Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
46701	Find the Concavity	f(x)=64x^2+128/x+3	$f (x) = 64 x^{2} + \frac{128}{x} + 3$
46702	Find the Concavity	f(x)=6sin(x)+6cos(x)	$f (x) = 6 \sin (x) + 6 \cos (x)$
46703	Find the Concavity	f(x)=6-5x^4	$f (x) = 6 - 5 x^{4}$
46704	Find the Concavity	f(x)=3x^4-16x^3+24x^2+48	$f (x) = 3 x^{4} - 16 x^{3} + 24 x^{2} + 48$
46705	Find the Concavity	f(x)=(x^2+6)/(x^2-4)	$f (x) = \frac{x^{2} + 6}{x^{2} - 4}$
46706	Find the Concavity	f(x)=(x+11)/(x^2-121)	$f (x) = \frac{x + 11}{x^{2} - 121}$
46707	Find the Concavity	f(x)=x^4-4x^3-90x^2+5x+4	$f (x) = x^{4} - 4 x^{3} - 90 x^{2} + 5 x + 4$
46708	Find the Derivative of the Integral	y=(sin(x))/(3x)+(3x)/(sin(x))	$y = \frac{\sin (x)}{3 x} + \frac{3 x}{\sin (x)}$
46709	Find the Derivative of the Integral	integral from -5 to 3x of square root of 15-t with respect to t	$\int_{- 5}^{3 x} \sqrt{15 - t} d t$
46710	Find the Derivative of the Integral	(d^102)/(dx^102)(sin(x))	$\frac{d^{102}}{d x^{102}} (\sin (x))$
46711	Find the Derivative of the Integral	xcos(x+y)-y^2=8	$x \cos (x + y) - y^{2} = 8$
46712	Find the Derivative of the Integral	y = natural log of \|1+t-t^3\|	$y = \ln (\| 1 + t - t^{3} \|)$
46713	Find the Derivative of the Integral	y=arcsin(4x+1)	$y = \arcsin (4 x + 1)$
46714	Find the Derivative of the Integral	y=(8x)/(9-cot(x))	$y = \frac{8 x}{9 - \cot (x)}$
46715	Find the Derivative of the Integral	y=arcsin(6x+1)	$y = \arcsin (6 x + 1)$
46716	Find the Derivative of the Integral	y=sin(tan(8x))	$y = \sin (\tan (8 x))$
46717	Find the Derivative of the Integral	tan(x-y)=y/(4+x^2)	$\tan (x - y) = \frac{y}{4 + x^{2}}$
46718	Find the Derivative of the Integral	integral from 1 to x of square root of 19-t with respect to t	$\int_{1}^{x} \sqrt{19 - t} d t$
46719	Find the Derivative of the Integral	y=csc(5x)^2	$y = \csc^{2} (5 x)$
46720	Find the Derivative of the Integral	integral from 0 to x of e^(t^2) with respect to t	$\int_{0}^{x} e^{t^{2}} d t$
46721	Expand the Logarithmic Expression	natural log of (7y)/(6z)	$\ln (\frac{7 y}{6 z})$
46722	Expand the Logarithmic Expression	natural log of cube root of y-8 , y>8	$\ln (\sqrt[3]{y - 8})$ , $y > 8$
46723	Find the Local Maxima and Minima	f(t)=7t+3/t	$f (t) = 7 t + \frac{3}{t}$
46724	Find the Local Maxima and Minima	f(x)=3x^4-20x^3+42x^2-36x	$f (x) = 3 x^{4} - 20 x^{3} + 42 x^{2} - 36 x$
46725	Find the Local Maxima and Minima	f(x)=-x^3+12x-7	$f (x) = - x^{3} + 12 x - 7$
46726	Find the Local Maxima and Minima	f(x)=16x^3-4x^4	$f (x) = 16 x^{3} - 4 x^{4}$
46727	Find the Local Maxima and Minima	f(x)=7 square root of 2cos(x)+7sin(x)^2	$f (x) = 7 \sqrt{2} \cos (x) + 7 \sin^{2} (x)$
46728	Find the Local Maxima and Minima	f(x)=4-x-x^2	$f (x) = 4 - x - x^{2}$
46729	Find the Local Maxima and Minima	f(x)=3-x^(2/3)	$f (x) = 3 - x^{\frac{2}{3}}$
46730	Find the Local Maxima and Minima	f(x)=x^3-12x^2-27x+2	$f (x) = x^{3} - 12 x^{2} - 27 x + 2$
46731	Find the Local Maxima and Minima	g(x)=230+8x^3+x^4	$g (x) = 230 + 8 x^{3} + x^{4}$
46732	Find the Local Maxima and Minima	f(x)=x square root of 144-x^2	$f (x) = x \sqrt{144 - x^{2}}$
46733	Find the Local Maxima and Minima	f(x)=x^2+120/x	$f (x) = x^{2} + \frac{120}{x}$
46734	Find the Inflection Points	1/3x^3-x^2+x+1	$\frac{1}{3} x^{3} - x^{2} + x + 1$
46735	Find the Inflection Points	5-7x^4	$5 - 7 x^{4}$
46736	Find the Inflection Points	natural log of x^2-8x+41	$\ln (x^{2} - 8 x + 41)$
46737	Find the Inflection Points	x^3-2x^2-4x+9	$x^{3} - 2 x^{2} - 4 x + 9$
46738	Find the Inflection Points	8x^2-8sin(2x)	$8 x^{2} - 8 \sin (2 x)$
46739	Find the Inflection Points	1/4x^4-2x^2	$\frac{1}{4} x^{4} - 2 x^{2}$
46740	Add	(7a^3-2a-2)+(-5a+3)	$(7 a^{3} - 2 a - 2) + (- 5 a + 3)$
46741	Find the Inflection Points	x^3-7x^2-5x+9	$x^{3} - 7 x^{2} - 5 x + 9$
46742	Find the Inflection Points	150+8x^3+x^4	$150 + 8 x^{3} + x^{4}$
46743	Find the Inflection Points	20e^x-e^(2x)	$20 e^{x} - e^{2 x}$
46744	Find the Inflection Points	x^3-6x^2+5x+6	$x^{3} - 6 x^{2} + 5 x + 6$
46745	Find the Inflection Points	9cos(x)^2-18sin(x)	$9 \cos^{2} (x) - 18 \sin (x)$
46746	Find the Inflection Points	log base 5 of 1+x^2	$\log_{5} (1 + x^{2})$
46747	Find the Inflection Points	4sin(x)+4cos(x)	$4 \sin (x) + 4 \cos (x)$
46748	Find the Inflection Points	x^3-7x^2	$x^{3} - 7 x^{2}$
46749	Find the Inflection Points	x^3-3x^2+9x	$x^{3} - 3 x^{2} + 9 x$
46750	Find the Inflection Points	x^3-18x^2+81x	$x^{3} - 18 x^{2} + 81 x$
46751	Find the Inflection Points	2sin(x)^3+3sin(x)+2	$2 \sin^{3} (x) + 3 \sin (x) + 2$
46752	Find the Inflection Points	(x^2)/2- natural log of x	$\frac{x^{2}}{2} - \ln (x)$
46753	Find the Roots (Zeros)	f(x)=4x^5-8x^4-5x^3+10x^2+x-2	$f (x) = 4 x^{5} - 8 x^{4} - 5 x^{3} + 10 x^{2} + x - 2$
46754	Find the Roots (Zeros)	f(x)=11x^3+124x^2+34x+11	$f (x) = 11 x^{3} + 124 x^{2} + 34 x + 11$
46755	Find the Roots (Zeros)	f(x)=3x^2-7x-5	$f (x) = 3 x^{2} - 7 x - 5$
46756	Expand the Logarithmic Expression	natural log of (6y)/(5z)	$\ln (\frac{6 y}{5 z})$
46757	Expand the Logarithmic Expression	log base 4 of x^5y^7	$\log_{4} (x^{5} y^{7})$
46758	Expand the Logarithmic Expression	natural log of (5y)/(3z)	$\ln (\frac{5 y}{3 z})$
46759	Expand the Logarithmic Expression	log base 6 of (6p)/(5k)	$\log_{6} (\frac{6 p}{5 k})$
46760	Find the Local Maxima and Minima	f(x)=x^3-27x+52	$f (x) = x^{3} - 27 x + 52$
46761	Find the Local Maxima and Minima	f(x)=64x^3-12x+4	$f (x) = 64 x^{3} - 12 x + 4$
46762	Find the Local Maxima and Minima	f(x)=-8x^3+24x+9	$f (x) = - 8 x^{3} + 24 x + 9$
46763	Find the Local Maxima and Minima	f(x)=216/(x^2+36)	$f (x) = \frac{216}{x^{2} + 36}$
46764	Find the Local Maxima and Minima	f(X)=4x^4-32x^2	$f (X) = 4 x^{4} - 32 x^{2}$
46765	Find the Local Maxima and Minima	f(x)=x^3+3x^2-45x+1	$f (x) = x^{3} + 3 x^{2} - 45 x + 1$
46766	Find the Local Maxima and Minima	f(x)=x^2+360/x	$f (x) = x^{2} + \frac{360}{x}$
46767	Find the Local Maxima and Minima	f(x)=x square root of 49-x^2	$f (x) = x \sqrt{49 - x^{2}}$
46768	Find the Local Maxima and Minima	f(x)=e^(x^3-3x)	$f (x) = e^{x^{3} - 3 x}$
46769	Find the Local Maxima and Minima	f(x)=(x^3+6x^2-3x)/(x^2+1)	$f (x) = \frac{x^{3} + 6 x^{2} - 3 x}{x^{2} + 1}$
46770	Find the Local Maxima and Minima	f(x)=4x square root of 5-x	$f (x) = 4 x \sqrt{5 - x}$
46771	Complete the Square	x^2+6x+25	$x^{2} + 6 x + 25$
46772	Find the Inflection Points	y=x^4-2x^3	$y = x^{4} - 2 x^{3}$
46773	Find the Inflection Points	y=2-x-x^3	$y = 2 - x - x^{3}$
46774	Find the Inflection Points	y=3x^5-20x^3	$y = 3 x^{5} - 20 x^{3}$
46775	Convert to a Simplified Fraction	0.585858	$0.585858$
46776	Solve by Factoring	9x^2-49=0	$9 x^{2} - 49 = 0$
46777	Evaluate from the Right	limit as x approaches 0 from the right of x^x	$lim_{x \to 0} x^{x}$
46778	Evaluate from the Right	limit as x approaches pi of cot(x)	$lim_{x \to π} \cot (x)$
46779	Evaluate from the Right	limit as x approaches pi/2 of 5e^(tan(x))	$lim_{x \to \frac{π}{2}} 5 e^{\tan (x)}$
46780	Evaluate from the Right	limit as x approaches 2 of natural log of x-2	$lim_{x \to 2} \ln (x - 2)$
46781	Evaluate from the Right	limit as x approaches pi of csc(x)	$lim_{x \to π} \csc (x)$
46782	Evaluate from the Right	limit as x approaches pi/9 of csc(9x)	$lim_{x \to \frac{π}{9}} \csc (9 x)$
46783	Convert to Regular Notation	2.5*10^-9	$2.5 \cdot 10^{- 9}$
46784	Solve by Factoring	8x^2-6x-5=0	$8 x^{2} - 6 x - 5 = 0$
46785	Solve by Factoring	x^5-3x=1	$x^{5} - 3 x = 1$
46786	Calculate the Square Root	49	$49$
46787	Find the Slope of the Tangent Line at x=1	f(x)=x^4-10x^2+9 , x=1	$f (x) = x^{4} - 10 x^{2} + 9$ , $x = 1$
46788	Find the Slope of the Tangent Line at x=2	f(x)=x^4-10x^2+9 ; x=2	$f (x) = x^{4} - 10 x^{2} + 9$ ; $x = 2$
46789	Find the Integral	xsec(x)^2	$x \sec^{2} (x)$
46790	Find the Integral	(cos(x))/(sin(x))	$\frac{\cos (x)}{\sin (x)}$
46791	Find the Integral	natural log of 4x+C	$\ln (4 x) + C$
46792	Verify the Identity	cos(theta)(tan(theta)+cot(theta))=csc(theta)	$\cos (θ (\tan (θ) + \cot (θ))) = \csc (θ)$
46793	Convert to Interval Notation	1/6<(2x-19)/12<=2/3	$\frac{1}{6} < \frac{2 x - 19}{12} \leq \frac{2}{3}$
46794	Convert to Interval Notation	\|2-3x\|>=-5	$\| 2 - 3 x \| \geq - 5$
46795	Convert to Interval Notation	324x^3-144x>0	$324 x^{3} - 144 x > 0$
46796	Convert to Interval Notation	4x^3-36x>0	$4 x^{3} - 36 x > 0$
46797	Convert to Interval Notation	x/(x-1)>2	$\frac{x}{x - 1} > 2$
46798	Find the Integral	2sin(t)	$2 \sin (t)$
46799	Find the Integral	1/2sin(2x)	$\frac{1}{2} \sin (2 x)$
46800	Find the Integral	integral of ( square root of x^2-9)/(x^3) with respect to x	$\int \frac{\sqrt{x^{2} - 9}}{x^{3}} d x$