Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
60801	Convert to Rectangular	theta=pi/4	$θ = \frac{π}{4}$
60802	Convert to Rectangular	15(cos((23pi)/12)+isin((23pi)/12))	$15 (\cos (\frac{23 π}{12}) + i \sin (\frac{23 π}{12}))$
60803	Convert to Rectangular	( square root of 7(cos(35 degrees )+isin(35 degrees )))^6	${(\sqrt{7} (\cos (35 °) + i \sin (35 °)))}^{6}$
60804	Find Where Increasing/Decreasing Using Derivatives	x^(1/7)(x+8)	$x^{\frac{1}{7}} (x + 8)$
60805	Find Where Increasing/Decreasing Using Derivatives	x square root of 16-x^2	$x \sqrt{16 - x^{2}}$
60806	Find Where Increasing/Decreasing Using Derivatives	x^3-9x	$x^{3} - 9 x$
60807	Find Where Increasing/Decreasing Using Derivatives	x-9x^(1/3)	$x - 9 x^{\frac{1}{3}}$
60808	Find Where Increasing/Decreasing Using Derivatives	1+1/x+1/(x^2)	$1 + \frac{1}{x} + \frac{1}{x^{2}}$
60809	Convert to Rectangular	r=4sec(theta)	$r = 4 \sec (θ)$
60810	Convert to Rectangular	r=9sin(theta)	$r = 9 \sin (θ)$
60811	Convert to Rectangular	r=7cos(theta)	$r = 7 \cos (θ)$
60812	Identify the Zeros and Their Multiplicities	f(x)=5x^6-105x^5+655x^4-35x^3-11760x^2+27440x	$f (x) = 5 x^{6} - 105 x^{5} + 655 x^{4} - 35 x^{3} - 11760 x^{2} + 27440 x$
60813	Find the Vertex	y^2-4y+12x-8=0	$y^{2} - 4 y + 12 x - 8 = 0$
60814	Find the Vertex	y=-2x^2+16x-30	$y = - 2 x^{2} + 16 x - 30$
60815	Find the Critical Points	y=x^4-4x^3	$y = x^{4} - 4 x^{3}$
60816	Find the Critical Points	y=x^2 square root of 9-x	$y = x^{2} \sqrt{9 - x}$
60817	Find the Critical Points	x^(19/9)+x^(10/9)	$x^{\frac{19}{9}} + x^{\frac{10}{9}}$
60818	Find the Critical Points	sin(5x)	$\sin (5 x)$
60819	Find the Critical Points	natural log of x-2x^2	$\ln (x) - 2 x^{2}$
60820	Find the Critical Points	e^(2x)+e^(-x)	$e^{2 x} + e^{- x}$
60821	Find the Critical Points	4x^3e^(-x)	$4 x^{3} e^{- x}$
60822	Find the Critical Points	square root of x	$\sqrt{x}$
60823	Find the Critical Points	square root of x^2+8	$\sqrt{x^{2} + 8}$
60824	Find the Critical Points	2x^3+3x^2-120x	$2 x^{3} + 3 x^{2} - 120 x$
60825	Find the Critical Points	(x+1)^5-5x-2	${(x + 1)}^{5} - 5 x - 2$
60826	Find the Domain	3x(x-3)^3	$3 x {(x - 3)}^{3}$
60827	Find the Local Maxima and Minima	f(x)=1/x	$f (x) = \frac{1}{x}$
60828	Find the Inflection Points	x^8 natural log of x	$x^{8} \ln (x)$
60829	Find the Inflection Points	natural log of x^2+100	$\ln (x^{2} + 100)$
60830	Find the Inflection Points	7cos(x)^2-14sin(x)	$7 \cos^{2} (x) - 14 \sin (x)$
60831	Expand the Logarithmic Expression	log base b of 576b	$\log_{b} (576 b)$
60832	Expand the Logarithmic Expression	log base 6 of (6p)/(11k)	$\log_{6} (\frac{6 p}{11 k})$
60833	Find the Local Maxima and Minima	f(x)=2x^2-16x+33	$f (x) = 2 x^{2} - 16 x + 33$
60834	Find the Local Maxima and Minima	f(x)=3x^3-81x	$f (x) = 3 x^{3} - 81 x$
60835	Find the Domain and Range	square root of 5x	$\sqrt{5 x}$
60836	Find the Domain and Range	x-4	$x - 4$
60837	Find the Domain and Range	x^3-1	$x^{3} - 1$
60838	Find the Domain and Range	x^2-2x+1	$x^{2} - 2 x + 1$
60839	Find Trig Functions Using Identities	sin(2arccos(x))	$\sin (2 \arccos (x))$
60840	Find the Area Between the Curves	y=2x^2-4y=-2x	$y = 2 x^{2} - 4 y = - 2 x$
60841	Find the Area Between the Curves	y=17x , y=x^2	$y = 17 x$ , $y = x^{2}$
60842	Find the Area Between the Curves	y=1-x^2 , y=1-5x	$y = 1 - x^{2}$ , $y = 1 - 5 x$
60843	Find the Area Between the Curves	y=15x , y=x^2	$y = 15 x$ , $y = x^{2}$
60844	Find the Area Between the Curves	y=1-25x^2 , y=0	$y = 1 - 25 x^{2}$ , $y = 0$
60845	Find the Area Between the Curves	y=100-x^2	$y = 100 - x^{2}$
60846	Find the Area Between the Curves	y=2/x , y=8x , y=1/8x	$y = \frac{2}{x}$ , $y = 8 x$ , $y = \frac{1}{8} x$
60847	Find the Area Between the Curves	y=81-x^2 ; [-9,9]	$y = 81 - x^{2}$ ; $[- 9, 9]$
60848	Find the Area Between the Curves	x=-2 , x=3 , y=3x , y=x^2-4	$x = - 2$ , $x = 3$ , $y = 3 x$ , $y = x^{2} - 4$
60849	Find the Area Between the Curves	x=2y^2 , x=4+y^2	$x = 2 y^{2}$ , $x = 4 + y^{2}$
60850	Find the Area Between the Curves	y=x^2-5 , y=13-3x	$y = x^{2} - 5$ , $y = 13 - 3 x$
60851	Find the Area Between the Curves	y=x^2-4x , y=2x	$y = x^{2} - 4 x$ , $y = 2 x$
60852	Find the Area Between the Curves	y=x^2-26 , y=9-2x	$y = x^{2} - 26$ , $y = 9 - 2 x$
60853	Find the Area Between the Curves	y=x^2 , y=4x	$y = x^{2}$ , $y = 4 x$
60854	Find the Area Between the Curves	y=x^2 , y=50-x^2	$y = x^{2}$ , $y = 50 - x^{2}$
60855	Find the Area Between the Curves	y=x^2 , y=72-x^2	$y = x^{2}$ , $y = 72 - x^{2}$
60856	Find the Area Between the Curves	y=x^2 , y=8-x^2	$y = x^{2}$ , $y = 8 - x^{2}$
60857	Find the Area Between the Curves	y=x^2 , y=6x-2x^2	$y = x^{2}$ , $y = 6 x - 2 x^{2}$
60858	Find the Area Between the Curves	y=-x^2+8x , y=0	$y = - x^{2} + 8 x$ , $y = 0$
60859	Find the Area Between the Curves	y=x^4-4x^2+2 ; y=x^2-2	$y = x^{4} - 4 x^{2} + 2$ ; $y = x^{2} - 2$
60860	Find the Area Between the Curves	y=xy=x^2	$y = x y = x^{2}$
60861	Find the Domain and Range	(x^2)/36+(y^2)/100=1	$\frac{x^{2}}{36} + \frac{y^{2}}{100} = 1$
60862	Find the Domain and Range	y=x^5-5x	$y = x^{5} - 5 x$
60863	Find the Absolute Max and Min over the Interval	f(x)=4x^3-6x^2-144x+1 , [-4,5]	$f (x) = 4 x^{3} - 6 x^{2} - 144 x + 1$ , $[- 4, 5]$
60864	Find the Absolute Max and Min over the Interval	f(x)=x^3-6x^2+9x+1 , [-3,6]	$f (x) = x^{3} - 6 x^{2} + 9 x + 1$ , $[- 3, 6]$
60865	Find the Second Derivative	y=e^x	$y = e^{x}$
60866	Find the Second Derivative	y=tan(x)	$y = \tan (x)$
60867	Write in Exponential Form	log of x=y	$\log (x) = y$
60868	Write in Exponential Form	cube root of x^2	$\sqrt[3]{x^{2}}$
60869	Find the Concavity	x/(x^2+2)	$\frac{x}{x^{2} + 2}$
60870	Find the Concavity	x^3-27x	$x^{3} - 27 x$
60871	Find the Concavity	natural log of x^2+1	$\ln (x^{2} + 1)$
60872	Write in Standard Form	16x^2+9y^2-32x+72y+16=0	$16 x^{2} + 9 y^{2} - 32 x + 72 y + 16 = 0$
60873	Write in Standard Form	x^2+y^2-8x-20y+115=0	$x^{2} + y^{2} - 8 x - 20 y + 115 = 0$
60874	Find Where Increasing/Decreasing Using Derivatives	y=x^4-2x^2	$y = x^{4} - 2 x^{2}$
60875	Find the Average Value of the Function	y=3e^(-x) ; [0,1]	$y = 3 e^{- x}$ ; $[0, 1]$
60876	Find the Average Value of the Function	f(x)=x^2+x-9 ; [0,18]	$f (x) = x^{2} + x - 9$ ; $[0, 18]$
60877	Find the Concavity	f(x)=9x^6-11x^5	$f (x) = 9 x^{6} - 11 x^{5}$
60878	Find the Concavity	f(x) = natural log of x^2-4x+13	$f (x) = \ln (x^{2} - 4 x + 13)$
60879	Find the Concavity	f(x)=x^2-7x-8	$f (x) = x^{2} - 7 x - 8$
60880	Find the Concavity	f(x)=4x^3+3x^2-6x+1	$f (x) = 4 x^{3} + 3 x^{2} - 6 x + 1$
60881	Find the Concavity	f(x)=2x^6-3x^5	$f (x) = 2 x^{6} - 3 x^{5}$
60882	Find the Concavity	f(x)=x^4-8x^2+8	$f (x) = x^{4} - 8 x^{2} + 8$
60883	Find the Concavity	f(x)=tan(x)	$f (x) = \tan (x)$
60884	Find the Concavity	f(x)=1/(x-2)	$f (x) = \frac{1}{x - 2}$
60885	Find the Derivative of the Integral	limit as x approaches 0 of ( integral from 0 to x of (t^2)/(t^4+1) with respect to t)/(x^3)	$lim_{x \to 0} \frac{\int_{0}^{x} \frac{t^{2}}{t^{4} + 1} d t}{x^{3}}$
60886	Find the Derivative of the Integral	g(x) = integral from 1 to x of 1/(t^3+5) with respect to t	$g (x) = \int_{1}^{x} \frac{1}{t^{3} + 5} d t$
60887	Find the Derivative of the Integral	g(x) = integral from 1 to x of 7/(t^3+5) with respect to t	$g (x) = \int_{1}^{x} \frac{7}{t^{3} + 5} d t$
60888	Find the Derivative of the Integral	h(x) = integral from 1 to square root of x of (z^2)/(z^4+1) with respect to z	$h (x) = \int_{1}^{\sqrt{x}} \frac{z^{2}}{z^{4} + 1} d z$
60889	Identify the Sequence	9 , 13 , 17 , 21	$9$ , $13$ , $17$ , $21$
60890	Find the Derivative of the Integral	integral from 1 to x of 7/(t^3+7) with respect to t	$\int_{1}^{x} \frac{7}{t^{3} + 7} d t$
60891	Find the Derivative of the Integral	integral from 0 to x of square root of t^3+t^5 with respect to t	$\int_{0}^{x} \sqrt{t^{3} + t^{5}} d t$
60892	Find the Derivative of the Integral	integral from 0 to x^3 of e^(-t) with respect to t	$\int_{0}^{x^{3}} e^{- t} d t$
60893	Find the x and y Intercepts	r=4+2sin(theta)	$r = 4 + 2 \sin (θ)$
60894	Find the x and y Intercepts	y=cot(3x)	$y = \cot (3 x)$
60895	Find the x and y Intercepts	y=1+1/x+1/(x^2)	$y = 1 + \frac{1}{x} + \frac{1}{x^{2}}$
60896	Solve by Factoring	3X^2-3=0	$3 X^{2} - 3 = 0$
60897	Evaluate from the Right	limit as x approaches 0 of (1+x)^(cot(x))	$lim_{x \to 0} {(1 + x)}^{\cot (x)}$
60898	Convert to a Simplified Fraction	0.60653066	$0.60653066$
60899	Convert to a Simplified Fraction	square root of 74	$\sqrt{74}$
60900	Find the Antiderivative	f(t)=7t	$f (t) = 7 t$