Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
62401	Find the Area Under the Curve	f(x)=4-x^2 , [-2,2]	$f (x) = 4 - x^{2}$ , $[- 2, 2]$
62402	Evaluate Using Summation Formulas	sum from 1 to 3 of 1/2j(2j^2+3j+5)	$\sum_{1}^{3} \frac{1}{2} j (2 j^{2} + 3 j + 5)$
62403	Find the Area Under the Curve	f(x)=1/x-1/e ; [1,e^3]	$f (x) = \frac{1}{x} - \frac{1}{e}$ ; $[1, e^{3}]$
62404	Find the Area Under the Curve	f(x)=12-3x^2 ; [0,7]	$f (x) = 12 - 3 x^{2}$ ; $[0, 7]$
62405	Find the Area Under the Curve	f(x)=2e^x-1 ; [-2,4]	$f (x) = 2 e^{x} - 1$ ; $[- 2, 4]$
62406	Find the Area Under the Curve	f(x)=2x+7 ; [1,5]	$f (x) = 2 x + 7$ ; $[1, 5]$
62407	Find the Area Under the Curve	f(x)=16-x^2 ; [-1,8]	$f (x) = 16 - x^{2}$ ; $[- 1, 8]$
62408	Find the Area Under the Curve	f(x)=2x-16 ; [7,11]	$f (x) = 2 x - 16$ ; $[7, 11]$
62409	Evaluate Using Summation Formulas	sum from k=1 to n of (k^2)/3	$\sum_{k = 1}^{n} \frac{k^{2}}{3}$
62410	Evaluate Using Summation Formulas	sum from k=1 to n of (k^2)/5	$\sum_{k = 1}^{n} \frac{k^{2}}{5}$
62411	Find the Roots (Zeros)	x^2-3x+2=0	$x^{2} - 3 x + 2 = 0$
62412	Determine if True	log base 3 of 9=( log of 9)/( log of 3)	$\log_{3} (9) = \frac{\log (9)}{\log (3)}$
62413	Find the x and y Intercepts	(2x^2-8)/(x^2-16)	$\frac{2 x^{2} - 8}{x^{2} - 16}$
62414	Find the x and y Intercepts	(x-5)(x^2-10x-50)	$(x - 5) (x^{2} - 10 x - 50)$
62415	Find the x and y Intercepts	x^2+2x-15	$x^{2} + 2 x - 15$
62416	Find the Volume	y=2x^2 , y=2 square root of x	$y = 2 x^{2}$ , $y = 2 \sqrt{x}$
62417	Find the Volume	y=4x^2 , y=0 , x=3	$y = 4 x^{2}$ , $y = 0$ , $x = 3$
62418	Find the Volume	y=5x , y=5 , x=0	$y = 5 x$ , $y = 5$ , $x = 0$
62419	Find the Volume	x=2 square root of 5y , x=0 , y=5	$x = 2 \sqrt{5 y}$ , $x = 0$ , $y = 5$
62420	Find the Volume	x=y^2 , x=3y	$x = y^{2}$ , $x = 3 y$
62421	Find the Volume	y=1/9x^2 , x=5 , y=0	$y = \frac{1}{9} x^{2}$ , $x = 5$ , $y = 0$
62422	Find the Volume	y = square root of x , y=0 , x=3	$y = \sqrt{x}$ , $y = 0$ , $x = 3$
62423	Find the Volume	y=1/x , y=0 , x=1 , x=3	$y = \frac{1}{x}$ , $y = 0$ , $x = 1$ , $x = 3$
62424	Find the Volume	y = square root of 25-x^2 , y=0 , x=0 , x=5	$y = \sqrt{25 - x^{2}}$ , $y = 0$ , $x = 0$ , $x = 5$
62425	Find the x and y Intercepts	x+10	$x + 10$
62426	Find the x and y Intercepts	x^4-8x^2+1	$x^{4} - 8 x^{2} + 1$
62427	Find the Function	c'(x)=9x-4	$c' (x) = 9 x - 4$
62428	Find the x and y Intercepts	x^4-3x^2-2	$x^{4} - 3 x^{2} - 2$
62429	Find the x and y Intercepts	x^3-4x^2	$x^{3} - 4 x^{2}$
62430	Find the x and y Intercepts	x^3-3x^2+3	$x^{3} - 3 x^{2} + 3$
62431	Find the Function	f'(x)=8x^7	$f' (x) = 8 x^{7}$
62432	Find the Function	f'(x)=2x-7	$f' (x) = 2 x - 7$
62433	Find the Function	f''(x)=32x^3-15x^2+8x	$f'' (x) = 32 x^{3} - 15 x^{2} + 8 x$
62434	Find the Function	f'(x)=-2f(x)	$f' (x) = - 2 f (x)$
62435	Find the Function	f'(x)=10x-7	$f' (x) = 10 x - 7$
62436	Find the Function	f''(x)=-2+30x-12x^2	$f'' (x) = - 2 + 30 x - 12 x^{2}$
62437	Find the Function	f''(x)=x^6-4x^4+x+1	$f'' (x) = x^{6} - 4 x^{4} + x + 1$
62438	Find the Domain	f(x) = natural log of x^2-64	$f (x) = \ln (x^{2} - 64)$
62439	Find the Domain	g(x) = square root of 6+5x	$g (x) = \sqrt{6 + 5 x}$
62440	Find the Domain	g(x)=x/(x^2+12x+27)	$g (x) = \frac{x}{x^{2} + 12 x + 27}$
62441	Find the Domain	h(x)=1/( fourth root of x^2-8x)	$h (x) = \frac{1}{\sqrt[4]{x^{2} - 8 x}}$
62442	Find the Domain	f(x)=(2(x^2-9))/(x^2-4)	$f (x) = \frac{2 (x^{2} - 9)}{x^{2} - 4}$
62443	Find Where Increasing/Decreasing	x^3-11x^2+39x-47	$x^{3} - 11 x^{2} + 39 x - 47$
62444	Find the Standard Form of the Parabola	y^2+5x-2y-24=0	$y^{2} + 5 x - 2 y - 24 = 0$
62445	Find the Standard Form of the Parabola	y^2-3x-2y-17=0	$y^{2} - 3 x - 2 y - 17 = 0$
62446	Find the Domain	f(x) = natural log of 2-x	$f (x) = \ln (2 - x)$
62447	Find the Domain	f(x) = natural log of x^2-14x	$f (x) = \ln (x^{2} - 14 x)$
62448	Find the Domain	f(x)=10x^4-60x^2	$f (x) = 10 x^{4} - 60 x^{2}$
62449	Find the Domain	f(x) = log base 4 of x^2-1	$f (x) = \log_{4} (x^{2} - 1)$
62450	Find the Sum of the Infinite Geometric Series	1 , 1/9 , 1/81 , 1/729	$1$ , $\frac{1}{9}$ , $\frac{1}{81}$ , $\frac{1}{729}$
62451	Identify the Polar Equation	r=1+3sin(theta)	$r = 1 + 3 \sin (θ)$
62452	Identify the Polar Equation	r=4+2sin(theta)	$r = 4 + 2 \sin (θ)$
62453	Identify the Polar Equation	r=3+2sin(theta)	$r = 3 + 2 \sin (θ)$
62454	Identify the Polar Equation	r=4sec(theta)	$r = 4 \sec (θ)$
62455	Identify the Polar Equation	r=7csc(theta)	$r = 7 \csc (θ)$
62456	Identify the Polar Equation	r=9csc(theta)	$r = 9 \csc (θ)$
62457	Solve for t	40=10(1.17)^t	$40 = 10 {(1.17)}^{t}$
62458	Solve for t	4cos(t)=0	$4 \cos (t) = 0$
62459	Solve for t	300=100e^(0.02t)	$300 = 100 e^{0.02 t}$
62460	Solve for t	-3.73=131.6(0.752)^(t-35) natural log of 0.752	$- 3.73 = 131.6 {(0.752)}^{t - 35} \ln (0.752)$
62461	Solve for t	3=e^(0.06t)	$3 = e^{0.06 t}$
62462	Solve for t	-32t+32=0	$- 32 t + 32 = 0$
62463	Solve for t	2t-3=0	$2 t - 3 = 0$
62464	Solve for t	2t-5=0	$2 t - 5 = 0$
62465	Solve for t	-2t+8=0	$- 2 t + 8 = 0$
62466	Solve for t	-2t+9=0	$- 2 t + 9 = 0$
62467	Solve for t	25=40/(1+11e^(-0.08t))	$25 = \frac{40}{1 + 11 e^{- 0.08 t}}$
62468	Solve for t	224t-16t^2=0	$224 t - 16 t^{2} = 0$
62469	Solve for t	208-32t=0	$208 - 32 t = 0$
62470	Solve for t	21=5+36t-16t^2	$21 = 5 + 36 t - 16 t^{2}$
62471	Solve for t	20=6+31t-16t^2	$20 = 6 + 31 t - 16 t^{2}$
62472	Solve for t	2=e^(0.0375t)	$2 = e^{0.0375 t}$
62473	Solve for t	-16t^2+16t+80=0	$- 16 t^{2} + 16 t + 80 = 0$
62474	Solve for t	-16t^2+96t+112=0	$- 16 t^{2} + 96 t + 112 = 0$
62475	Solve for t	17=5+29t-16t^2	$17 = 5 + 29 t - 16 t^{2}$
62476	Solve for t	19=16t^2	$19 = 16 t^{2}$
62477	Solve for t	192-32t=0	$192 - 32 t = 0$
62478	Solve for t	0=-4.9t^2+40t	$0 = - 4.9 t^{2} + 40 t$
62479	Solve for t	10=20te^(-0.06t)	$10 = 20 t e^{- 0.06 t}$
62480	Solve for t	1000=100(1+0.06/4)^t	$1000 = 100 {(1 + \frac{0.06}{4})}^{t}$
62481	Solve for t	12e^(-t)cos(t)-12e^(-t)sin(t)=0	$12 e^{- t} \cos (t) - 12 e^{- t} \sin (t) = 0$
62482	Solve for t	14=20-15(2/3)^(t/25)	$14 = 20 - 15 {(\frac{2}{3})}^{\frac{t}{25}}$
62483	Solve for t	(1+0.70/365)^(365t)=2	${(1 + \frac{0.7}{365})}^{365 t} = 2$
62484	Solve for t	0=-16t^2+64t	$0 = - 16 t^{2} + 64 t$
62485	Solve for t	0=-16t^2+96t+112	$0 = - 16 t^{2} + 96 t + 112$
62486	Solve for t	0=-16t^2+96t+256	$0 = - 16 t^{2} + 96 t + 256$
62487	Solve for t	0=-32t+16	$0 = - 32 t + 16$
62488	Solve for s	(d^2s)/(dt^2)=64	$\frac{d^{2} s}{d t^{2}} = 64$
62489	Solve for r	r^2-6r+9=0	$r^{2} - 6 r + 9 = 0$
62490	Solve for r	r^4=16	$r^{4} = 16$
62491	Solve for r	r^2+8r+16=0	$r^{2} + 8 r + 16 = 0$
62492	Solve for t	(t+5)^2+42=13(t+5)	${(t + 5)}^{2} + 42 = 13 (t + 5)$
62493	Solve for s	s=-4/(1-0.5)	$s = \frac{- 4}{(1 - 0.5)}$
62494	Solve for s	2s-21296/(s^2)=0	$2 s - \frac{21296}{s^{2}} = 0$
62495	Solve for s	(ds)/(dt)=36t(9t^2-7)^3	$\frac{d s}{d t} = 36 t {(9 t^{2} - 7)}^{3}$
62496	Solve for n	a_n=17-5n	$a_{n} = 17 - 5 n$
62497	Solve for n	a_n=4n-2	$a_{n} = 4 n - 2$
62498	Solve for n	-e^(n+7)=-5	$- e^{n + 7} = - 5$
62499	Solve for n	n^2+2n+1=0	$n^{2} + 2 n + 1 = 0$
62500	Solve for p	(dp)/(dt)=kP	$\frac{d p}{d t} = k P$