Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
60401	Find the Derivative - d/dt	96-32t	$96 - 32 t$
60402	Find the Derivative - d/dt	(t^5 natural log of t)	$(t^{5} \ln (t))$
60403	Find the Derivative - d/dt	-(t+1)sin((t^2)/2)	$- (t + 1) \sin (\frac{t^{2}}{2})$
60404	Find the Derivative - d/dt	(e^(7t)+e^(-7t))/(e^(5t))	$\frac{e^{7 t} + e^{- 7 t}}{e^{5 t}}$
60405	Find the Derivative - d/dr	(4pir^3)/3	$\frac{4 π r^{3}}{3}$
60406	Find the Derivative - d/dr	(d^2)/(dr^2)(pir^2)	$\frac{d^{2}}{d r^{2}} (π r^{2})$
60407	Find the Derivative - d/df	f'(1)	$f' (1)$
60408	Find the Derivative - d/da	a^3	$a^{3}$
60409	Find the Derivative - d/da	ax^2+bx+c	$a x^{2} + b x + c$
60410	Find the Derivative - d/da	ax^3+bx^2+cx+d	$a x^{3} + b x^{2} + c x + d$
60411	Find the Area Between the Curves	y=2x-x^2 , y=-2x	$y = 2 x - x^{2}$ , $y = - 2 x$
60412	Find the Area Between the Curves	y=2 square root of x , y=(x^2)/4	$y = 2 \sqrt{x}$ , $y = \frac{x^{2}}{4}$
60413	Find the Area Between the Curves	y=20x , y=x^2	$y = 20 x$ , $y = x^{2}$
60414	Find the Area Between the Curves	y=3/x , y=12x , y=1/3x	$y = \frac{3}{x}$ , $y = 12 x$ , $y = \frac{1}{3} x$
60415	Find the Area Between the Curves	y=8x-x^2 , y=2x	$y = 8 x - x^{2}$ , $y = 2 x$
60416	Find the Area Between the Curves	y=7x , y=x^2	$y = 7 x$ , $y = x^{2}$
60417	Find the Area Between the Curves	y=4x-x^2 , y=-4x	$y = 4 x - x^{2}$ , $y = - 4 x$
60418	Find the Area Between the Curves	y=4x^2 ; y=36	$y = 4 x^{2}$ ; $y = 36$
60419	Find the Area Between the Curves	x=-5 , x=2 , y=10x , y=x^2-11	$x = - 5$ , $x = 2$ , $y = 10 x$ , $y = x^{2} - 11$
60420	Find the Area Between the Curves	x=-2 , x=1 , y=11x , y=x^2-12	$x = - 2$ , $x = 1$ , $y = 11 x$ , $y = x^{2} - 12$
60421	Find the Area Between the Curves	y=x^2-3 , y=1	$y = x^{2} - 3$ , $y = 1$
60422	Find the Area Between the Curves	y=x^2-4 , y=5	$y = x^{2} - 4$ , $y = 5$
60423	Find the Area Between the Curves	y=-x^2+2x , y=0	$y = - x^{2} + 2 x$ , $y = 0$
60424	Find the Area Between the Curves	y=x^2-1 , y=3	$y = x^{2} - 1$ , $y = 3$
60425	Find the Area Between the Curves	y=x^2-28 , y=7-2x	$y = x^{2} - 28$ , $y = 7 - 2 x$
60426	Find the Domain and Range	y=(2x^2)/(x^2-1)	$y = \frac{2 x^{2}}{x^{2} - 1}$
60427	Find the Second Derivative	y = fourth root of x	$y = \sqrt[4]{x}$
60428	Find the Second Derivative	s=6t^3-3t^6	$s = 6 t^{3} - 3 t^{6}$
60429	Find the Second Derivative	x^2+6y^2=6	$x^{2} + 6 y^{2} = 6$
60430	Write in Exponential Form	3 = log base 8 of 512	$3 = \log_{8} (512)$
60431	Find the Inflection Points	f(x)=4x^3-48x-4	$f (x) = 4 x^{3} - 48 x - 4$
60432	Find the Inflection Points	f(x)=x^4-8x^2+1	$f (x) = x^{4} - 8 x^{2} + 1$
60433	Find the Inflection Points	f(x)=x^6-10x^4	$f (x) = x^{6} - 10 x^{4}$
60434	Find the Inflection Points	f(x)=x^3-12x^2+36x	$f (x) = x^{3} - 12 x^{2} + 36 x$
60435	Find the Inflection Points	f(x) = natural log of x^2-2x+10	$f (x) = \ln (x^{2} - 2 x + 10)$
60436	Solve for B	(B/(2x^3+14x^2))÷((5x-35)/(10x^2-490))=1	$\frac{B}{2 x^{3} + 14 x^{2}} \div \frac{5 x - 35}{10 x^{2} - 490} = 1$
60437	Solve for t	e^( fourth root of t)=x^4	$e^{\sqrt[4]{t}} = x^{4}$
60438	Solve for y	8^2+y^2=289	$8^{2} + y^{2} = 289$
60439	Solve for y	x=2 square root of 5y	$x = 2 \sqrt{5 y}$
60440	Solve for y	2x-y=3	$2 x - y = 3$
60441	Solve for y	(dy)/(dx)=8x^7y	$\frac{d y}{d x} = 8 x^{7} y$
60442	Solve for y	(dy)/(dx)=3x^2y	$\frac{d y}{d x} = 3 x^{2} y$
60443	Solve for k	T=2pi square root of m/k	$T = 2 π \sqrt{\frac{m}{k}}$
60444	Solve for n	sum from n=1 to infinity of (-144)(1/2)^(n-1)	$\sum_{n = 1}^{\infty} (- 144) {(\frac{1}{2})}^{n - 1}$
60445	Solve for c	4^2+5^2=c^2	$4^{2} + 5^{2} = c^{2}$
60446	Solve for c	c=(577sin(4.8 degrees ))/(sin(86.2 degrees ))	$c = \frac{577 \sin (4.8 °)}{\sin (86.2 °)}$
60447	Solve for h	h(x)=6x+1	$h (x) = 6 x + 1$
60448	Solve for P	P(14)=5000e^(( natural log of 29/25)/2(14))	$P (14) = 5000 e^{\frac{\ln (\frac{29}{25})}{2} (14)}$
60449	Solve for t	0=-16t^2+96t+640	$0 = - 16 t^{2} + 96 t + 640$
60450	Solve for t	176t-16t^2=0	$176 t - 16 t^{2} = 0$
60451	Solve for t	-16t^2+96t+432=0	$- 16 t^{2} + 96 t + 432 = 0$
60452	Solve for t	36=12(1.25)^t	$36 = 12 {(1.25)}^{t}$
60453	Solve for t	4 fourth root of t^3=0	$4 \sqrt[4]{t^{3}} = 0$
60454	Solve for t	4000=2000(1+0.033/2)^(2t)	$4000 = 2000 {(1 + \frac{0.033}{2})}^{2 t}$
60455	Find the Antiderivative	(dy)/(dx)=(2y)/(2x+1)	$\frac{d y}{d x} = \frac{2 y}{2 x + 1}$
60456	Find the Foci	((x+4)^2)/9-((y+3)^2)/16=1	$\frac{{(x + 4)}^{2}}{9} - \frac{{(y + 3)}^{2}}{16} = 1$
60457	Find the Maximum/Minimum Value	x+25/x	$x + \frac{25}{x}$
60458	Find the Maximum/Minimum Value	x^3e^(-x)	$x^{3} e^{- x}$
60459	Find the Area Under the Curve	y=3/x ; [1,10]	$y = \frac{3}{x}$ ; $[1, 10]$
60460	Find the Area Under the Curve	y=5/x ; [1,10]	$y = \frac{5}{x}$ ; $[1, 10]$
60461	Find the Asymptotes	f(x)=(6x)/(x^2-36)	$f (x) = \frac{6 x}{x^{2} - 36}$
60462	Find the Asymptotes	f(x)=1/(x^2-81)	$f (x) = \frac{1}{x^{2} - 81}$
60463	Find the Area Under the Curve	y=x^4 ; [1,2]	$y = x^{4}$ ; $[1, 2]$
60464	Find the Focus	x=2y^2	$x = 2 y^{2}$
60465	Find the Domain	g(x) = square root of 3+8x	$g (x) = \sqrt{3 + 8 x}$
60466	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of 7xe^(1/x)-7x	$lim_{x \to \infty} 7 x e^{\frac{1}{x}} - 7 x$
60467	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of e^x+3x^2-4x^3	$lim_{x \to \infty} e^{x} + 3 x^{2} - 4 x^{3}$
60468	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of 3xe^(1/x)-3x	$lim_{x \to \infty} 3 x e^{\frac{1}{x}} - 3 x$
60469	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of (x^2+1)/(x^(5/3)+6)	$lim_{x \to \infty} \frac{x^{2} + 1}{x^{\frac{5}{3}} + 6}$
60470	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (cos(5x)-1)/(x^2)	$lim_{x \to 0} \frac{\cos (5 x) - 1}{x^{2}}$
60471	Evaluate Using L'Hospital's Rule	limit as theta approaches pi/2 of (1-sin(theta))/(1+cos(6theta))	$lim_{θ \to \frac{π}{2}} \frac{1 - \sin (θ)}{1 + \cos (6 θ)}$
60472	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (16e^(x/4)-16-4x-1/2x^2)/(x^3)	$lim_{x \to 0} \frac{16 e^{\frac{x}{4}} - 16 - 4 x - \frac{1}{2} x^{2}}{x^{3}}$
60473	Evaluate Using L'Hospital's Rule	limit as x approaches 1 of ( natural log of x)/(19x-x^2-18)	$lim_{x \to 1} \frac{(\ln (x))}{19 x - x^{2} - 18}$
60474	Find Where Increasing/Decreasing Using Derivatives	f(x)=1/(x+5)	$f (x) = \frac{1}{x + 5}$
60475	Find Where Increasing/Decreasing Using Derivatives	f(x)=6x^6-11x^5	$f (x) = 6 x^{6} - 11 x^{5}$
60476	Find Where Increasing/Decreasing Using Derivatives	f(x)=x^3+x^2-8x+5	$f (x) = x^{3} + x^{2} - 8 x + 5$
60477	Find Where Increasing/Decreasing Using Derivatives	f(x)=e^(7x)+e^(-x)	$f (x) = e^{7 x} + e^{- x}$
60478	Find Where Increasing/Decreasing Using Derivatives	f(x)=2x^3-3x^2-36x	$f (x) = 2 x^{3} - 3 x^{2} - 36 x$
60479	Find Where Increasing/Decreasing Using Derivatives	f(x)=2x^3-3x^2-72x	$f (x) = 2 x^{3} - 3 x^{2} - 72 x$
60480	Find Where Increasing/Decreasing Using Derivatives	f(x)=x^3-27x-7	$f (x) = x^{3} - 27 x - 7$
60481	Find the Vertices	(x^2)/25+(y^2)/81=1	$\frac{x^{2}}{25} + \frac{y^{2}}{81} = 1$
60482	Find the x and y Intercepts	6x^4+8x^3	$6 x^{4} + 8 x^{3}$
60483	Find the Maximum/Minimum Value	f(x)=x^2-4x+1	$f (x) = x^{2} - 4 x + 1$
60484	Find the Maximum/Minimum Value	f(x)=x^3-6x^2+9x	$f (x) = x^{3} - 6 x^{2} + 9 x$
60485	Convert to Rectangular Coordinates	(5,30 degrees )	$(5, 30 °)$
60486	Convert to Rectangular Coordinates	(3,(7pi)/4)	$(3, \frac{7 π}{4})$
60487	Find the Critical Points	g(y)=(y-1)/(y^2-y+1)	$g (y) = \frac{y - 1}{y^{2} - y + 1}$
60488	Find the Critical Points	f(x)=x^3-48x	$f (x) = x^{3} - 48 x$
60489	Find the Critical Points	f(x)=x^3-12x+4	$f (x) = x^{3} - 12 x + 4$
60490	Find the Critical Points	f(x)=x^2-6x+5	$f (x) = x^{2} - 6 x + 5$
60491	Find the Critical Points	f(x)=x^3+12x-4	$f (x) = x^{3} + 12 x - 4$
60492	Find the Critical Points	f(x)=4x^3-3x^4	$f (x) = 4 x^{3} - 3 x^{4}$
60493	Find the Critical Points	f(x)=3x-5	$f (x) = 3 x - 5$
60494	Find the Critical Points	f(x)=10x^3+30x^2-720x+93	$f (x) = 10 x^{3} + 30 x^{2} - 720 x + 93$
60495	Find the Critical Points	f(x)=2x^3-15x^2+24x	$f (x) = 2 x^{3} - 15 x^{2} + 24 x$
60496	Find the Critical Points	f(x)=2x^3-15x^2+36x+1	$f (x) = 2 x^{3} - 15 x^{2} + 36 x + 1$
60497	Find the Local Maxima and Minima	x square root of 15-x	$x \sqrt{15 - x}$
60498	Find the Local Maxima and Minima	x square root of 81-x^2	$x \sqrt{81 - x^{2}}$
60499	Find the Local Maxima and Minima	5x^4-10x^2+15	$5 x^{4} - 10 x^{2} + 15$
60500	Find the Inverse	y=7^x	$y = 7^{x}$