Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
46201	Find the Tangent Line at the Point	y=(1+3x)^8 , (0,1)	$y = {(1 + 3 x)}^{8}$ , $(0, 1)$
46202	Find the Tangent Line at the Point	y=x^3-2x+2 , (4,58)	$y = x^{3} - 2 x + 2$ , $(4, 58)$
46203	Find the Tangent Line at the Point	h(t)=t^3 , (2,8)	$h (t) = t^{3}$ , $(2, 8)$
46204	Find the Tangent Line at the Point	3(x^2+y^2)^2=100(x^2-y^2) , (-4,2)	$3 {(x^{2} + y^{2})}^{2} = 100 (x^{2} - y^{2})$ , $(- 4, 2)$
46205	Find the Tangent Line at the Point	y=x^3-2x+1 , (4,57)	$y = x^{3} - 2 x + 1$ , $(4, 57)$
46206	Find the Tangent Line at the Point	y=2x^3 , (1,2)	$y = 2 x^{3}$ , $(1, 2)$
46207	Find the Tangent Line at the Point	16(x^2+y^2)^2=289xy^2 ; (1,4)	$16 {(x^{2} + y^{2})}^{2} = 289 x y^{2}$ ; $(1, 4)$
46208	Find the Tangent Line at the Point	h(t)=2t^3 , (-1,-2)	$h (t) = 2 t^{3}$ , $(- 1, - 2)$
46209	Find the Tangent Line at the Point	5e^xcos(x) , (0,5)	$5 e^{x} \cos (x)$ , $(0, 5)$
46210	Find the Tangent Line at the Point	x^2+2xy-y^2+x=20 , (3,4)	$x^{2} + 2 x y - y^{2} + x = 20$ , $(3, 4)$
46211	Find the Tangent Line at the Point	y=(e^(2x)-3)^2 , (0,4)	$y = {(e^{2 x} - 3)}^{2}$ , $(0, 4)$
46212	Find the Tangent Line at the Point	(x-y-1)^3=x ; (1,-1)	${(x - y - 1)}^{3} = x$ ; $(1, - 1)$
46213	Find the Tangent Line at the Point	y=x^4e^(-x) , (1,1/e)	$y = x^{4} e^{- x}$ , $(1, \frac{1}{e})$
46214	Find the Tangent Line at the Point	x^2+y^2=(5x^2+2y^2-x)^2 , (0,0.5)	$x^{2} + y^{2} = {(5 x^{2} + 2 y^{2} - x)}^{2}$ , $(0, 0.5)$
46215	Find the Tangent Line at the Point	y=16xsin(x) , (pi/2,8pi)	$y = 16 x \sin (x)$ , $(\frac{π}{2}, 8 π)$
46216	Find the Tangent Line at the Point	f(x)=((x+1)/(x-3))^2 ; (7,4)	$f (x) = {(\frac{x + 1}{x - 3})}^{2}$ ; $(7, 4)$
46217	Find the Tangent Line at the Point	y=8 square root of x , (4,16)	$y = 8 \sqrt{x}$ , $(4, 16)$
46218	Find the Tangent Line at the Point	y^4-4y^2=x^4-9x^2 , (-3,2)	$y^{4} - 4 y^{2} = x^{4} - 9 x^{2}$ , $(- 3, 2)$
46219	Find the Tangent Line at the Point	f(x)=x^3 , (1,1)	$f (x) = x^{3}$ , $(1, 1)$
46220	Find the Tangent Line at the Point	y = square root of 3x , (3,3)	$y = \sqrt{3 x}$ , $(3, 3)$
46221	Find the Tangent Line at the Point	y=sin(8x)+sin(8x)^2 , (0,0)	$y = \sin (8 x) + \sin^{2} (8 x)$ , $(0, 0)$
46222	Find the Tangent Line at the Point	f(x)=x^2+1 , (2,5)	$f (x) = x^{2} + 1$ , $(2, 5)$
46223	Find the Tangent Line at the Point	y=3x^3+4x+5 , (2,37)	$y = 3 x^{3} + 4 x + 5$ , $(2, 37)$
46224	Find the Tangent Line at the Point	h(t)=-t^3 , (1,-1)	$h (t) = - t^{3}$ , $(1, - 1)$
46225	Find the Tangent Line at the Point	(y-3)^2=4(x-5) , (9,-1)	${(y - 3)}^{2} = 4 (x - 5)$ , $(9, - 1)$
46226	Find the Tangent Line at the Point	4x^2+2y^2=12 , (1,2)	$4 x^{2} + 2 y^{2} = 12$ , $(1, 2)$
46227	Find the Tangent Line at the Point	y=7x-4 square root of x , (1,3)	$y = 7 x - 4 \sqrt{x}$ , $(1, 3)$
46228	Find the Tangent Line at the Point	y = fifth root of 2x^3+8x , (2,2)	$y = \sqrt[5]{2 x^{3} + 8 x}$ , $(2, 2)$
46229	Find the Tangent Line at the Point	y=2x^3 , (-2,-16)	$y = 2 x^{3}$ , $(- 2, - 16)$
46230	Find the Tangent Line at the Point	y=7x-6 square root of x , (1,1)	$y = 7 x - 6 \sqrt{x}$ , $(1, 1)$
46231	Find the Tangent Line at the Point	x^2+2xy-y^2+x=46 , (5,8)	$x^{2} + 2 x y - y^{2} + x = 46$ , $(5, 8)$
46232	Find the Tangent Line at the Point	x^2+2xy-y^2+x=51 , (5,7)	$x^{2} + 2 x y - y^{2} + x = 51$ , $(5, 7)$
46233	Find the Tangent Line at the Point	x^2+2xy-y^2+x=5 , (3,7)	$x^{2} + 2 x y - y^{2} + x = 5$ , $(3, 7)$
46234	Find the Tangent Line at the Point	g(x)=7-x^2 ; (1,6)	$g (x) = 7 - x^{2}$ ; $(1, 6)$
46235	Find the Tangent Line at the Point	x^2+y^2=25 (3,4)	$x^{2} + y^{2} = 25$ $(3, 4)$
46236	Find the Tangent Line at the Point	h(t)=-t^3 , (2,-8)	$h (t) = - t^{3}$ , $(2, - 8)$
46237	Find the Tangent Line at the Point	f(x)=(1-x)(x^2-2)^2 ; (2,-4)	$f (x) = (1 - x) {(x^{2} - 2)}^{2}$ ; $(2, - 4)$
46238	Find the Function	f'(x)=sin(x^2)	$f' (x) = \sin (x^{2})$
46239	Find the Volume	y=x^2 , y=4 , x=0	$y = x^{2}$ , $y = 4$ , $x = 0$
46240	Find the Volume	y=4-4x^2 , y=0	$y = 4 - 4 x^{2}$ , $y = 0$
46241	Find the Volume	x=2 square root of 3y , x=0 , y=7	$x = 2 \sqrt{3 y}$ , $x = 0$ , $y = 7$
46242	Find the Volume	x=2 square root of y , x=0 , y=9	$x = 2 \sqrt{y}$ , $x = 0$ , $y = 9$
46243	Find the Volume	y=1/49x^2 , x=5 , y=0	$y = \frac{1}{49} x^{2}$ , $x = 5$ , $y = 0$
46244	Find the Volume	y = square root of 16-x^2 , y=0	$y = \sqrt{16 - x^{2}}$ , $y = 0$
46245	Find the x and y Intercepts	x^3+3x^2-4x-12	$x^{3} + 3 x^{2} - 4 x - 12$
46246	Find the x and y Intercepts	-3x^3(x-2)^2(x+5)	$- 3 x^{3} {(x - 2)}^{2} (x + 5)$
46247	Find the Average Value of the Function	f(x)=8x-6 , [0,3]	$f (x) = 8 x - 6$ , $[0, 3]$
46248	Convert to Scientific Notation	0.000781	$0.000781$
46249	Evaluate the Derivative at x>1	y=( natural log of x)^( natural log of x) , x>1	$y = {(\ln (x))}^{\ln (x)}$ , $x > 1$
46250	Evaluate the Derivative at x=p/3	y=8sin(x)cos(x) ; x=pi/3	$y = 8 \sin (x) \cos (x)$ ; $x = \frac{π}{3}$
46251	Evaluate the Derivative at x=0	xy+4e^y=4e , x=0	$x y + 4 e^{y} = 4 e$ , $x = 0$
46252	Find the Asymptotes	y=(8e^x)/(e^x-6)	$y = \frac{8 e^{x}}{e^{x} - 6}$
46253	Find the Asymptotes	y=(x^2+3)/(8x-5x^2)	$y = \frac{x^{2} + 3}{8 x - 5 x^{2}}$
46254	Find the Asymptotes	y=(4e^x)/(e^x-9)	$y = \frac{4 e^{x}}{e^{x} - 9}$
46255	Find the Asymptotes	y=(e^x+1)/(1-e^x)	$y = \frac{e^{x} + 1}{1 - e^{x}}$
46256	Find the Asymptotes	y=(x^3)/(x^2+3x-10)	$y = \frac{x^{3}}{x^{2} + 3 x - 10}$
46257	Find the Asymptotes	y=5-4x-x^3	$y = 5 - 4 x - x^{3}$
46258	Find the Asymptotes	y=(4x)/(x^2-9)	$y = \frac{4 x}{x^{2} - 9}$
46259	Find the Asymptotes	y=(4e^x)/(e^x-3)	$y = \frac{4 e^{x}}{e^{x} - 3}$
46260	Find the Asymptotes	y=(2x^2+1)/(3x^2+2x-1)	$y = \frac{2 x^{2} + 1}{3 x^{2} + 2 x - 1}$
46261	Find the Inflection Points	f(x)=2sin(x)+2cos(x)	$f (x) = 2 \sin (x) + 2 \cos (x)$
46262	Find the Inflection Points	f(x)=12x^2-12sin(2x)	$f (x) = 12 x^{2} - 12 \sin (2 x)$
46263	Find the Inflection Points	f(x)=(x^2+16)/x	$f (x) = \frac{x^{2} + 16}{x}$
46264	Find the Inflection Points	f(x)=x^3-3x^2+21x-19	$f (x) = x^{3} - 3 x^{2} + 21 x - 19$
46265	Find the Inflection Points	f(x)=6-5x^4	$f (x) = 6 - 5 x^{4}$
46266	Find the Inflection Points	f(x)=2x^3-6x-6	$f (x) = 2 x^{3} - 6 x - 6$
46267	Find the Inflection Points	f(x)=2x^4-4x^3+1	$f (x) = 2 x^{4} - 4 x^{3} + 1$
46268	Find the Inflection Points	f(x)=-2x^5+10x^4	$f (x) = - 2 x^{5} + 10 x^{4}$
46269	Find the Inflection Points	g(x)=3x^5-30x^4	$g (x) = 3 x^{5} - 30 x^{4}$
46270	Find the Inflection Points	f(x)=x+2sin(x)	$f (x) = x + 2 \sin (x)$
46271	Find the Inflection Points	f(x)=x+4cos(x)	$f (x) = x + 4 \cos (x)$
46272	Find the Inflection Points	f(x)=4sin(x)+sin(2x)	$f (x) = 4 \sin (x) + \sin (2 x)$
46273	Find the Inflection Points	f(x)=5sin(x)+5cos(x)	$f (x) = 5 \sin (x) + 5 \cos (x)$
46274	Split Using Partial Fraction Decomposition	(x-72)/(x^2+x-72)	$\frac{x - 72}{x^{2} + x - 72}$
46275	Split Using Partial Fraction Decomposition	(3x+5)/(x^2+4x+3)	$\frac{3 x + 5}{x^{2} + 4 x + 3}$
46276	Split Using Partial Fraction Decomposition	(5x-13)/((x-3)(x-2))	$\frac{5 x - 13}{(x - 3) (x - 2)}$
46277	Split Using Partial Fraction Decomposition	(9x^2-84x+157)/(2x^3-3x^2-29x+60)	$\frac{9 x^{2} - 84 x + 157}{2 x^{3} - 3 x^{2} - 29 x + 60}$
46278	Find the Second Derivative	f(x)=20x^3-36x^2	$f (x) = 20 x^{3} - 36 x^{2}$
46279	Find the Second Derivative	f(x)=8x^-7	$f (x) = 8 x^{- 7}$
46280	Find the Second Derivative	f(x)=6x^3+5x^2+7x	$f (x) = 6 x^{3} + 5 x^{2} + 7 x$
46281	Find the Second Derivative	x(t)=10sin(t)	$x (t) = 10 \sin (t)$
46282	Find the Second Derivative	g(x)=-8sin((3x)/2+1)	$g (x) = - 8 \sin (\frac{3 x}{2} + 1)$
46283	Find the Second Derivative	f(x)=5x^-5	$f (x) = 5 x^{- 5}$
46284	Find the Second Derivative	f(x)=cos(2x)	$f (x) = \cos (2 x)$
46285	Find the Second Derivative	h(s)=s^3(s^2-4s+4)	$h (s) = s^{3} (s^{2} - 4 s + 4)$
46286	Find the Second Derivative	f(x)=6x^5-5x^4+4x^3+8x^2+3	$f (x) = 6 x^{5} - 5 x^{4} + 4 x^{3} + 8 x^{2} + 3$
46287	Find the Second Derivative	f(x)=3 natural log of sec(x)+tan(x)	$f (x) = 3 \ln (\sec (x) + \tan (x))$
46288	Find the Second Derivative	f(x)=8x^2+7x	$f (x) = 8 x^{2} + 7 x$
46289	Find the Second Derivative	f(x)=5x^2-10x-8/(x^4)	$f (x) = 5 x^{2} - 10 x - \frac{8}{x^{4}}$
46290	Find the Second Derivative	s(t)=13t^2	$s (t) = 13 t^{2}$
46291	Find the Second Derivative	f(x)=2cos(x/2)	$f (x) = 2 \cos (\frac{x}{2})$
46292	Find the Second Derivative	g(t)=t^2(4t+9)^4	$g (t) = t^{2} {(4 t + 9)}^{4}$
46293	Find the Second Derivative	f(x)=7e^(-x)-2e^(-7x)	$f (x) = 7 e^{- x} - 2 e^{- 7 x}$
46294	Find the Second Derivative	d(x)=2x^3-7x^2-9	$d (x) = 2 x^{3} - 7 x^{2} - 9$
46295	Find the Second Derivative	f(x)=6x^10+2x^3-0.5x+2	$f (x) = 6 x^{10} + 2 x^{3} - 0.5 x + 2$
46296	Find the Second Derivative	f(x)=5e^(-x)-3e^(-5x)	$f (x) = 5 e^{- x} - 3 e^{- 5 x}$
46297	Find the Second Derivative	f(x)=5x^2-13x-6/(x^4)	$f (x) = 5 x^{2} - 13 x - \frac{6}{x^{4}}$
46298	Find the Second Derivative	f(x)=4x^3+5x^2+9x	$f (x) = 4 x^{3} + 5 x^{2} + 9 x$
46299	Find the Second Derivative	g(t)=8/(9t^4)	$g (t) = \frac{8}{9 t^{4}}$
46300	Find the Second Derivative	f(x)=sin(9x^2)	$f (x) = \sin (9 x^{2})$