Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
47901	Find the Roots (Zeros)	f(x)=3x^2-7x-11	$f (x) = 3 x^{2} - 7 x - 11$
47902	Find the Roots (Zeros)	f(x)=x^4-8x^3+15x^2+58x+34	$f (x) = x^{4} - 8 x^{3} + 15 x^{2} + 58 x + 34$
47903	Find the Roots (Zeros)	f(x)=2^x-x^3+3	$f (x) = 2^{x} - x^{3} + 3$
47904	Find the Roots (Zeros)	f(x)=cot(x)	$f (x) = \cot (x)$
47905	Add	(3t-3)+(6t^2+4t+13)+(-8t^2+11t-1)	$(3 t - 3) + (6 t^{2} + 4 t + 13) + (- 8 t^{2} + 11 t - 1)$
47906	Add	2 square root of x+2 square root of x	$2 \sqrt{x} + 2 \sqrt{x}$
47907	Find the Inflection Points	x^4-10x^3+24x^2+3x+5	$x^{4} - 10 x^{3} + 24 x^{2} + 3 x + 5$
47908	Find the Inflection Points	(5x)/(x^2+16)	$\frac{5 x}{x^{2} + 16}$
47909	Find the Inflection Points	x^3-9x^2+27x-27	$x^{3} - 9 x^{2} + 27 x - 27$
47910	Find the Inflection Points	x^2-sin(2x)	$x^{2} - \sin (2 x)$
47911	Find the Inflection Points	x^3-7x^2-24x+5	$x^{3} - 7 x^{2} - 24 x + 5$
47912	Find the Inflection Points	natural log of x^2-4x+29	$\ln (x^{2} - 4 x + 29)$
47913	Find the Inflection Points	x^3-3x^2-9x+4	$x^{3} - 3 x^{2} - 9 x + 4$
47914	Find the Inflection Points	6sin(x)+sin(2x)	$6 \sin (x) + \sin (2 x)$
47915	Find the Inflection Points	(x+4)^(2/7)	${(x + 4)}^{\frac{2}{7}}$
47916	Find the Inflection Points	(x^3)/3-2x^2-5x	$\frac{x^{3}}{3} - 2 x^{2} - 5 x$
47917	Find the Inflection Points	x^3+12x^2+48x-4	$x^{3} + 12 x^{2} + 48 x - 4$
47918	Find the Inflection Points	12x^2-12sin(2x)	$12 x^{2} - 12 \sin (2 x)$
47919	Find the Inflection Points	12x+12e^x	$12 x + 12 e^{x}$
47920	Find the Inflection Points	(x+4)/(x^2-5x-36)	$\frac{x + 4}{x^{2} - 5 x - 36}$
47921	Find the Inflection Points	-2/(x^2-x-6)	$\frac{- 2}{x^{2} - x - 6}$
47922	Find the Inflection Points	(x+5)^(4/7)	${(x + 5)}^{\frac{4}{7}}$
47923	Find the Inflection Points	x^4-3x^2-1	$x^{4} - 3 x^{2} - 1$
47924	Find the Inflection Points	11x^4-66x^2	$11 x^{4} - 66 x^{2}$
47925	Find the Inflection Points	(5x^2)/(x^2-9)	$\frac{5 x^{2}}{x^{2} - 9}$
47926	Find the Inflection Points	x^3-5x-1	$x^{3} - 5 x - 1$
47927	Expand the Logarithmic Expression	natural log of 8/(5x^5y)	$\ln (\frac{8}{5 x^{5} y})$
47928	Expand the Logarithmic Expression	log base 3 of (3p)/(5k)	$\log_{3} (\frac{3 p}{5 k})$
47929	Expand the Logarithmic Expression	natural log of fifth root of (4x^2-1)/(4x^2+1)	$\ln (\sqrt[5]{\frac{4 x^{2} - 1}{4 x^{2} + 1}})$
47930	Expand the Logarithmic Expression	log base b of (b^5x^2)/(y^3)	$\log_{b} (\frac{b^{5} x^{2}}{y^{3}})$
47931	Expand the Logarithmic Expression	log of square root of c^4d	$\log (\sqrt{c^{4} d})$
47932	Expand the Logarithmic Expression	log base 2 of (s^7)/(5t^2)	$\log_{2} (\frac{s^{7}}{5 t^{2}})$
47933	Expand the Logarithmic Expression	natural log of 6/(5x^5y)	$\ln (\frac{6}{5 x^{5} y})$
47934	Expand the Logarithmic Expression	natural log of cube root of y-9 , y>9	$\ln (\sqrt[3]{y - 9})$ , $y > 9$
47935	Expand the Logarithmic Expression	log base 3 of 6x	$\log_{3} (6 x)$
47936	Expand the Logarithmic Expression	log base 4 of (4p)/(11k)	$\log_{4} (\frac{4 p}{11 k})$
47937	Expand the Logarithmic Expression	log of 10x square root of x-3	$\log (10 x \sqrt{x - 3})$
47938	Expand the Logarithmic Expression	log base 4 of fourth root of (x^2y^10)/(z^9)	$\log_{4} (\sqrt[4]{\frac{x^{2} y^{10}}{z^{9}}})$
47939	Expand the Logarithmic Expression	log of (z^3)/( square root of xy^3)	$\log (\frac{z^{3}}{\sqrt{x y^{3}}})$
47940	Expand the Logarithmic Expression	natural log of (5y)/(2z)	$\ln (\frac{5 y}{2 z})$
47941	Find the Local Maxima and Minima	f(x)=x^3+9x^2+15x+1	$f (x) = x^{3} + 9 x^{2} + 15 x + 1$
47942	Find the Local Maxima and Minima	f(x)=81x+16/x	$f (x) = 81 x + \frac{16}{x}$
47943	Find the Local Maxima and Minima	f(x)=64x^3-12x+9	$f (x) = 64 x^{3} - 12 x + 9$
47944	Find the Local Maxima and Minima	f(x)=(5e^x)/(x^5)	$f (x) = \frac{5 e^{x}}{x^{5}}$
47945	Find the Local Maxima and Minima	f(x)=1/3x^3-4x^2+16x-1	$f (x) = \frac{1}{3} x^{3} - 4 x^{2} + 16 x - 1$
47946	Find the Local Maxima and Minima	f(x)=x^2+400/x	$f (x) = x^{2} + \frac{400}{x}$
47947	Find the Local Maxima and Minima	g(x)=- square root of x^2+6x+18	$g (x) = - \sqrt{x^{2} + 6 x + 18}$
47948	Find the Local Maxima and Minima	f(x)=x^2(2-5x)^3	$f (x) = x^{2} {(2 - 5 x)}^{3}$
47949	Find the Local Maxima and Minima	f(x)=(x^2-14x+49)/(x-10)	$f (x) = \frac{x^{2} - 14 x + 49}{x - 10}$
47950	Find the Local Maxima and Minima	f(x)=(3x)/(x^2+25)	$f (x) = \frac{3 x}{x^{2} + 25}$
47951	Find the Local Maxima and Minima	f(x)=5x^5-25x	$f (x) = 5 x^{5} - 25 x$
47952	Find the Local Maxima and Minima	f(x)=5x^2+3x-1	$f (x) = 5 x^{2} + 3 x - 1$
47953	Find the Local Maxima and Minima	f(x)=x^3-3x^2-24x-2	$f (x) = x^{3} - 3 x^{2} - 24 x - 2$
47954	Find the Local Maxima and Minima	f(x)=7x square root of 2-x	$f (x) = 7 x \sqrt{2 - x}$
47955	Find the Local Maxima and Minima	f(x)=1/3x^3-2x^2	$f (x) = \frac{1}{3} x^{3} - 2 x^{2}$
47956	Find the Local Maxima and Minima	f(x)=(x^3)/2-6x	$f (x) = \frac{x^{3}}{2} - 6 x$
47957	Find the Local Maxima and Minima	f(x)=250+8x^3+x^4	$f (x) = 250 + 8 x^{3} + x^{4}$
47958	Find the Local Maxima and Minima	f(x)=-1-x^(4/5)	$f (x) = - 1 - x^{\frac{4}{5}}$
47959	Find the Local Maxima and Minima	f(x)=x^3-75x+2	$f (x) = x^{3} - 75 x + 2$
47960	Find the Local Maxima and Minima	f(x)=4x+7x^(4/7)	$f (x) = 4 x + 7 x^{\frac{4}{7}}$
47961	Find the Local Maxima and Minima	f(x)=(3e^x)/(x^4)	$f (x) = \frac{3 e^{x}}{x^{4}}$
47962	Find the Local Maxima and Minima	f(x)=x^3-12x^2+45x-8	$f (x) = x^{3} - 12 x^{2} + 45 x - 8$
47963	Find the Local Maxima and Minima	f(x)=16x^4-96x^2	$f (x) = 16 x^{4} - 96 x^{2}$
47964	Find the Local Maxima and Minima	f(x)=9x+1/x	$f (x) = 9 x + \frac{1}{x}$
47965	Find the Local Maxima and Minima	f(x)=x^3-27x+57	$f (x) = x^{3} - 27 x + 57$
47966	Find the Local Maxima and Minima	f(x)=x^3-75x+5	$f (x) = x^{3} - 75 x + 5$
47967	Find the Local Maxima and Minima	f(x)=5x^3+15x-2	$f (x) = 5 x^{3} + 15 x - 2$
47968	Find the Local Maxima and Minima	f(x)=-7x^3+21x+3	$f (x) = - 7 x^{3} + 21 x + 3$
47969	Find the Local Maxima and Minima	f(x)=x^3-3x-5	$f (x) = x^{3} - 3 x - 5$
47970	Find the Local Maxima and Minima	f(x)=1/3x^3-x^2+x-3	$f (x) = \frac{1}{3} x^{3} - x^{2} + x - 3$
47971	Find the Local Maxima and Minima	f(x)=2x^3-6x+3	$f (x) = 2 x^{3} - 6 x + 3$
47972	Find the Local Maxima and Minima	f(x)=2x+98/x	$f (x) = 2 x + \frac{98}{x}$
47973	Find the Local Maxima and Minima	f(x)=x^3-12x+25	$f (x) = x^{3} - 12 x + 25$
47974	Find the Local Maxima and Minima	f(x)=3x^3+9x^2-27x+5	$f (x) = 3 x^{3} + 9 x^{2} - 27 x + 5$
47975	Find the Local Maxima and Minima	f(x)=2x^2+4000/x+10	$f (x) = 2 x^{2} + \frac{4000}{x} + 10$
47976	Find the Local Maxima and Minima	f(x)=x square root of x^2+4	$f (x) = x \sqrt{x^{2} + 4}$
47977	Expand the Logarithmic Expression	natural log of square root of x^5	$\ln (\sqrt{x^{5}})$
47978	Expand the Logarithmic Expression	log base 3 of 4x^3	$\log_{3} (4 x^{3})$
47979	Verify the Identity	sin(theta)^2(1+cot(theta)^2)=1	$\sin^{2} (θ (1 + \cot^{2} (θ))) = 1$
47980	Verify the Identity	cos(theta)-sec(theta)=-sin(theta)tan(theta)	$\cos (θ) - \sec (θ) = - \sin (θ) \tan (θ)$
47981	Verify the Identity	tan(theta)=(sin(theta))/(cos(theta))	$\tan (θ) = \frac{\sin (θ)}{\cos (θ)}$
47982	Verify the Identity	tan(theta)^2=-3/2sec(theta)	$\tan^{2} (θ) = - \frac{3}{2} \sec (θ)$
47983	Find the Integral	integral from 0 to infinity of xe^(-x^2) with respect to x	$\int_{0}^{\infty} x e^{- x^{2}} d x$
47984	Find the Integral	(dy)/(e^y)	$\frac{d y}{e^{y}}$
47985	Find the Integral	1/(y-1)	$\frac{1}{y - 1}$
47986	Find the Integral	csc(2x)	$\csc (2 x)$
47987	Find the Integral	(e^(5/t))/(3t^2)	$\frac{e^{\frac{5}{t}}}{3 t^{2}}$
47988	Find the Integral	integral of (arccos(2x))/( square root of 1-4x^2) with respect to x	$\int \frac{\arccos (2 x)}{\sqrt{1 - 4 x^{2}}} d x$
47989	Find the Integral	sin(xdx)^2	$\sin^{2} (x d x)$
47990	Find the Integral	sin(x)^7	$\sin^{7} (x)$
47991	Find the Integral	4x^-1	$4 x^{- 1}$
47992	Find the Integral	12cos(2x)^3	$12 \cos^{3} (2 x)$
47993	Find the Integral	2/y	$\frac{2}{y}$
47994	Find the Integral	integral of 1/(5+ square root of 2x) with respect to x	$\int \frac{1}{5 + \sqrt{2 x}} d x$
47995	Find the Integral	x^3 square root of x	$x^{3} \sqrt{x}$
47996	Find the Integral	integral of e^(-8x) with respect to x	$\int e^{- 8 x} d x$
47997	Find the Integral	1/(cos(y)^2)	$\frac{1}{\cos^{2} (y)}$
47998	Find the Integral	integral from -k to k of square root of k^2-x^2 with respect to x	$\int_{- k}^{k} \sqrt{k^{2} - x^{2}} d x$
47999	Find the Integral	natural log of xdx	$\ln (x) d x$
48000	Find the Integral	integral of (4sin(x))/(3+cos(x)) with respect to x	$\int \frac{4 \sin (x)}{3 + \cos (x)} d x$