Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
53101	Find the Tangent Line at (1,-2)	y^2=x^3+3x^2 , (1,-2)	$y^{2} = x^{3} + 3 x^{2}$ , $(1, - 2)$
53102	Find the Tangent Line at (8,4)	y = square root of 2x , (8,4)	$y = \sqrt{2 x}$ , $(8, 4)$
53103	Find the Tangent Line at (v(3),1)	x^2+y^2=9 ( square root of 3,1)	$x^{2} + y^{2} = 9$ $(\sqrt{3}, 1)$
53104	Find the Tangent Line at (0,0.25)	x^2+y^2=(4x^2+4y^2-x)^2 , (0,0.25)	$x^{2} + y^{2} = {(4 x^{2} + 4 y^{2} - x)}^{2}$ , $(0, 0.25)$
53105	Find the Tangent Line at x=0	(4x-5)/(x+1) x=0	$\frac{4 x - 5}{x + 1}$ $x = 0$
53106	Find the Tangent Line at x=25	y=5x^(1/2)+x^(3/2) ; x=25	$y = 5 x^{\frac{1}{2}} + x^{\frac{3}{2}}$ ; $x = 25$
53107	Find the Tangent Line at (-4,0)	y=(x^3-16x)^12 , (-4,0)	$y = {(x^{3} - 16 x)}^{12}$ , $(- 4, 0)$
53108	Find the Tangent Line at (-2,-8)	y=x^3 , (-2,-8)	$y = x^{3}$ , $(- 2, - 8)$
53109	Find the Tangent Line at (4,p/12)	y=1/3arctan(1/4x) , (4,pi/12)	$y = \frac{1}{3} \arctan (\frac{1}{4} x)$ , $(4, \frac{π}{12})$
53110	Find the Tangent Line at (1,2)	x^2+2xy-y^2+x=2 , (1,2)	$x^{2} + 2 x y - y^{2} + x = 2$ , $(1, 2)$
53111	Find the Tangent Line at x=25	y=9x^(1/2)+x^(3/2) , x=25	$y = 9 x^{\frac{1}{2}} + x^{\frac{3}{2}}$ , $x = 25$
53112	Find the Tangent Line at (4,3/16)	f(x)=3/((x^2-3x)^2) , (4,3/16)	$f (x) = \frac{3}{{(x^{2} - 3 x)}^{2}}$ , $(4, \frac{3}{16})$
53113	Find the Tangent Line at x=16	y=-5x^(1/2)+x^(3/2) ; x=16	$y = - 5 x^{\frac{1}{2}} + x^{\frac{3}{2}}$ ; $x = 16$
53114	Find the Tangent Line at (2p,0)	sin(sin(x)) , (2pi,0)	$\sin (\sin (x))$ , $(2 π, 0)$
53115	Find the Tangent Line at (0,p/3)	sin(3y)=x ; (0,pi/3)	$\sin (3 y) = x$ ; $(0, \frac{π}{3})$
53116	Find the Tangent Line at x=7	y=1/(x-5) , x=7	$y = \frac{1}{x - 5}$ , $x = 7$
53117	Find the Tangent Line at x=1	y=x^2-8x-5 , x=1	$y = x^{2} - 8 x - 5$ , $x = 1$
53118	Find the Tangent Line at (4,0.2)	y=( square root of x)/(x+6) , (4,0.2)	$y = \frac{\sqrt{x}}{x + 6}$ , $(4, 0.2)$
53119	Find the Tangent Line at (4p,0)	sin(sin(x)) , (4pi,0)	$\sin (\sin (x))$ , $(4 π, 0)$
53120	Find the Tangent Line at (1,-9)	y=x^3-9x , (1,-9)	$y = x^{3} - 9 x$ , $(1, - 9)$
53121	Find the Tangent Line at x=-2	y=x(16x^-2+2) ; x=-2	$y = x (16 x^{- 2} + 2)$ ; $x = - 2$
53122	Find the Tangent Line at (-1,3)	x^2y^2=9 , (-1,3)	$x^{2} y^{2} = 9$ , $(- 1, 3)$
53123	Find the Tangent Line at (3,23)	y=x^3-2x+2 (3,23)	$y = x^{3} - 2 x + 2$ $(3, 23)$
53124	Find the Tangent Line at x=1	(12x-3)^(1/2) x=1	${(12 x - 3)}^{\frac{1}{2}}$ $x = 1$
53125	Find the Tangent Line at (p/6,1)	y=2sin(x) , (pi/6,1)	$y = 2 \sin (x)$ , $(\frac{π}{6}, 1)$
53126	Find the Tangent Line at (1,4)	y=5x-x^2 , (1,4)	$y = 5 x - x^{2}$ , $(1, 4)$
53127	Find the Tangent Line at (2,5p/6)	y=arcsin(x/4) , (2,(5pi)/6)	$y = \arcsin (\frac{x}{4})$ , $(2, \frac{5 π}{6})$
53128	Find the Tangent Line at (8,2)	y=x^(1/3) , (8,2)	$y = x^{\frac{1}{3}}$ , $(8, 2)$
53129	Find the Tangent Line at a=0	-2e^(5x) , a=0	$- 2 e^{5 x}$ , $a = 0$
53130	Find the Tangent Line at x=9	y=9x^(1/2)+x^(3/2) ; x=9	$y = 9 x^{\frac{1}{2}} + x^{\frac{3}{2}}$ ; $x = 9$
53131	Find the Tangent Line at x=4	y=125/(x^2+25) , x=4	$y = \frac{125}{x^{2} + 25}$ , $x = 4$
53132	Find the Tangent Line at (1,2)	y=2 square root of x , (1,2)	$y = 2 \sqrt{x}$ , $(1, 2)$
53133	Find the Tangent Line at x=-p/2	cot(x) , x=-pi/2	$\cot (x)$ , $x = - \frac{π}{2}$
53134	Find the Tangent Line at (0,p/8)	cos(4y)=x ; (0,pi/8)	$\cos (4 y) = x$ ; $(0, \frac{π}{8})$
53135	Find the Tangent Line at x=a	y=8+4x^2-2x^3 , x=a	$y = 8 + 4 x^{2} - 2 x^{3}$ , $x = a$
53136	Find the Tangent Line at x=4	y=216/(x^2+36) , x=4	$y = \frac{216}{x^{2} + 36}$ , $x = 4$
53137	Find the Tangent Line at (2,13)	y=2x^3-x^2+1 , (2,13)	$y = 2 x^{3} - x^{2} + 1$ , $(2, 13)$
53138	Find the Tangent Line at (1,p/8)	y=1/2arctan(x) ; (1,pi/8)	$y = \frac{1}{2} \arctan (x)$ ; $(1, \frac{π}{8})$
53139	Find the Tangent Line at (2,-7)	y^2-3x^2=37 (2,-7)	$y^{2} - 3 x^{2} = 37$ $(2, - 7)$
53140	Find the Tangent Line at (p/3,6)	y=6sec(x)-12cos(x) , (pi/3,6)	$y = 6 \sec (x) - 12 \cos (x)$ , $(\frac{π}{3}, 6)$
53141	Find the Concavity	(x+6)/(x^2-36)	$\frac{x + 6}{x^{2} - 36}$
53142	Find the Concavity	60x^3-30x	$60 x^{3} - 30 x$
53143	Find the Concavity	-2x^4+36x^2	$- 2 x^{4} + 36 x^{2}$
53144	Find the Concavity	(x^2-12x+37)e^x	$(x^{2} - 12 x + 37) e^{x}$
53145	Find the Concavity	(x+1)/(x^2-7x-8)	$\frac{x + 1}{x^{2} - 7 x - 8}$
53146	Find the Concavity	x^3-6x^2+27x-38	$x^{3} - 6 x^{2} + 27 x - 38$
53147	Find the Concavity	x^5-15x^3	$x^{5} - 15 x^{3}$
53148	Find the Concavity	-x^4+36x^3-36x+7	$- x^{4} + 36 x^{3} - 36 x + 7$
53149	Find the Concavity	x^3-7x^2-5x+8	$x^{3} - 7 x^{2} - 5 x + 8$
53150	Find the Concavity	6sec(x-pi/2)	$6 \sec (x - \frac{π}{2})$
53151	Find the Concavity	1350x-0.18x^3	$1350 x - 0.18 x^{3}$
53152	Find the Concavity	3cos(x)^2-6sin(x)	$3 \cos^{2} (x) - 6 \sin (x)$
53153	Find the Concavity	(x^2+64)/x	$\frac{x^{2} + 64}{x}$
53154	Find the Concavity	-x^3-15x^2-75x+2	$- x^{3} - 15 x^{2} - 75 x + 2$
53155	Find the Concavity	x^4-32x^2+6	$x^{4} - 32 x^{2} + 6$
53156	Find the Concavity	(x^2+5x)/(25-x^2)	$\frac{(x^{2} + 5 x)}{25 - x^{2}}$
53157	Find the Concavity	1/2x^4-4x^2+7	$\frac{1}{2} x^{4} - 4 x^{2} + 7$
53158	Find the Concavity	11x+11e^x	$11 x + 11 e^{x}$
53159	Find the Concavity	6-5x^4	$6 - 5 x^{4}$
53160	Find the Concavity	19x+19e^x	$19 x + 19 e^{x}$
53161	Find the Concavity	10-6x^2+2x^3	$10 - 6 x^{2} + 2 x^{3}$
53162	Find the Concavity	6x^2-x^3	$6 x^{2} - x^{3}$
53163	Find the Concavity	x^4-8x^3	$x^{4} - 8 x^{3}$
53164	Find the Concavity	-x^3-9x^2+81x	$- x^{3} - 9 x^{2} + 81 x$
53165	Find the Concavity	(x+11)/(x^2-121)	$\frac{x + 11}{x^{2} - 121}$
53166	Find the Concavity	2x^4-16x^3+36x^2	$2 x^{4} - 16 x^{3} + 36 x^{2}$
53167	Find the Concavity	6e^xx+12e^x	$6 e^{x} x + 12 e^{x}$
53168	Find the Concavity	((x-1)^2)/(x^2+1)	$\frac{{(x - 1)}^{2}}{x^{2} + 1}$
53169	Find the Concavity	-x^6+24x^5-24x+19	$- x^{6} + 24 x^{5} - 24 x + 19$
53170	Find the Concavity	x^3+3x^2	$x^{3} + 3 x^{2}$
53171	Find the Concavity	x+sin(2x)+1	$x + \sin (2 x) + 1$
53172	Find the Concavity	5x^(2/3)+x^(5/3)	$5 x^{\frac{2}{3}} + x^{\frac{5}{3}}$
53173	Find the Concavity	(7x^2)/(x^2+36)	$\frac{7 x^{2}}{x^{2} + 36}$
53174	Find the Range	y=cos(arccos(x))	$y = \cos (\cos^{-1} (x))$
53175	Find the GCF	9x+36	$9 x + 36$
53176	Find the Quadratic Equation	5+4i , 5-4i , -1	$5 + 4 i$ , $5 - 4 i$ , $- 1$
53177	Find the Average Rate of Change	f(x)=x^(3/2) , [9,16]	$f (x) = x^{\frac{3}{2}}$ , $[9, 16]$
53178	Find the Average Rate of Change	f(t)=2t^2-5 , [3,3.1]	$f (t) = 2 t^{2} - 5$ , $[3, 3.1]$
53179	Find the Average Rate of Change	y=4x^2 , [0,7/4]	$y = 4 x^{2}$ , $[0, \frac{7}{4}]$
53180	Find the Average Rate of Change	v(t)=3t^2-e^t , [0,2]	$v (t) = 3 t^{2} - e^{t}$ , $[0, 2]$
53181	Find the Second Term	a_n=3n-2	$a_{n} = 3 n - 2$
53182	Find the Third Term	a_n=3n-2	$a_{n} = 3 n - 2$
53183	Find the Second Term	a_n=7n-8	$a_{n} = 7 n - 8$
53184	Find the Fourth Term	80 , 40 , 20	$80$ , $40$ , $20$
53185	Find the Second Term	a_n=2n-5	$a_{n} = 2 n - 5$
53186	Find the Concavity	f(x)=x^5-8	$f (x) = x^{5} - 8$
53187	Find the Area Between the Curves	y=x^2 , y=2x-2 , x=1 , x=2	$y = x^{2}$ , $y = 2 x - 2$ , $x = 1$ , $x = 2$
53188	Find the Area Between the Curves	y=3x-x^2 , y=10	$y = 3 x - x^{2}$ , $y = 10$
53189	Find the Area Between the Curves	y=8 , y = square root of x , x=0	$y = 8$ , $y = \sqrt{x}$ , $x = 0$
53190	Find the Area Between the Curves	y=5 cube root of x , y=0 , x=1	$y = 5 \sqrt[3]{x}$ , $y = 0$ , $x = 1$
53191	Find the Area Between the Curves	y=x^2-4x , y=x-4	$y = x^{2} - 4 x$ , $y = x - 4$
53192	Find the Area Between the Curves	y=x y=x^2-3x+3	$y = x$ $y = x^{2} - 3 x + 3$
53193	Find the Area Between the Curves	y=x+1 , y=0 , x=0 , x=7	$y = x + 1$ , $y = 0$ , $x = 0$ , $x = 7$
53194	Find the Area Between the Curves	y^2-4x=4 , x-y=2	$y^{2} - 4 x = 4$ , $x - y = 2$
53195	Find the Area Between the Curves	y = cube root of x , y=x	$y = \sqrt[3]{x}$ , $y = x$
53196	Find the Area Between the Curves	y = square root of 9-x^2 , y=0	$y = \sqrt{9 - x^{2}}$ , $y = 0$
53197	Find the Domain and Range	y=7cos(x)	$y = 7 \cos (x)$
53198	Find the Domain and Range	y=4sec(x)	$y = 4 \sec (x)$
53199	Find the Domain and Range	y=cot(1/6x)	$y = \cot (\frac{1}{6} x)$
53200	Find the Domain and Range	2x+3y=18	$2 x + 3 y = 18$