Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
20401	Evaluate the Limit	( limit as x approaches pi/4 of 1-tan(x))/(sin(x)-cos(x))	$\frac{lim_{x \to \frac{π}{4}} 1 - \tan (x)}{\sin (x) - \cos (x)}$
20402	Find the Tangent Line at the Point	A^5+B^5=244 , (3,244)	$A^{5} + B^{5} = 244$ , $(3, 244)$
20403	Find the Tangent Line at the Point	x^2y^2=49 , (1,7)	$x^{2} y^{2} = 49$ , $(1, 7)$
20404	Find the Tangent Line at the Point	x^2y^2=64 , (-1,-8)	$x^{2} y^{2} = 64$ , $(- 1, - 8)$
20405	Find the Tangent Line at the Point	(dy)/(dx)=4x-7 , (4,5)	$\frac{d y}{d x} = 4 x - 7$ , $(4, 5)$
20406	Find the Tangent Line at the Point	(dy)/(dx)=5x-4 , (2,3)	$\frac{d y}{d x} = 5 x - 4$ , $(2, 3)$
20407	Find the Tangent Line at the Point	(dy)/(dx)=3x-6 , (3,4)	$\frac{d y}{d x} = 3 x - 6$ , $(3, 4)$
20408	Find the Tangent Line at the Point	cube root of x+ cube root of y^4=2 , (1,1)	$\sqrt[3]{x} + \sqrt[3]{y^{4}} = 2$ , $(1, 1)$
20409	Find the Tangent Line at the Point	x^2y^2=16 , (-1,-4)	$x^{2} y^{2} = 16$ , $(- 1, - 4)$
20410	Find the Tangent Line at the Point	x^2y^2=25 , (1,-5)	$x^{2} y^{2} = 25$ , $(1, - 5)$
20411	Find the Tangent Line at the Point	x^2y^2=36 , (-1,-6)	$x^{2} y^{2} = 36$ , $(- 1, - 6)$
20412	Find the Tangent Line at the Point	(dy)/(dt)=1/4t , (0,15)	$\frac{d y}{d t} = \frac{1}{4} t$ , $(0, 15)$
20413	Find the Tangent Line at the Point	sin(y)=5x^4-5 , (1,pi)	$\sin (y) = 5 x^{4} - 5$ , $(1, π)$
20414	Find the Tangent Line at the Point	(dy)/(dx)=2x-3 , (4,5)	$\frac{d y}{d x} = 2 x - 3$ , $(4, 5)$
20415	Find the Tangent Line at the Point	(dy)/(dx)=2x-5 , (2,3)	$\frac{d y}{d x} = 2 x - 5$ , $(2, 3)$
20416	Find the Tangent Line at the Point	(x^2)/2+(y^2)/8=16 , (4,8)	$\frac{x^{2}}{2} + \frac{y^{2}}{8} = 16$ , $(4, 8)$
20417	Find the Tangent Line at the Point	x^2+xy-y^2=11 , (3,1)	$x^{2} + x y - y^{2} = 11$ , $(3, 1)$
20418	Find the Tangent Line at the Point	x^2+xy-y^2=-11 , (1,4)	$x^{2} + x y - y^{2} = - 11$ , $(1, 4)$
20419	Find the Tangent Line at the Point	x^3+y^3=65 , (4,1)	$x^{3} + y^{3} = 65$ , $(4, 1)$
20420	Find the Tangent Line at the Point	x^2+y^2=32 , (-4,4)	$x^{2} + y^{2} = 32$ , $(- 4, 4)$
20421	Find the Tangent Line at the Point	x^2+y^2=25 , (4,3)	$x^{2} + y^{2} = 25$ , $(4, 3)$
20422	Find the Tangent Line at the Point	x^2+y^2=41 , (-5,4)	$x^{2} + y^{2} = 41$ , $(- 5, 4)$
20423	Find the Tangent Line at the Point	x^2+y^2=36 , (-2,-3)	$x^{2} + y^{2} = 36$ , $(- 2, - 3)$
20424	Find the Tangent Line at the Point	x^2+y^2-2x+4y=8 , (4,0)	$x^{2} + y^{2} - 2 x + 4 y = 8$ , $(4, 0)$
20425	Find the Tangent Line at the Point	x^2+4xy+y^2=13 , (2,1)	$x^{2} + 4 x y + y^{2} = 13$ , $(2, 1)$
20426	Find the Tangent Line at the Point	x^2+xy-y^2=-1 , (3,5)	$x^{2} + x y - y^{2} = - 1$ , $(3, 5)$
20427	Find the Tangent Line at the Point	y^2=(x^2)/(xy-1024)*(at) , (256,8)	$y^{2} = \frac{x^{2}}{x y - 1024} \cdot (a t)$ , $(256, 8)$
20428	Find the Tangent Line at the Point	y^2=x^3+3x^2 , (1,2)	$y^{2} = x^{3} + 3 x^{2}$ , $(1, 2)$
20429	Find the Tangent Line at the Point	y^2(y^2-16)=x^2(x^2-17) , (0,-4)	$y^{2} (y^{2} - 16) = x^{2} (x^{2} - 17)$ , $(0, - 4)$
20430	Find the Tangent Line at the Point	y^2=4x , (1,2)	$y^{2} = 4 x$ , $(1, 2)$
20431	Find the Tangent Line at the Point	y^2=5x^4-x^2 , (-1,2)	$y^{2} = 5 x^{4} - x^{2}$ , $(- 1, 2)$
20432	Find the Tangent Line at the Point	x^4y^4=16 , (2,1)	$x^{4} y^{4} = 16$ , $(2, 1)$
20433	Find the Tangent Line at the Point	xe^y+ye^x=1 , (0,1)	$x e^{y} + y e^{x} = 1$ , $(0, 1)$
20434	Find the Tangent Line at the Point	y=x^2+3 , (-4,19)	$y = x^{2} + 3$ , $(- 4, 19)$
20435	Find the Tangent Line at the Point	y=x^2-1 , (5,24)	$y = x^{2} - 1$ , $(5, 24)$
20436	Find the Tangent Line at the Point	y = fourth root of x , (1,1)	$y = \sqrt[4]{x}$ , $(1, 1)$
20437	Find the Tangent Line at the Point	y=x^2-x^4 , (1,0)	$y = x^{2} - x^{4}$ , $(1, 0)$
20438	Find the Tangent Line at the Point	y=x^2+5 , (-2,9)	$y = x^{2} + 5$ , $(- 2, 9)$
20439	Find dy/dx	x^2y^2=64	$x^{2} y^{2} = 64$
20440	Find the Tangent Line at the Point	y=x^3 , (1,1)	$y = x^{3}$ , $(1, 1)$
20441	Find the Tangent Line at the Point	y=x^3 , (-1,-1)	$y = x^{3}$ , $(- 1, - 1)$
20442	Find the Tangent Line at the Point	y=x^3-16x+5 , (4,5)	$y = x^{3} - 16 x + 5$ , $(4, 5)$
20443	Find the Tangent Line at the Point	y=x^3 , (-2,-8)	$y = x^{3}$ , $(- 2, - 8)$
20444	Find the Tangent Line at the Point	y=x^2+4 , (-1,5)	$y = x^{2} + 4$ , $(- 1, 5)$
20445	Find the Tangent Line at the Point	y=x^2+4 , (3,13)	$y = x^{2} + 4$ , $(3, 13)$
20446	Find the Tangent Line at the Point	y=x^2-5 , (2,-1)	$y = x^{2} - 5$ , $P (2, - 1)$
20447	Find the Tangent Line at the Point	y=x^2-5x-2 , (3,-8)	$y = x^{2} - 5 x - 2$ , $(3, - 8)$
20448	Find the Tangent Line at the Point	y=( square root of x)/(x+3) , (1,0.25)	$y = \frac{\sqrt{x}}{x + 3}$ , $(1, 0.25)$
20449	Find the Tangent Line at the Point	y=( square root of x)/(x+9) , (1,0.1)	$y = \frac{\sqrt{x}}{x + 9}$ , $(1, 0.1)$
20450	Find the Tangent Line at the Point	4xy^3+5xy=36 , (4,1)	$4 x y^{3} + 5 x y = 36$ , $(4, 1)$
20451	Find the Tangent Line at the Point	48(x^2+y^2)^2=625xy^2 , (3,4)	$48 {(x^{2} + y^{2})}^{2} = 625 x y^{2}$ , $(3, 4)$
20452	Find the Tangent Line at the Point	y=(x^2-1)/(x^2+x+1) , (1,0)	$y = \frac{x^{2} - 1}{x^{2} + x + 1}$ , $(1, 0)$
20453	Find the Tangent Line at the Point	y=(1+5x)^15 , (0,1)	$y = {(1 + 5 x)}^{15}$ , $(0, 1)$
20454	Find the Tangent Line at the Point	y=(2x+1)/(x+2) , (1,1)	$y = \frac{2 x + 1}{x + 2}$ , $(1, 1)$
20455	Find the Tangent Line at the Point	y=(3x)/(x-2) , (4,6)	$y = \frac{3 x}{x - 2}$ , $(4, 6)$
20456	Find the Tangent Line at the Point	y=(5x)/(x-3) , (4,20)	$y = \frac{5 x}{x - 3}$ , $(4, 20)$
20457	Find the Tangent Line at the Point	y=(7x)/(x-3)*(at) , (6,14)	$y = \frac{7 x}{x - 3} \cdot (a t)$ , $(6, 14)$
20458	Find the Tangent Line at the Point	y=36/(x^2+2) , (1,12)	$y = \frac{36}{x^{2} + 2}$ , $(1, 12)$
20459	Find the Tangent Line at the Point	y=(3x)/((2x-5)^2) , (2,6)	$y = \frac{3 x}{{(2 x - 5)}^{2}}$ , $(2, 6)$
20460	Find the Tangent Line at the Point	y = square root of 2x , (32,8)	$y = \sqrt{2 x}$ , $(32, 8)$
20461	Find the Tangent Line at the Point	y = square root of x , (4,2)	$y = \sqrt{x}$ , $(4, 2)$
20462	Find the Tangent Line at the Point	y=8/(sin(x)+cos(x)) , (0,8)	$y = \frac{8}{\sin (x) + \cos (x)}$ , $(0, 8)$
20463	Find the Tangent Line at the Point	y = square root of 7x , (7,7)	$y = \sqrt{7 x}$ , $(7, 7)$
20464	Find the Tangent Line at the Point	y=(8x)/(x^2+1) , (1,4)	$y = \frac{8 x}{x^{2} + 1}$ , $(1, 4)$
20465	Find the Tangent Line at the Point	y=e^(sin(h(x))) , (0,1)	$y = e^{\sinh (x)}$ , $(0, 1)$
20466	Find the Tangent Line at the Point	y=(x^3-16x)^10 , (4,0)	$y = {(x^{3} - 16 x)}^{10}$ , $(4, 0)$
20467	Find the Tangent Line at the Point	8x^2+y^2=89 , (-1,9)	$8 x^{2} + y^{2} = 89$ , $(- 1, 9)$
20468	Find the Tangent Line at the Point	4x^2+9y^2=72 , (3,2)	$4 x^{2} + 9 y^{2} = 72$ , $(3, 2)$
20469	Find the Tangent Line at the Point	4x^2+xy+4y^2=9 , (1,1)	$4 x^{2} + x y + 4 y^{2} = 9$ , $(1, 1)$
20470	Find the Tangent Line at the Point	2y^2- square root of x=28 , (16,4)	$2 y^{2} - \sqrt{x} = 28$ , $(16, 4)$
20471	Find the Tangent Line at the Point	4y^2- square root of x=12 , (16,2)	$4 y^{2} - \sqrt{x} = 12$ , $(16, 2)$
20472	Find the Tangent Line at the Point	4cos(x)sin(y)=5y , ( square root of 2,-1/2)	$4 \cos (x) \sin (y) = 5 y$ , $(\sqrt{2}, - \frac{1}{2})$
20473	Find the Tangent Line at the Point	2(x^2+y^2)^2=25(x^2-y^2) , (-3,-1)	$2 {(x^{2} + y^{2})}^{2} = 25 (x^{2} - y^{2})$ , $(- 3, - 1)$
20474	Find the Tangent Line at the Point	15(x^2+y^2)^2=289(x^2-y^2) , (4,1)	$15 {(x^{2} + y^{2})}^{2} = 289 (x^{2} - y^{2})$ , $(4, 1)$
20475	Find the Tangent Line at the Point	2x^2+y^2=17 , (-2,3)	$2 x^{2} + y^{2} = 17$ , $(- 2, 3)$
20476	Find the Tangent Line at the Point	2x^2+y^2=22 , (3,2)	$2 x^{2} + y^{2} = 22$ , $(3, 2)$
20477	Find the Tangent Line at the Point	2x^2+y^2=33 , (2,5)	$2 x^{2} + y^{2} = 33$ , $(2, 5)$
20478	Find the Tangent Line at the Point	2x^2+y^2=43 , (-3,5)	$2 x^{2} + y^{2} = 43$ , $(- 3, 5)$
20479	Find the Tangent Line at the Point	y^2-2x^3=33 , (2,-7)	$y^{2} - 2 x^{3} = 33$ , $(2, - 7)$
20480	Find the Tangent Line at the Point	y^4+x^3=y^2+11x , (0,1)	$y^{4} + x^{3} = y^{2} + 11 x$ , $(0, 1)$
20481	Find the Area Between the Curves	y=-x+2 , y=x^2	$y = - x + 2$ , $y = x^{2}$
20482	Find the Area Between the Curves	y=x , y=x^3	$y = x$ , $y = x^{3}$
20483	Find the Area Between the Curves	y=x-1/75x^3 , y=0	$y = x - \frac{1}{75} x^{3}$ , $y = 0$
20484	Find the Area Between the Curves	y=sin(x) , x=0 , x=pi	$y = \sin (x)$ , $x = 0$ , $x = π$
20485	Find the x and y Intercepts	f(x)=x^3-12x	$f (x) = x^{3} - 12 x$
20486	Find the Area Between the Curves	y=x-1 , y=x^2-4x+3 , y=3	$y = x - 1$ , $y = x^{2} - 4 x + 3$ , $y = 3$
20487	Find the Area Between the Curves	z=4-y^2 , x^2+y^2=2x , z=0	$z = 4 - y^{2}$ , $x^{2} + y^{2} = 2 x$ , $z = 0$
20488	Find the Volume	x=y^(1/3) , x=0 , y=64	$x = y^{\frac{1}{3}}$ , $x = 0$ , $y = 64$
20489	Find the Volume	y^2=2x , x=2y	$y^{2} = 2 x$ , $x = 2 y$
20490	Find the Volume	y=(x-2)^2 , y=x	$y = {(x - 2)}^{2}$ , $y = x$
20491	Find the Volume	y=3/x , x=7 , x=14 , y=0	$y = \frac{3}{x}$ , $x = 7$ , $x = 14$ , $y = 0$
20492	Find the Volume	y=-7x^2+21x , y=3x	$y = - 7 x^{2} + 21 x$ , $y = 3 x$
20493	Find the Volume	y=x^2 , y=4x	$y = x^{2}$ , $y = 4 x$
20494	Find the Volume	y=x , y=0 , x=2 , x=4	$y = x$ , $y = 0$ , $x = 2$ , $x = 4$
20495	Find the Volume	y=x(5-x)^2 , y=x+2	$y = x {(5 - x)}^{2}$ , $y = x + 2$
20496	Find the Volume	y=x+2 , y=x^2	$y = x + 2$ , $y = x^{2}$
20497	Find the Volume	y=0 , x=2 , y = square root of x	$y = 0$ , $x = 2$ , $y = \sqrt{x}$
20498	Find the Volume	y=2x^2 , y=0 , x=2	$y = 2 x^{2}$ , $y = 0$ , $x = 2$
20499	Find the Volume	y=1/x , x=1 , x=2 , y=0	$y = \frac{1}{x}$ , $x = 1$ , $x = 2$ , $y = 0$
20500	Find the Volume	y=x^2 , x=2 , y=0	$y = x^{2}$ , $x = 2$ , $y = 0$