Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
44801	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (1-cos(x))/(2sin(x)^2)	$lim_{x \to 0} \frac{1 - \cos (x)}{2 \sin^{2} (x)}$
44802	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (sin(x))/(5x+3sin(x))	$lim_{x \to 0} \frac{\sin (x)}{5 x + 3 \sin (x)}$
44803	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of cos(x)	$lim_{x \to \infty} \cos (x)$
44804	Evaluate Using L'Hospital's Rule	limit as x approaches 1 of (5x)/(x-1)-5/( natural log of x)	$lim_{x \to 1} \frac{5 x}{x - 1} - \frac{5}{\ln (x)}$
44805	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of 9x- natural log of x	$lim_{x \to \infty} 9 x - \ln (x)$
44806	Evaluate Using L'Hospital's Rule	limit as x approaches negative infinity of xe^x	$lim_{x \to - \infty} x e^{x}$
44807	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of ( natural log of x+1)/( log base 2 of x)	$lim_{x \to \infty} \frac{\ln (x + 1)}{\log_{2} (x)}$
44808	Find the Horizontal Tangent Line	25x^2+16y^2+200x-160y+400=0	$25 x^{2} + 16 y^{2} + 200 x - 160 y + 400 = 0$
44809	Find the Asymptotes	f(x)=(x+2)/(x^3-9x^2+14x)	$f (x) = \frac{x + 2}{x^{3} - 9 x^{2} + 14 x}$
44810	Find the Asymptotes	f(x)=3/(x^2-2x-15)	$f (x) = \frac{3}{x^{2} - 2 x - 15}$
44811	Find the Asymptotes	f(x)=6-7/x	$f (x) = 6 - \frac{7}{x}$
44812	Find the Asymptotes	f(x)=7-8/x	$f (x) = 7 - \frac{8}{x}$
44813	Find the Asymptotes	f(x)=(x+11)/(x^2-121)	$f (x) = \frac{x + 11}{x^{2} - 121}$
44814	Find the Asymptotes	g(t)=(t-6)/(t^2+36)	$g (t) = \frac{t - 6}{t^{2} + 36}$
44815	Find the Maximum/Minimum Value	x^2+2x+18	$x^{2} + 2 x + 18$
44816	Find the Second Derivative	8x^-3	$8 x^{- 3}$
44817	Find the Second Derivative	8csc(x)	$8 \csc (x)$
44818	Find the Second Derivative	e^(7x^2)	$e^{7 x^{2}}$
44819	Find the Second Derivative	e^(8x)	$e^{8 x}$
44820	Find the Second Derivative	e^(11x)cos(x)	$e^{11 x} \cos (x)$
44821	Find the Second Derivative	cos(6x^2)	$\cos (6 x^{2})$
44822	Find the Second Derivative	7e^(-x)-4e^(-7x)	$7 e^{- x} - 4 e^{- 7 x}$
44823	Find the Second Derivative	natural log of sec(5x)+tan(5x)	$\ln (\sec (5 x) + \tan (5 x))$
44824	Find the Second Derivative	x^(22/7)	$x^{\frac{22}{7}}$
44825	Find the Third Derivative	14x^3-34x^2	$14 x^{3} - 34 x^{2}$
44826	Find the Third Derivative	6x^-4	$6 x^{- 4}$
44827	Find the Second Derivative	(7x-1)/(7x+1)	$\frac{7 x - 1}{7 x + 1}$
44828	Find the Fourth Derivative	e^(8x)	$e^{8 x}$
44829	Find the Fourth Derivative	x^(22/7)	$x^{\frac{22}{7}}$
44830	Find the Second Derivative	-x/(7y)	$- \frac{x}{7 y}$
44831	Find the Second Derivative	5xcos(x^2)	$5 x \cos (x^{2})$
44832	Find the Fourth Derivative	14x^3-34x^2	$14 x^{3} - 34 x^{2}$
44833	Find the Fourth Derivative	3x^2+5e^x	$3 x^{2} + 5 e^{x}$
44834	Find the Second Derivative	256cos(2x)	$256 \cos (2 x)$
44835	Find the Second Derivative	17e^(x^2)	$17 e^{x^{2}}$
44836	Find the Second Derivative	19e^(x^2)	$19 e^{x^{2}}$
44837	Find the Second Derivative	14x^3-34x^2	$14 x^{3} - 34 x^{2}$
44838	Find the Antiderivative	1/( square root of 16-x^2)	$\frac{1}{\sqrt{16 - x^{2}}}$
44839	Find the Antiderivative	4x^-5	$4 x^{- 5}$
44840	Find the Antiderivative	5sin(x)^2cos(x)	$5 \sin^{2} (x) \cos (x)$
44841	Find the Antiderivative	4x-x^3	$4 x - x^{3}$
44842	Find the Antiderivative	x^2cos(x)	$x^{2} \cos (x)$
44843	Find the Antiderivative	1/2sin(2x)	$\frac{1}{2} \sin (2 x)$
44844	Find the Antiderivative	cube root of y	$\sqrt[3]{y}$
44845	Find the Antiderivative	x^3 square root of x	$x^{3} \sqrt{x}$
44846	Find the Antiderivative	cube root of x^5	$\sqrt[3]{x^{5}}$
44847	Find the Antiderivative	1/((3x)^2)	$\frac{1}{{(3 x)}^{2}}$
44848	Find the Antiderivative	sec(x)(sec(x)+tan(x))	$\sec (x (\sec (x) + \tan (x)))$
44849	Find the Antiderivative	sec(x)(tan(x)-sec(x))	$\sec (x (\tan (x) - \sec (x)))$
44850	Find the Antiderivative	1/(x^2)dx	$\frac{1}{x^{2}} d x$
44851	Find the Antiderivative	(x-2)	$(x - 2)$
44852	Find the Antiderivative	-10x^4+8x^3	$- 10 x^{4} + 8 x^{3}$
44853	Find the Antiderivative	-tan(x)	$- \tan (x)$
44854	Find the Antiderivative	4sec(theta)tan(theta)	$4 \sec (θ) \tan (θ)$
44855	Find the Antiderivative	-1/7x^(-8/7)	$- \frac{1}{7} x^{- \frac{8}{7}}$
44856	Find the Antiderivative	3^x natural log of 3	$3^{x} \ln (3)$
44857	Find the Antiderivative	e^(-5x^3)	$e^{- 5 x^{3}}$
44858	Find the Antiderivative	( sixth root of x)^3	${(\sqrt[6]{x})}^{3}$
44859	Find the Antiderivative	( square root of x)/3	$\frac{\sqrt{x}}{3}$
44860	Find the Antiderivative	x^(3/2)+2x+1	$x^{\frac{3}{2}} + 2 x + 1$
44861	Find the Antiderivative	18x	$18 x$
44862	Find the Antiderivative	cos(9x)	$\cos (9 x)$
44863	Find the Roots (Zeros)	324x^3-144x	$324 x^{3} - 144 x$
44864	Find the Roots (Zeros)	x^3-13x^2+60x-100	$x^{3} - 13 x^{2} + 60 x - 100$
44865	Find the Antiderivative	-5sin(3x)	$- 5 \sin (3 x)$
44866	Find the Antiderivative	1/2sec(x)^2	$\frac{1}{2} \sec^{2} (x)$
44867	Find the Antiderivative	(x^3-4x-1)/(2x^3)	$\frac{x^{3} - 4 x - 1}{2 x^{3}}$
44868	Find the Domain and Range	y=2e^x-1	$y = 2 e^{x} - 1$
44869	Find the Area Between the Curves	y=\|3x\| , y=x^2-4	$y = \| 3 x \|$ , $y = x^{2} - 4$
44870	Find the Area Between the Curves	y=6x^2-2 , y=4x	$y = 6 x^{2} - 2$ , $y = 4 x$
44871	Find the Tangent Line at (0,2)	y=x^4+2e^x , (0,2)	$y = x^{4} + 2 e^{x}$ , $(0, 2)$
44872	Find the Tangent Line at (0,0)	y=9xe^x , (0,0)	$y = 9 x e^{x}$ , $(0, 0)$
44873	Find the Tangent Line at (1,1)	9x^2+xy+9y^2=19 , (1,1)	$9 x^{2} + x y + 9 y^{2} = 19$ , $(1, 1)$
44874	Find the Linearization at a=8	f(x)=x^(2/3) , a=8	$f (x) = x^{\frac{2}{3}}$ , $a = 8$
44875	Find the Linearization at a=16	f(x)=x^(1/2) , a=16	$f (x) = x^{\frac{1}{2}}$ , $a = 16$
44876	Find the Asymptotes	4x^2-9y^2=36	$4 x^{2} - 9 y^{2} = 36$
44877	Find the Derivative Using Chain Rule - d/dr	r=sec( square root of theta)tan(1/theta)	$r = \sec (\sqrt{θ}) \tan (\frac{1}{θ})$
44878	Find the Derivative Using Chain Rule - d/dd	(d^118)/(dx^118)(sin(x))	$\frac{d^{118}}{d x^{118}} (\sin (x))$
44879	Find the Derivative Using Chain Rule - d/dy	sin(xy^2)	$\sin (x y^{2})$
44880	Find the Derivative Using Chain Rule - d/dx	y=tan(2x^4)	$y = \tan (2 x^{4})$
44881	Find the Derivative Using Chain Rule - d/dx	y=cos(7sin(x))	$y = \cos (7 \sin (x))$
44882	Find the Derivative Using Chain Rule - d/dx	y=(6x+7)^9	$y = {(6 x + 7)}^{9}$
44883	Find the Derivative Using Chain Rule - d/dx	y=(3x+7)^11	$y = {(3 x + 7)}^{11}$
44884	Find the Derivative Using Chain Rule - d/dx	y=(4x+3)^4(x+1)^-3	$y = {(4 x + 3)}^{4} {(x + 1)}^{- 3}$
44885	Find the Derivative Using Chain Rule - d/dx	y=(2x+9)^10	$y = {(2 x + 9)}^{10}$
44886	Find the Derivative Using Chain Rule - d/dx	(d^118)/(dx^118)(sin(x))	$\frac{d^{118}}{d x^{118}} (\sin (x))$
44887	Find Where Increasing/Decreasing Using Derivatives	1/5x^5+7/2x^4+71/3x^3+77x^2+120x	$\frac{1}{5} x^{5} + \frac{7}{2} x^{4} + \frac{71}{3} x^{3} + 77 x^{2} + 120 x$
44888	Find Where Increasing/Decreasing Using Derivatives	x^3-27x+5	$x^{3} - 27 x + 5$
44889	Find Where Increasing/Decreasing Using Derivatives	3x^4-16x^3+24x^2	$3 x^{4} - 16 x^{3} + 24 x^{2}$
44890	Find Where Increasing/Decreasing Using Derivatives	300x-x^3	$300 x - x^{3}$
44891	Find Where Increasing/Decreasing Using Derivatives	2x^4+3x^3	$2 x^{4} + 3 x^{3}$
44892	Convert to Rectangular	r=3sec(theta)	$r = 3 \sec (θ)$
44893	Find the Difference Quotient	f(x)=-2x^2-3x-4	$f (x) = - 2 x^{2} - 3 x - 4$
44894	Find the Asymptotes	(x^2-12x-108)/(x^2-24x+108)	$\frac{x^{2} - 12 x - 108}{x^{2} - 24 x + 108}$
44895	Find the Asymptotes	(x-2)/(x^2-4)	$\frac{x - 2}{x^{2} - 4}$
44896	Find the Asymptotes	(x^2-5x-50)/(x^2-15x+50)	$\frac{x^{2} - 5 x - 50}{x^{2} - 15 x + 50}$
44897	Find the Asymptotes	x/(x^2-16)	$\frac{x}{x^{2} - 16}$
44898	Find the Domain	(1-4t)/(5+t)	$\frac{1 - 4 t}{5 + t}$
44899	Find the Domain	(1-3t)/(5+t)	$\frac{1 - 3 t}{5 + t}$
44900	Find the Derivative of the Integral	y=(5(1-sin(x)))/(2cos(x))	$y = \frac{5 (1 - \sin (x))}{2 \cos (x)}$