ , $y = 4 x$ , $y = x^{2} - 5$
60007	Find the Area Between the Curves	x=-5 , x=1 , y=2x , y=x^2-3	$x = - 5$ , $x = 1$ , $y = 2 x$ , $y = x^{2} - 3$
60008	Find the Area Between the Curves	y=x^(15/14) , y=13x^(1/14)	$y = x^{\frac{15}{14}}$ , $y = 13 x^{\frac{1}{14}}$
60009	Find the Area Between the Curves	y=10x , y=x^2	$y = 10 x$ , $y = x^{2}$
60010	Find the Area Between the Curves	y=2/x , y=8x , y=1/2x , x>0	$y = \frac{2}{x}$ , $y = 8 x$ , $y = \frac{1}{2} x$ , $x > 0$
60011	Find the Area Between the Curves	y=19x , y=x^2	$y = 19 x$ , $y = x^{2}$
60012	Find the Derivative - d/dt	(-e^(-t)t+e^(-t))/(e^t)	$\frac{(- e^{- t} t + e^{- t})}{e^{t}}$
60013	Find the Derivative - d/dt	4.905t^2	$4.905 t^{2}$
60014	Find the Derivative - d/dt	arccsc(-8t^2)	$arccsc (- 8 t^{2})$
60015	Find the Derivative - d/dt	t-t^-1	$t - t^{- 1}$
60016	Find the Derivative - d/dy	2xy^2	$2 x y^{2}$
60017	Find the Derivative - d/dy	cube root of y	$\sqrt[3]{y}$
60018	Find the Derivative - d/dy	8xe^(xy)	$8 x e^{x y}$
60019	Find the Derivative - d/dy	9y	$9 y$
60020	Find the Derivative - d/dy	y^-2	$y^{- 2}$
60021	Find the Local Maxima and Minima	f(x,y)=x^2+xy+y^2-31y+320	$f (x, y) = x^{2} + x y + y^{2} - 31 y + 320$
60022	Find the Local Maxima and Minima	y=x natural log of x	$y = x \ln (x)$
60023	Find the Second Derivative	y = square root of x	$y = \sqrt{x}$
60024	Find the Second Derivative	x^2+25y^2=100	$x^{2} + 25 y^{2} = 100$
60025	Divide	52/3	$\frac{52}{3}$
60026	Find the Inflection Points	f(x)=1/4x^4-x^3+6	$f (x) = \frac{1}{4} x^{4} - x^{3} + 6$
60027	Find the Mean	8 , 6 , 9 , 12 , 19 , 7 , 10 , 8	$8$ , $6$ , $9$ , $12$ , $19$ , $7$ , $10$ , $8$
60028	Find the Area Under the Curve	y=2x ; [3,6]	$y = 2 x$ ; $[3, 6]$
60029	Find the Area Under the Curve	y=6/x ; [1,7]	$y = \frac{6}{x}$ ; $[1, 7]$
60030	Find the Area Under the Curve	y=9/x ; [1,5]	$y = \frac{9}{x}$ ; $[1, 5]$
60031	Find the Area Under the Curve	y=8/x ; [1,10]	$y = \frac{8}{x}$ ; $[1, 10]$
60032	Find the Inverse	4 square root of x	$4 \sqrt{x}$
60033	Find the Inverse	fourth root of x	$\sqrt[4]{x}$
60034	Find the Antiderivative	g(t)=e^(-6t)	$g (t) = e^{- 6 t}$
60035	Find the Antiderivative	h(t)=3cos(t)	$h (t) = 3 \cos (t)$
60036	Find the Antiderivative	h(z)=4/z	$h (z) = \frac{4}{z}$
60037	Find the Antiderivative	f(x)=x^8	$f (x) = x^{8}$
60038	Find the Antiderivative	f(x)=7x^(2/5)+8x^(-4/5)	$f (x) = 7 x^{\frac{2}{5}} + 8 x^{- \frac{4}{5}}$
60039	Find the Antiderivative	f(x)=7x^(2/5)+3x^(-4/5)	$f (x) = 7 x^{\frac{2}{5}} + 3 x^{- \frac{4}{5}}$
60040	Find the Antiderivative	f(x)=7x^2	$f (x) = 7 x^{2}$
60041	Find the Antiderivative	f(x)=6x^5-7x^4-6x^2	$f (x) = 6 x^{5} - 7 x^{4} - 6 x^{2}$
60042	Find the Antiderivative	f(x)=7/(x^6)	$f (x) = \frac{7}{x^{6}}$
60043	Find the Antiderivative	f(x)=5/x	$f (x) = \frac{5}{x}$
60044	Find the Antiderivative	f(x)=3/x	$f (x) = \frac{3}{x}$
60045	Find the Antiderivative	f(t)=csc(t)^2	$f (t) = \csc^{2} (t)$
60046	Find Where Increasing/Decreasing Using Derivatives	f(x)=x^4-18x^2+81	$f (x) = x^{4} - 18 x^{2} + 81$
60047	Find Where Increasing/Decreasing Using Derivatives	f(x)=3x^4-28x^3+60x^2	$f (x) = 3 x^{4} - 28 x^{3} + 60 x^{2}$
60048	Find Where Increasing/Decreasing Using Derivatives	f(x)=(2x)/(x^2+1)	$f (x) = \frac{2 x}{x^{2} + 1}$
60049	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of (e^x)/(x^5)	$lim_{x \to \infty} \frac{e^{x}}{x^{5}}$
60050	Find the Vertices	(y^2)/25-(x^2)/9=1	$\frac{y^{2}}{25} - \frac{x^{2}}{9} = 1$
60051	Find the Vertices	(x^2)/16+(y^2)/7=1	$\frac{x^{2}}{16} + \frac{y^{2}}{7} = 1$
60052	Find the Roots (Zeros)	4x^3-16x	$4 x^{3} - 16 x$
60053	Find the Roots (Zeros)	x^2-8x+15	$x^{2} - 8 x + 15$
60054	Find the Fourth Derivative	f(x)=x^3	$f (x) = x^{3}$
60055	Find the Critical Points	f(x)=5x^3+45x^2-105x+14	$f (x) = 5 x^{3} + 45 x^{2} - 105 x + 14$
60056	Find the Inflection Points	y=(x^2-9)/(x-5)	$y = \frac{x^{2} - 9}{x - 5}$
60057	Find the Inflection Points	y=xe^x	$y = x e^{x}$
60058	Find the Inflection Points	y=xe^(-x)	$y = x e^{- x}$
60059	Find the Roots (Zeros)	2x^3-11x^2+12x+9=0	$2 x^{3} - 11 x^{2} + 12 x + 9 = 0$
60060	Find the Foci	x^2-y^2=1	$x^{2} - y^{2} = 1$
60061	Find the Foci	(y^2)/36-(x^2)/64=1	$\frac{y^{2}}{36} - \frac{x^{2}}{64} = 1$
60062	Find the Foci	(x^2)/144+(y^2)/169=1	$\frac{x^{2}}{144} + \frac{y^{2}}{169} = 1$
60063	Find dy/dt	y=t( natural log of 11t)^2	$y = t \ln^{2} (11 t)$
60064	Find dx/dy	x^2-3xy=10	$x^{2} - 3 x y = 10$
60065	Find dA/dt	(dA)/(dt)=2pi(40)(0.04)	$\frac{d A}{d t} = 2 π (40) (0.04)$
60066	Find the Directrix	y^2=36x	$y^{2} = 36 x$
60067	Find the Local Maxima and Minima	x square root of 1-x	$x \sqrt{1 - x}$
60068	Solve for t	200=35e^(3t)+57	$200 = 35 e^{3 t} + 57$
60069	Solve for n1	n_1/(20.2) square root of 30/(310^-3)=n_2/(20.5) square root of 30/(2.7*10^-4)	$\frac{n_{1}}{2 \cdot 0.2} \cdot \sqrt{\frac{30}{3 \cdot 10^{- 3}}} = \frac{n_{2}}{2 \cdot 0.5} \sqrt{\frac{30}{2.7 \cdot 10^{- 4}}}$
60070	Solve for y	x=2 square root of y	$x = 2 \sqrt{y}$
60071	Solve for y	(dy)/(dt)=ky	$\frac{d y}{d t} = k y$
60072	Solve for y	y=2(15)^1.9-cot(0.5)*15	$y = 2 {(15)}^{1.9} - \cot (0.5 (15))$
60073	Solve for y	y^2=2y	$y^{2} = 2 y$
60074	Solve for a	3(b-2a)-6(4a+3b)=7	$3 (b - 2 a) - 6 (4 a + 3 b) = 7$
60075	Find the Local Maxima and Minima	f(x)=x^(6/5)-6x^(1/5)	$f (x) = x^{\frac{6}{5}} - 6 x^{\frac{1}{5}}$
60076	Find the Local Maxima and Minima	f(x)=2x^3-9x^2+12x-3	$f (x) = 2 x^{3} - 9 x^{2} + 12 x - 3$
60077	Find the Concavity	f'(x)=x^4-6x^2-8x-3	$f' (x) = x^{4} - 6 x^{2} - 8 x - 3$
60078	Find the Third Derivative	2^x	$2^{x}$
60079	Find the Concavity	f(x)=x^4-7x^3	$f (x) = x^{4} - 7 x^{3}$
60080	Find the Derivative of the Integral	integral from 1 to square root of x of (z^2)/(z^4+1) with respect to z	$\int_{1}^{\sqrt{x}} \frac{z^{2}}{z^{4} + 1} d z$
60081	Find Where Increasing/Decreasing Using Derivatives	(\|4-x^2\|)/(x-2)	$\frac{\| 4 - x^{2} \|}{x - 2}$
60082	Find the Concavity	x^4-6x^2	$x^{4} - 6 x^{2}$
60083	Find the Critical Points	x^3-6x^2+9x+1	$x^{3} - 6 x^{2} + 9 x + 1$
60084	Find the Critical Points	6x^4+8x^3	$6 x^{4} + 8 x^{3}$
60085	Solve by Factoring	x^4-8x=0	$x^{4} - 8 x = 0$
60086	Convert to a Simplified Fraction	square root of 48	$\sqrt{48}$
60087	Find the x and y Intercepts	y=x^4-4x^2	$y = x^{4} - 4 x^{2}$
60088	Find the x and y Intercepts	-2x+4y-6=0	$- 2 x + 4 y - 6 = 0$
60089	Find the Antiderivative	f(t)=5t	$f (t) = 5 t$
60090	Find the Antiderivative	f(x)=2/( square root of x)	$f (x) = \frac{2}{\sqrt{x}}$
60091	Find the Antiderivative	f(x)=7/x	$f (x) = \frac{7}{x}$
60092	Find the Antiderivative	f(x)=4x+7	$f (x) = 4 x + 7$
60093	Find the Antiderivative	f(x)=20x^19	$f (x) = 20 x^{19}$
60094	Find the Antiderivative	f(x) = square root of 7	$f (x) = \sqrt{7}$
60095	Find the Antiderivative	f(x) = fifth root of x^2	$f (x) = \sqrt[5]{x^{2}}$
60096	Find the Antiderivative	f(x)=6^x	$f (x) = 6^{x}$
60097	Find the Antiderivative	f(x)=6x^(1/5)-18x^(4/5)	$f (x) = 6 x^{\frac{1}{5}} - 18 x^{\frac{4}{5}}$
60098	Find the Antiderivative	f(x)=6x+5	$f (x) = 6 x + 5$
60099	Find the Antiderivative	f(x)=e^(11x)	$f (x) = e^{11 x}$
60100	Find the Antiderivative	r(t)=5/(t^2)	$r (t) = \frac{5}{t^{2}}$