Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
60601	Evaluate from the Right	limit as x approaches infinity of x^(1/x)	$lim_{x \to \infty} x^{\frac{1}{x}}$
60602	Find the Area Between the Curves	y=x^4-2x^3 , y=0	$y = x^{4} - 2 x^{3}$ , $y = 0$
60603	Find the Area Between the Curves	y=-x^3+x^2+16x , y=4x	$y = - x^{3} + x^{2} + 16 x$ , $y = 4 x$
60604	Find the Area Between the Curves	y=x^2+1 ; y=2x-2 ; -1<=x<=2	$y = x^{2} + 1$ ; $y = 2 x - 2$ ; $- 1 \leq x \leq 2$
60605	Find the Area Between the Curves	y=x^2 ; y=8-x^2 ; y=4x+12	$y = x^{2}$ ; $y = 8 - x^{2}$ ; $y = 4 x + 12$
60606	Find the Area Between the Curves	x=-2 , x=1 , y=3x , y=x^2-4	$x = - 2$ , $x = 1$ , $y = 3 x$ , $y = x^{2} - 4$
60607	Find the Area Between the Curves	x=-5 , x=2 , y=6x , y=x^2-7	$x = - 5$ , $x = 2$ , $y = 6 x$ , $y = x^{2} - 7$
60608	Find the Area Between the Curves	y=4-x^2 , y=0	$y = 4 - x^{2}$ , $y = 0$
60609	Find the Area Between the Curves	y=5x , y=x^2	$y = 5 x$ , $y = x^{2}$
60610	Find the Area Between the Curves	y=6x^2-18x , y=-6x	$y = 6 x^{2} - 18 x$ , $y = - 6 x$
60611	Find the Area Between the Curves	y=6x-x^2 , y=-2x	$y = 6 x - x^{2}$ , $y = - 2 x$
60612	Find the Area Between the Curves	x=y^2-6y , x=y-y^2	$x = y^{2} - 6 y$ , $x = y - y^{2}$
60613	Find the Area Between the Curves	y = square root of x , x=0 , y=2 , y=9	$y = \sqrt{x}$ , $x = 0$ , $y = 2$ , $y = 9$
60614	Find the Area Between the Curves	y=\|7x\| , y=x^2-8	$y = \| 7 x \|$ , $y = x^{2} - 8$
60615	Find the Area Between the Curves	y=11x , y=x^2	$y = 11 x$ , $y = x^{2}$
60616	Find the Area Between the Curves	y=14x , y=x^2	$y = 14 x$ , $y = x^{2}$
60617	Find the Maximum/Minimum Value	f(x,y)=x^2+xy+y^2-4y+5	$f (x, y) = x^{2} + x y + y^{2} - 4 y + 5$
60618	Find the Local Maxima and Minima	f(x,y)=20xy-x^3-10y^2	$f (x, y) = 20 x y - x^{3} - 10 y^{2}$
60619	Find the Local Maxima and Minima	f(x,y)=x^2+xy+y^2-3x+2	$f (x, y) = x^{2} + x y + y^{2} - 3 x + 2$
60620	Find the Maximum/Minimum Value	y=x^2-4x+3	$y = x^{2} - 4 x + 3$
60621	Find the Maximum/Minimum Value	y=x^2-6x+5	$y = x^{2} - 6 x + 5$
60622	Find the Maximum/Minimum Value	y=3x^(2/3)-2x	$y = 3 x^{\frac{2}{3}} - 2 x$
60623	Find the Local Maxima and Minima	f(x,y)=x^3+y^3-30xy	$f (x, y) = x^{3} + y^{3} - 30 x y$
60624	Find the Local Maxima and Minima	y=f'(x)	$y = f' (x)$
60625	Find the Local Maxima and Minima	y=x^2-8x+15	$y = x^{2} - 8 x + 15$
60626	Find the Local Maxima and Minima	y=x^3-3x^2-1	$y = x^{3} - 3 x^{2} - 1$
60627	Find the Local Maxima and Minima	y=x^3-6x^2-63x	$y = x^{3} - 6 x^{2} - 63 x$
60628	Find the Local Maxima and Minima	y=x^5-5x	$y = x^{5} - 5 x$
60629	Find the Local Maxima and Minima	y=x^4-8x^2	$y = x^{4} - 8 x^{2}$
60630	Find the Derivative - d/dh	pir square root of r^2+h^2	$π r \sqrt{r^{2} + h^{2}}$
60631	Find the Derivative - d/dh	h/3	$\frac{h}{3}$
60632	Find the Derivative - d/dd	d/(dx)x^3	$\frac{d}{d x} x^{3}$
60633	Find the Derivative - d/db	1/2bh	$\frac{1}{2} b h$
60634	Find the Derivative - d/dr	5/(r^3)	$\frac{5}{r^{3}}$
60635	Find the Derivative - d/dq	q = square root of 12r-r^3	$q = \sqrt{12 r - r^{3}}$
60636	Find the Derivative - d/dt	(e^(8t)+e^(-8t))/(e^(6t))	$\frac{e^{8 t} + e^{- 8 t}}{e^{6 t}}$
60637	Find the Derivative - d/dt	(t^2)/4	$\frac{t^{2}}{4}$
60638	Find the Derivative - d/dt	(t^3)/3	$\frac{t^{3}}{3}$
60639	Find the Derivative - d/dt	( square root of t)/(2t-7)	$\frac{\sqrt{t}}{2 t - 7}$
60640	Find the Derivative - d/dt	(800t)/(t+2)	$\frac{800 t}{t + 2}$
60641	Find the Derivative - d/dt	7-(1.01)^(-t^2)	$7 - {(1.01)}^{- t^{2}}$
60642	Find the Derivative - d/dt	8cos(t)	$8 \cos (t)$
60643	Find the Derivative - d/dt	-2sin(2t)	$- 2 \sin (2 t)$
60644	Find the Derivative - d/dt	fifth root of t-5e^t	$\sqrt[5]{t} - 5 e^{t}$
60645	Find the Derivative - d/dt	square root of 1+t	$\sqrt{1 + t}$
60646	Find the Derivative - d/dt	10 square root of t	$10 \sqrt{t}$
60647	Find the Derivative - d/dt	e^(-4t)	$e^{- 4 t}$
60648	Find the Derivative - d/dt	e^(-6/(t^7))	$e^{- \frac{6}{t^{7}}}$
60649	Find the Derivative - d/dt	e^(-st)	$e^{- s t}$
60650	Find the Derivative - d/dt	sin(4t)	$\sin (4 t)$
60651	Find the Derivative - d/dt	t( natural log of 5t)^2	$t \ln^{2} (5 t)$
60652	Find the Derivative - d/dt	sin(t)-cos(t)	$\sin (t) - \cos (t)$
60653	Find the Derivative - d/dt	t^5	$t^{5}$
60654	Find the Second Derivative	f(x)=5/2x^2-e^x	$f (x) = \frac{5}{2} x^{2} - e^{x}$
60655	Find the Second Derivative	f(x)=e^(2x)	$f (x) = e^{2 x}$
60656	Find the Second Derivative	f(x)=-7x^9+5x^2	$f (x) = - 7 x^{9} + 5 x^{2}$
60657	Find the Second Derivative	f(x)=(x^3)/3-2x^2-32x	$f (x) = \frac{x^{3}}{3} - 2 x^{2} - 32 x$
60658	Find the Second Derivative	f(x)=(x^2-2x)/(x+1)	$f (x) = \frac{x^{2} - 2 x}{x + 1}$
60659	Solve by Substitution	5x^2-y^2=89 , xy=30	$5 x^{2} - y^{2} = 89$ , $x y = 30$
60660	Find the Foci	(y^2)/25-(x^2)/9=1	$\frac{y^{2}}{25} - \frac{x^{2}}{9} = 1$
60661	Identify the Polar Equation	r=5csc(theta)	$r = 5 \csc (θ)$
60662	Identify the Polar Equation	r=7cos(theta)	$r = 7 \cos (θ)$
60663	Find the Difference Quotient	f(x)=-3x	$f (x) = - 3 x$
60664	Find the Asymptotes	(3x-3)/(x^2-4)	$\frac{3 x - 3}{x^{2} - 4}$
60665	Solve for t	192t-16t^2=0	$192 t - 16 t^{2} = 0$
60666	Solve for t	16000000000=5915000e^(0.049t)	$16000000000 = 5915000 e^{0.049 t}$
60667	Solve for t	160t-16t^2=0	$160 t - 16 t^{2} = 0$
60668	Solve for s	8s^-0.75-1=0	$8 s^{- 0.75} - 1 = 0$
60669	Solve for k	sum from k=0 to 10 of 3(1/2)^k	$\sum_{k = 0}^{10} 3 {(\frac{1}{2})}^{k}$
60670	Solve for c	2000=-18000(0+64)^(-1/2)+c	$2000 = - 18000 {(0 + 64)}^{- \frac{1}{2}} + c$
60671	Solve for n	sum from i=1 to n of (4i+7)/(n^2)	$\sum_{i = 1}^{n} \frac{4 i + 7}{n^{2}}$
60672	Solve for y	y/6-3=5-5/6y	$\frac{y}{6} - 3 = 5 - \frac{5}{6} y$
60673	Solve for y	2x+3y=11	$2 x + 3 y = 11$
60674	Solve for y	x=4y-y^2	$x = 4 y - y^{2}$
60675	Solve for y	x=y^(3/2)	$x = y^{\frac{3}{2}}$
60676	Solve for y	x=y^2-1	$x = y^{2} - 1$
60677	Solve for y	-3(y-5)=24	$- 3 (y - 5) = 24$
60678	Solve for y	4x+y^2=12	$4 x + y^{2} = 12$
60679	Solve for y	4x+3y=24	$4 x + 3 y = 24$
60680	Solve for t	x=e^(-t)	$x = e^{- t}$
60681	Solve for t	y=m/(1+ce^(-kmt))	$y = \frac{m}{1 + c e^{- km t}}$
60682	Solve for u	3u^2=24u-6	$3 u^{2} = 24 u - 6$
60683	Solve for t	x = square root of t	$x = \sqrt{t}$
60684	Solve for t	c(t)=3te^(-1/30t)	$c (t) = 3 t e^{- \frac{1}{30} t}$
60685	Solve for t	6=10e^(-0.11t)	$6 = 10 e^{(- 0.11 t)}$
60686	Solve for x	square root of x+3=8	$\sqrt{x} + 3 = 8$
60687	Solve for y	(dy)/(dt)=63t^6	$\frac{d y}{d t} = 63 t^{6}$
60688	Solve for y	(dy)/(dx)=1/x	$\frac{d y}{d x} = \frac{1}{x}$
60689	Solve for y	(dy)/(dx)=(5y)/x	$\frac{d y}{d x} = \frac{5 y}{x}$
60690	Solve for z	z^2+10z+5=80	$z^{2} + 10 z + 5 = 80$
60691	Solve for y	x=y-y^2	$x = y - y^{2}$
60692	Solve for y	x=y^2-2y	$x = y^{2} - 2 y$
60693	Solve for y	y=2^(5(-1))*3^(4(-1)^2)	$y = 2^{5 (- 1)} \cdot 3^{4 {(- 1)}^{2}}$
60694	Find the Asymptotes	y=x^3+3x^2	$y = x^{3} + 3 x^{2}$
60695	Find the Asymptotes	y=(x^2+5x)/(25-x^2)	$y = \frac{x^{2} + 5 x}{25 - x^{2}}$
60696	Solve for b	b^2+5b-35=3b	$b^{2} + 5 b - 35 = 3 b$
60697	Convert to Radical Form	2x^(3/2)	$2 x^{\frac{3}{2}}$
60698	Find the Area Under the Curve	y=64-x^3 , [2,4]	$y = 64 - x^{3}$ , $[2, 4]$
60699	Find the Maximum/Minimum Value	x^3-3/2x^2	$x^{3} - \frac{3}{2} x^{2}$
60700	Find the Area Under the Curve	y=2/x ; [1,6]	$y = \frac{2}{x}$ ; $[1, 6]$