Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
44001	Find the Inflection Points	x^4+4x^3-18x^2	$x^{4} + 4 x^{3} - 18 x^{2}$
44002	Find the Inflection Points	x+2cos(x)	$x + 2 \cos (x)$
44003	Expand the Logarithmic Expression	natural log of x^2y^3	$\ln (x^{2} y^{3})$
44004	Find the Second Derivative	y=3sin(x)cos(x)	$y = 3 \sin (x) \cos (x)$
44005	Find the Second Derivative	y=2tan(x)	$y = 2 \tan (x)$
44006	Find the Second Derivative	y=e^(-8x^2)	$y = e^{- 8 x^{2}}$
44007	Find the Second Derivative	y=2cot(x)	$y = 2 \cot (x)$
44008	Find the Second Derivative	xy+7e^y=7e	$x y + 7 e^{y} = 7 e$
44009	Find the Second Derivative	s=7t^3-3t^7	$s = 7 t^{3} - 3 t^{7}$
44010	Find the Second Derivative	y=10xsin(x^2)	$y = 10 x \sin (x^{2})$
44011	Write in Exponential Form	log base 16 of 2=1/4	$\log_{16} (2) = \frac{1}{4}$
44012	Find the Fourth Derivative	y=10xsin(x^2)	$y = 10 x \sin (x^{2})$
44013	Find Where Increasing/Decreasing Using Derivatives	f(x)=x^3-27x+9	$f (x) = x^{3} - 27 x + 9$
44014	Divide	48÷3	$48 \div 3$
44015	Divide	42/2	$\frac{42}{2}$
44016	Divide	(x^3-6x-20)/(x+5)	$\frac{x^{3} - 6 x - 20}{x + 5}$
44017	Divide	60/3	$\frac{60}{3}$
44018	Divide	7.5/2	$\frac{7.5}{2}$
44019	Divide	28/3	$\frac{28}{3}$
44020	Divide	(pi/2)÷2	$\frac{π}{2} \div 2$
44021	Divide	63/3	$\frac{63}{3}$
44022	Divide	(2pi)÷4	$2 π \div 4$
44023	Divide	78/6	$\frac{78}{6}$
44024	Find the Maximum/Minimum Value	f(x,y)=x^2+y^2-6x-10	$f (x, y) = x^{2} + y^{2} - 6 x - 10$
44025	Convert to a Decimal	(3pi)/4	$\frac{3 π}{4}$
44026	Convert to a Decimal	(5pi)/4	$\frac{5 π}{4}$
44027	Find the Antiderivative	x natural log of x-x	$x \ln (x) - x$
44028	Find the Antiderivative	sec(2x)^2	$\sec^{2} (2 x)$
44029	Find the Antiderivative	96-32x	$96 - 32 x$
44030	Find the Antiderivative	xcos(x^2)	$x \cos (x^{2})$
44031	Find the Roots (Zeros)	2x^2-1	$2 x^{2} - 1$
44032	Find the Antiderivative	x^2 square root of x^3+1	$x^{2} \sqrt{x^{3} + 1}$
44033	Find the Antiderivative	2 natural log of x	$2 \ln (x)$
44034	Find the Antiderivative	4cos(1/4pix)	$4 \cos (\frac{1}{4} π x)$
44035	Find the Area Between the Curves	y=3x-x^2 , y=x^2	$y = 3 x - x^{2}$ , $y = x^{2}$
44036	Find the Inflection Points	f(x)=2sin(x)^3+3sin(x)-2	$f (x) = 2 \sin^{3} (x) + 3 \sin (x) - 2$
44037	Find the Tangent Line at the Point	y=3xe^x , (0,0)	$y = 3 x e^{x}$ , $(0, 0)$
44038	Find the Tangent Line at the Point	y=4xsin(x) , (pi/2,2pi)	$y = 4 x \sin (x)$ , $(\frac{π}{2}, 2 π)$
44039	Find the Tangent Line at the Point	y=x^4+8e^x , (0,8)	$y = x^{4} + 8 e^{x}$ , $(0, 8)$
44040	Find the Tangent Line at the Point	y=5x-x^2 , (1,4)	$y = 5 x - x^{2}$ , $(1, 4)$
44041	Find the Tangent Line at the Point	y=6x-x^2 , (1,5)	$y = 6 x - x^{2}$ , $(1, 5)$
44042	Find the Derivative Using Chain Rule - d/dx	y=tan(6x^5)	$y = \tan (6 x^{5})$
44043	Find the Derivative Using Chain Rule - d/dx	y=sin(x^5)	$y = \sin (x^{5})$
44044	Find the Derivative Using Chain Rule - d/dx	y=cos(x^6)	$y = \cos (x^{6})$
44045	Find Where Increasing/Decreasing Using Derivatives	6x^5-15x^4+10x^3	$6 x^{5} - 15 x^{4} + 10 x^{3}$
44046	Find Where Increasing/Decreasing Using Derivatives	(x+5)^(6/7)	${(x + 5)}^{\frac{6}{7}}$
44047	Find Where Increasing/Decreasing Using Derivatives	7x^4-42x^2	$7 x^{4} - 42 x^{2}$
44048	Find the Second Derivative	f(x)=10e^x	$f (x) = 10 e^{x}$
44049	Find the Fourth Derivative	f(x)=(2x+1)^5	$f (x) = {(2 x + 1)}^{5}$
44050	Find the Third Derivative	f(x)=10e^x	$f (x) = 10 e^{x}$
44051	Find the Fourth Derivative	f(x)=4x^-4	$f (x) = 4 x^{- 4}$
44052	Evaluate Using L'Hospital's Rule	limit as x approaches 2 of (x-2)/(x^2-4)	$lim_{x \to 2} \frac{x - 2}{x^{2} - 4}$
44053	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (e^x-cos(x))/(4sin(x))	$lim_{x \to 0} \frac{e^{x} - \cos (x)}{4 \sin (x)}$
44054	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of (8-3x)/(9x^2+11)	$lim_{x \to \infty} \frac{8 - 3 x}{9 x^{2} + 11}$
44055	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of x^(9/x)	$lim_{x \to \infty} x^{\frac{9}{x}}$
44056	Convert from Radians to Degrees	0 degrees	$0 °$
44057	Find the Linearization at a=27	f(x)=x^(2/3) , a=27	$f (x) = x^{\frac{2}{3}}$ , $a = 27$
44058	Find the Linearization at a=32	f(x)=x^(4/5) , a=32	$f (x) = x^{\frac{4}{5}}$ , $a = 32$
44059	Find the Linearization at a=25	f(x)=x^(1/2) , a=25	$f (x) = x^{\frac{1}{2}}$ , $a = 25$
44060	Find the Linearization at a=0	f(x) = cube root of 1+x , a=0	$f (x) = \sqrt[3]{1 + x}$ , $a = 0$
44061	Find the Tangent Line at (0,0)	y=6xe^x , (0,0)	$y = 6 x e^{x}$ , $(0, 0)$
44062	Find the Asymptotes	y=5/(2x^2-11x-21)	$y = \frac{5}{2 x^{2} - 11 x - 21}$
44063	Find the Domain	f(x)=1/10	$f (x) = \frac{1}{10}$
44064	Find the Domain	f(x)=(3x^3-x^2-27x+9)/(x^2+4x+3)	$f (x) = \frac{3 x^{3} - x^{2} - 27 x + 9}{x^{2} + 4 x + 3}$
44065	Determine if Rational	1.73205080	$1.7320508$
44066	Find the Concavity	-5x^4+4x^3-20x-20	$- 5 x^{4} + 4 x^{3} - 20 x - 20$
44067	Find the Concavity	x square root of x+12	$x \sqrt{x + 12}$
44068	Find the Concavity	3x^4-24x^3+30x^2	$3 x^{4} - 24 x^{3} + 30 x^{2}$
44069	Find the Concavity	-x^4-2x^3+72x^2-13	$- x^{4} - 2 x^{3} + 72 x^{2} - 13$
44070	Find the Concavity	1/4x^4-3/2x^2	$\frac{1}{4} x^{4} - \frac{3}{2} x^{2}$
44071	Eliminate the Parameter	x=sin(1/2theta) , y=cos(1/2theta)	$x = \sin (\frac{1}{2} θ)$ , $y = \cos (\frac{1}{2} θ)$
44072	Find the Second Derivative	81cos(3x)	$81 \cos (3 x)$
44073	Find the Second Derivative	7xcos(x^2)	$7 x \cos (x^{2})$
44074	Find the Second Derivative	1/4sin(2x)	$\frac{1}{4} \sin (2 x)$
44075	Find the Second Derivative	[2csc(x)]	$[2 \csc (x)]$
44076	Find the Fourth Derivative	square root of 4x-8	$\sqrt{4 x - 8}$
44077	Find the Fourth Derivative	11e^(x^2)	$11 e^{x^{2}}$
44078	Find the Second Derivative	11e^(x^2)	$11 e^{x^{2}}$
44079	Find the Critical Points	f(x)=(2x)/(x^2+9)	$f (x) = \frac{2 x}{x^{2} + 9}$
44080	Find the Critical Points	f(x)=8x^3-12x^2-144x	$f (x) = 8 x^{3} - 12 x^{2} - 144 x$
44081	Find the Critical Points	f(x)=-3x^4+20x^3-24x^2	$f (x) = - 3 x^{4} + 20 x^{3} - 24 x^{2}$
44082	Find the Critical Points	f(x)=sin(x)^2- square root of 3sin(x)	$f (x) = \sin^{2} (x) - \sqrt{3} \sin (x)$
44083	Find the Critical Points	f(x)=cos(2x)	$f (x) = \cos (2 x)$
44084	Find the Domain	( cube root of x-2)/(x^3-2)	$\frac{\sqrt[3]{x - 2}}{x^{3} - 2}$
44085	Find the Derivative Using Quotient Rule - d/dx	y=(6x+5)/( square root of x)	$y = \frac{6 x + 5}{\sqrt{x}}$
44086	Find the Derivative Using Quotient Rule - d/dx	y=(x^6)/(x^4)	$y = \frac{x^{6}}{x^{4}}$
44087	Find the x and y Intercepts	(x^2+6)(36-x^2)	$(x^{2} + 6) (36 - x^{2})$
44088	Find the Domain and Range	g(t) = square root of 1-3^t	$g (t) = \sqrt{1 - 3^{t}}$
44089	Find the Derivative of the Integral	y=xsin(1/x)	$y = x \sin (\frac{1}{x})$
44090	Find the Derivative of the Integral	y=x^(2cos(x))	$y = x^{2 \cos (x)}$
44091	Find the Derivative of the Integral	y=(sec(x)+csc(x))/(csc(x))	$y = \frac{\sec (x) + \csc (x)}{\csc (x)}$
44092	Find the Concavity	f(x)=x^2-5x+8	$f (x) = x^{2} - 5 x + 8$
44093	Find the Concavity	f(x)=8-7x^4	$f (x) = 8 - 7 x^{4}$
44094	Find the Concavity	f(x)=2sin(x)^3+3sin(x)-2	$f (x) = 2 \sin^{3} (x) + 3 \sin (x) - 2$
44095	Find the Concavity	f(x)=5x^2-5sin(2x)	$f (x) = 5 x^{2} - 5 \sin (2 x)$
44096	Find the Concavity	f(x)=x square root of x+27	$f (x) = x \sqrt{x + 27}$
44097	Find the Absolute Max and Min over the Interval	f(x)=3x^3-3x^2-3x+5 ; [-1,0]	$f (x) = 3 x^{3} - 3 x^{2} - 3 x + 5$ ; $[- 1, 0]$
44098	Find the Absolute Max and Min over the Interval	f(x)=15x^4-4x^3 , [-2,2]	$f (x) = 15 x^{4} - 4 x^{3}$ , $[- 2, 2]$
44099	Evaluate Using the Squeeze Theorem	limit as x approaches infinity of (1+1/x)^x	$lim_{x \to \infty} {(1 + \frac{1}{x})}^{x}$
44100	Find the Maximum/Minimum Value	x^2+4x+18	$x^{2} + 4 x + 18$