Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
43601	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of x^6e^(-x^5)	$lim_{x \to \infty} x^{6} e^{- x^{5}}$
43602	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (e^(7x)-1-7x)/(x^2)	$lim_{x \to 0} \frac{e^{7 x} - 1 - 7 x}{x^{2}}$
43603	Evaluate the Summation	sum from k=1 to infinity of (1/2)^k	$\sum_{k = 1}^{\infty} {(\frac{1}{2})}^{k}$
43604	Find the Domain	f(x) = natural log of x^2-18x	$f (x) = \ln (x^{2} - 18 x)$
43605	Find the Domain	f(x)=1+1/(2x^(1/2))	$f (x) = 1 + \frac{1}{2 x^{\frac{1}{2}}}$
43606	Find the Derivative of the Integral	y=(5tan(x))/(6sec(x))	$y = \frac{5 \tan (x)}{6 \sec (x)}$
43607	Find the Inflection Points	y=5x^4-x^5	$y = 5 x^{4} - x^{5}$
43608	Find the Asymptotes	y=(x^2-x)/(x^2-6x+5)	$y = \frac{x^{2} - x}{x^{2} - 6 x + 5}$
43609	Find Where Increasing/Decreasing	y=-(x+3)^2	$y = - {(x + 3)}^{2}$
43610	Multiply	12*2	$12 \cdot 2$
43611	Find the Normal Line at @POINT	y=x^4+8e^x , (0,8)	$y = x^{4} + 8 e^{x}$ , $(0, 8)$
43612	Find the Normal Line at @POINT	y=x^4+2e^x , (0,2)	$y = x^{4} + 2 e^{x}$ , $(0, 2)$
43613	Find the Normal Line at @POINT	y=9xe^x , (0,0)	$y = 9 x e^{x}$ , $(0, 0)$
43614	Divide	38/2	$\frac{38}{2}$
43615	Divide	56/4	$\frac{56}{4}$
43616	Find the Second Derivative	7tan(x)	$7 \tan (x)$
43617	Find the Second Derivative	-8cos(x)	$- 8 \cos (x)$
43618	Find the Second Derivative	5sec(x)	$5 \sec (x)$
43619	Find the Third Derivative	3xsin(x)	$3 x \sin (x)$
43620	Find the Fourth Derivative	2 natural log of x	$2 \ln (x)$
43621	Find dy/dx at (0,p/10)	cos(5y)=x ; (0,pi/10)	$\cos (5 y) = x$ ; $(0, \frac{π}{10})$
43622	Find dy/dx at (3,2)	x^3+y^3=6xy-1 , (3,2)	$x^{3} + y^{3} = 6 x y - 1$ , $(3, 2)$
43623	Find dx/dy at (0,p/10)	cos(5y)=x ; (0,pi/10)	$\cos (5 y) = x$ ; $(0, \frac{π}{10})$
43624	Evaluate the Summation	sum from n=0 to 1 of n+6	$\sum_{n = 0}^{1} n + 6$
43625	Find the Inflection Points	f(x)=(x-2)/(x^2-5x+6)	$f (x) = \frac{x - 2}{x^{2} - 5 x + 6}$
43626	Find the Second Derivative	y=cos(x)^2	$y = \cos^{2} (x)$
43627	Find the Second Derivative	y=xcos(x^2)	$y = x \cos (x^{2})$
43628	Find the Second Derivative	w=8z^2e^z	$w = 8 z^{2} e^{z}$
43629	Find the Second Derivative	xy+5e^y=5e	$x y + 5 e^{y} = 5 e$
43630	Find the Tangent Line at (-2,1)	(x^2+4)y=8 , (-2,1)	$(x^{2} + 4) y = 8$ , $(- 2, 1)$
43631	Find the Local Maxima and Minima	x^4-x^5	$x^{4} - x^{5}$
43632	Find Where Increasing/Decreasing Using Derivatives	f(x)=(3x)/(x^2+25)	$f (x) = \frac{3 x}{x^{2} + 25}$
43633	Find Where Increasing/Decreasing Using Derivatives	f(x)=2/(x+7)	$f (x) = \frac{2}{x + 7}$
43634	Find the Derivative Using Chain Rule - d/dx	y=tan(2x^5)	$y = \tan (2 x^{5})$
43635	Find Where Increasing/Decreasing Using Derivatives	(x^2)/(x^2-64)	$\frac{x^{2}}{x^{2} - 64}$
43636	Convert to a Decimal	pi/12	$\frac{π}{12}$
43637	Find the Asymptotes	(1+x^4)/(x^2-x^4)	$\frac{1 + x^{4}}{x^{2} - x^{4}}$
43638	Find the Local Maxima and Minima	f(x)=1/7x^7-x	$f (x) = \frac{1}{7} x^{7} - x$
43639	Find the Inflection Points	x^3+15x^2	$x^{3} + 15 x^{2}$
43640	Find the Inflection Points	3x^4+12x^3	$3 x^{4} + 12 x^{3}$
43641	Find the Antiderivative	sin(2theta)	$\sin (2 θ)$
43642	Find the Antiderivative	2sin(x)cos(x)	$2 \sin (x) \cos (x)$
43643	Find the Antiderivative	4x^-1	$4 x^{- 1}$
43644	Find the Antiderivative	(y^2)/4	$\frac{y^{2}}{4}$
43645	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of (x^4)/(3x^2-7x)	$lim_{x \to \infty} \frac{x^{4}}{3 x^{2} - 7 x}$
43646	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of xtan(1/x)	$lim_{x \to \infty} x \tan (\frac{1}{x})$
43647	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of x/( square root of x^2+1)	$lim_{x \to \infty} \frac{x}{\sqrt{x^{2} + 1}}$
43648	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of x^(2/x)	$lim_{x \to \infty} x^{\frac{2}{x}}$
43649	Find the Concavity	f(x)=2sin(x)^3+3sin(x)+1	$f (x) = 2 \sin^{3} (x) + 3 \sin (x) + 1$
43650	Find the Concavity	f(x)=3x^2-3sin(2x)	$f (x) = 3 x^{2} - 3 \sin (2 x)$
43651	Find the Concavity	(2x)/(4x^2-1)	$\frac{2 x}{4 x^{2} - 1}$
43652	Find the Critical Points	x^3-12x+1	$x^{3} - 12 x + 1$
43653	Find the Asymptotes	f(x)=2/(x+7)	$f (x) = \frac{2}{x + 7}$
43654	Find the Domain and Range	square root of x-6	$\sqrt{x - 6}$
43655	Find the Second Derivative	4xsin(x^2)	$4 x \sin (x^{2})$
43656	Find the Third Derivative	4xsin(x^2)	$4 x \sin (x^{2})$
43657	Find the Third Derivative	6e^x-x^3	$6 e^{x} - x^{3}$
43658	Divide	9.8/2	$\frac{9.8}{2}$
43659	Multiply	15*9	$15 \cdot 9$
43660	Multiply	13*5	$13 \cdot 5$
43661	Find the Maximum/Minimum Value	f(x)=x-2sin(x)	$f (x) = x - 2 \sin (x)$
43662	Evaluate the Summation	sum from i=1 to 8 of 5(1/3)^(i-1)	$\sum_{i = 1}^{8} 5 {(\frac{1}{3})}^{i - 1}$
43663	Evaluate the Summation	sum from m=1 to 135 of 3m	$\sum_{m = 1}^{135} 3 m$
43664	Find the Inflection Points	f(x)=(2x)/(4x^2-9)	$f (x) = \frac{2 x}{4 x^{2} - 9}$
43665	Find the Area Between the Curves	y=x^2 , y = square root of x	$y = x^{2}$ , $y = \sqrt{x}$
43666	Find the Derivative Using Chain Rule - d/dx	y=tan(3x^5)	$y = \tan (3 x^{5})$
43667	Find the Derivative Using Chain Rule - d/dx	y=tan(4x^5)	$y = \tan (4 x^{5})$
43668	Find the Derivative Using Chain Rule - d/dx	y=tan(pix)	$y = \tan (π x)$
43669	Find the Derivative Using Chain Rule - d/dx	y=tan(2x^3)	$y = \tan (2 x^{3})$
43670	Find Where Increasing/Decreasing Using Derivatives	3x^3-6x^2+3x-5	$3 x^{3} - 6 x^{2} + 3 x - 5$
43671	Find Where Increasing/Decreasing Using Derivatives	2x-2cos(x)	$2 x - 2 \cos (x)$
43672	Find Where Increasing/Decreasing Using Derivatives	(x^2)/((x-2)^3)	$\frac{x^{2}}{{(x - 2)}^{3}}$
43673	Find the Linearization at a=-1	f(x)=x^4+6x^2 , a=-1	$f (x) = x^{4} + 6 x^{2}$ , $a = - 1$
43674	Find the Linearization at a=p/3	f(x)=sin(x) , a=pi/3	$f (x) = \sin (x)$ , $a = \frac{π}{3}$
43675	Find the Second Derivative	6x^2+y^2=1	$6 x^{2} + y^{2} = 1$
43676	Find the Third Derivative	y=cos(3x)	$y = \cos (3 x)$
43677	Find the Third Derivative	y=ax^3+bx+c	$y = a x^{3} + b x + c$
43678	Find the Third Derivative	y=9x^5	$y = 9 x^{5}$
43679	Find the Fourth Derivative	y=9x^5	$y = 9 x^{5}$
43680	Find the Fourth Derivative	y=ax^3+bx+c	$y = a x^{3} + b x + c$
43681	Find the Fourth Derivative	y=-8cos(x)	$y = - 8 \cos (x)$
43682	Find the Fourth Derivative	y=cos(3x)	$y = \cos (3 x)$
43683	Find the Second Derivative	y=ax^3+bx+c	$y = a x^{3} + b x + c$
43684	Find the Second Derivative	y=4tan(x)	$y = 4 \tan (x)$
43685	Find the Second Derivative	y=9x^5	$y = 9 x^{5}$
43686	Find the Second Derivative	y=cos(3x)	$y = \cos (3 x)$
43687	Find Where Increasing/Decreasing Using Derivatives	f(x)=4x^2(12+x)^2	$f (x) = 4 x^{2} {(12 + x)}^{2}$
43688	Find the Local Maxima and Minima	25x+4/x	$25 x + \frac{4}{x}$
43689	Find the Local Maxima and Minima	4x^3-3x^2-6x+17	$4 x^{3} - 3 x^{2} - 6 x + 17$
43690	Find the Difference Quotient	f(x) = square root of 2x+8	$f (x) = \sqrt{2 x + 8}$
43691	Find the Inflection Points	8x^4-48x^2	$8 x^{4} - 48 x^{2}$
43692	Add	2x+2x	$2 x + 2 x$
43693	Find the Second Derivative	f(x)=3x-4x^(9/10)	$f (x) = 3 x - 4 x^{\frac{9}{10}}$
43694	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of (7x^2)/(x-x^3)	$lim_{x \to \infty} \frac{7 x^{2}}{x - x^{3}}$
43695	Find the Antiderivative	16x	$16 x$
43696	Find the Antiderivative	1/(x^2-2x+2)	$\frac{1}{x^{2} - 2 x + 2}$
43697	Find the Antiderivative	(cos(x))/(sin(x)^2)	$\frac{\cos (x)}{\sin^{2} (x)}$
43698	Find the Critical Points	f(x)=(x^2)/(x^2-49)	$f (x) = \frac{x^{2}}{x^{2} - 49}$
43699	Find the Critical Points	g(x)=x^8-4x^6	$g (x) = x^{8} - 4 x^{6}$
43700	Find the Critical Points	f(x)=x square root of 144-x^2	$f (x) = x \sqrt{144 - x^{2}}$