Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
44501	Find the Third Derivative	y=(x^4)/4+8/9x^3-x^2+8x-5	$y = \frac{x^{4}}{4} + \frac{8}{9} x^{3} - x^{2} + 8 x - 5$
44502	Find the Third Derivative	y=(x-5)(x+3)(x+4)	$y = (x - 5) (x + 3) (x + 4)$
44503	Evaluate the Summation	sum from n=1 to 25 of 3n-2	$\sum_{n = 1}^{25} 3 n - 2$
44504	Evaluate the Summation	sum from j=1 to 5 of 2j-5	$\sum_{j = 1}^{5} 2 j - 5$
44505	Evaluate the Summation	sum from j=1 to 4 of (2ij+8j)^2	$\sum_{j = 1}^{4} {(2 i j + 8 j)}^{2}$
44506	Evaluate the Summation	sum from j=1 to 5 of 4j-9	$\sum_{j = 1}^{5} 4 j - 9$
44507	Convert to a Decimal	(5pi)/3	$\frac{5 π}{3}$
44508	Convert to a Decimal	pi/8	$\frac{π}{8}$
44509	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of xsin((5pi)/x)	$lim_{x \to \infty} x \sin (\frac{5 π}{x})$
44510	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of (cos(x))/x	$lim_{x \to \infty} \frac{\cos (x)}{x}$
44511	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of ( natural log of x^101)/(x^3-1)	$lim_{x \to \infty} \frac{\ln (x^{101})}{x^{3} - 1}$
44512	Evaluate Using L'Hospital's Rule	limit as t approaches infinity of ( square root of t+t^2)/(5t-t^2)	$lim_{t \to \infty} \frac{\sqrt{t} + t^{2}}{5 t - t^{2}}$
44513	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of (3e^x)/(9+2e^(5x))	$lim_{x \to \infty} \frac{3 e^{x}}{9 + 2 e^{5 x}}$
44514	Evaluate Using L'Hospital's Rule	limit as x approaches 1 of (x-1)/(x^3-1)	$lim_{x \to 1} \frac{x - 1}{x^{3} - 1}$
44515	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of ( natural log of square root of x)/(x^2)	$lim_{x \to \infty} \frac{\ln (\sqrt{x})}{x^{2}}$
44516	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of (6x)/(15x-8)	$lim_{x \to \infty} \frac{6 x}{15 x - 8}$
44517	Find the Area Under the Curve	f(x)=x^2-2x-15 , [-1,7]	$f (x) = x^{2} - 2 x - 15$ , $[- 1, 7]$
44518	Find the Tangent Line at the Point	y=6xe^x , (0,0)	$y = 6 x e^{x}$ , $(0, 0)$
44519	Find the Tangent Line at the Point	sin(sin(x)) , (3pi,0)	$\sin (\sin (x))$ , $(3 π, 0)$
44520	Find the Tangent Line at the Point	y=3x^3+x+3 , (5,383)	$y = 3 x^{3} + x + 3$ , $(5, 383)$
44521	Find the Tangent Line at the Point	y=x^4+2x^2-x , (1,2)	$y = x^{4} + 2 x^{2} - x$ , $(1, 2)$
44522	Find the Tangent Line at the Point	y=14/(1+e^(-x)) , (0,7)	$y = \frac{14}{(1 + e^{- x})}$ , $(0, 7)$
44523	Find the Tangent Line at the Point	y = natural log of x^2-5x+1 , (5,0)	$y = \ln (x^{2} - 5 x + 1)$ , $(5, 0)$
44524	Find the Tangent Line at the Point	y=6e^x+x , (0,6)	$y = 6 e^{x} + x$ , $(0, 6)$
44525	Find the Antiderivative	81/(x^4)	$\frac{81}{x^{4}}$
44526	Find the Antiderivative	1/(x square root of x^2-1)	$\frac{1}{x \sqrt{x^{2} - 1}}$
44527	Find the Antiderivative	1/(e^x+1)	$\frac{1}{e^{x} + 1}$
44528	Find the Antiderivative	2x^3-6 square root of x+10x+9	$2 x^{3} - 6 \sqrt{x} + 10 x + 9$
44529	Find the Antiderivative	cube root of x^7	$\sqrt[3]{x^{7}}$
44530	Find the Antiderivative	\|2x-5\|	$\| 2 x - 5 \|$
44531	Find the Antiderivative	cos(x)+sin(x)	$\cos (x) + \sin (x)$
44532	Find the Antiderivative	8x^7	$8 x^{7}$
44533	Find the Antiderivative	e^(2x-1)	$e^{2 x - 1}$
44534	Find the Antiderivative	10x^9	$10 x^{9}$
44535	Find the Antiderivative	18x^2	$18 x^{2}$
44536	Find the Roots (Zeros)	x^4+27x^2-324	$x^{4} + 27 x^{2} - 324$
44537	Find the Antiderivative	(8x^3)e^(x^4)	$(8 x^{3}) e^{x^{4}}$
44538	Find the Antiderivative	x^2sin(x)	$x^{2} \sin (x)$
44539	Find the Antiderivative	1/3e^(3x)	$\frac{1}{3} e^{3 x}$
44540	Find the Antiderivative	e^(-2y)	$e^{- 2 y}$
44541	Find the Antiderivative	7/(cos(x)^2)	$\frac{7}{\cos^{2} (x)}$
44542	Find the Antiderivative	3x-7	$3 x - 7$
44543	Find the Antiderivative	3sec(x)^2	$3 \sec^{2} (x)$
44544	Find the Antiderivative	-3e^x	$- 3 e^{x}$
44545	Find the Antiderivative	sin(pi/2x)	$\sin (\frac{π}{2} x)$
44546	Find the Antiderivative	e^xsin(x)	$e^{x} \sin (x)$
44547	Find the Antiderivative	9sin(x)	$9 \sin (x)$
44548	Find the Antiderivative	5sec(x)^2-3/2 square root of x	$5 \sec^{2} (x) - \frac{3}{2} \sqrt{x}$
44549	Find the Antiderivative	cos(7x)	$\cos (7 x)$
44550	Find the Antiderivative	sin(x)^3cos(x)	$\sin^{3} (x) \cos (x)$
44551	Find the Antiderivative	14x	$14 x$
44552	Find the Roots (Zeros)	x^2+3x-2	$x^{2} + 3 x - 2$
44553	Find the Roots (Zeros)	-(x^2-121)/((x^2+121)^2)	$- \frac{x^{2} - 121}{{(x^{2} + 121)}^{2}}$
44554	Find the Antiderivative	-20e^(-1/2x)	$- 20 e^{- \frac{1}{2} x}$
44555	Find the Antiderivative	(x^3+2x^2-4)/(x^2)	$\frac{x^{3} + 2 x^{2} - 4}{x^{2}}$
44556	Find the Antiderivative	3/(x^5)	$\frac{3}{x^{5}}$
44557	Find the Antiderivative	sec(4x)	$\sec (4 x)$
44558	Find the Antiderivative	1/2(e^x+e^(-x))	$\frac{1}{2} (e^{x} + e^{- x})$
44559	Find the Antiderivative	-1/3cos(3x)	$- \frac{1}{3} \cos (3 x)$
44560	Find the Antiderivative	-5/x+c	$- \frac{5}{x} + c$
44561	Find the Antiderivative	(y^4)/4	$\frac{y^{4}}{4}$
44562	Find the Antiderivative	(2x)/pi	$\frac{2 x}{π}$
44563	Find the Antiderivative	1/(4 square root of x)	$\frac{1}{4 \sqrt{x}}$
44564	Find the Antiderivative	-5sin(3x)+C	$- 5 \sin (3 x) + C$
44565	Find Amplitude, Period, and Phase Shift	y=-1/5cos(1/5x)	$y = - \frac{1}{5} \cos (\frac{1}{5} x)$
44566	Find the x and y Intercepts	y=6x^2+6x-12	$y = 6 x^{2} + 6 x - 12$
44567	Find the x and y Intercepts	y=5-4x-x^3	$y = 5 - 4 x - x^{3}$
44568	Find the Second Derivative	(x^2-3x-54)/(x+6)	$\frac{x^{2} - 3 x - 54}{x + 6}$
44569	Find the Second Derivative	12xcos(x)	$12 x \cos (x)$
44570	Find the Second Derivative	5x^2-13x-6/(x^3)	$5 x^{2} - 13 x - \frac{6}{x^{3}}$
44571	Find the Fourth Derivative	cos(2x+pi/6)	$\cos (2 x + \frac{π}{6})$
44572	Find the Fourth Derivative	7e^(-4x)	$7 e^{- 4 x}$
44573	Find the Second Derivative	-1/4sin(2x)	$- \frac{1}{4} \sin (2 x)$
44574	Find the Third Derivative	3x-4x^(5/6)	$3 x - 4 x^{\frac{5}{6}}$
44575	Find the Third Derivative	cos(2x+pi/6)	$\cos (2 x + \frac{π}{6})$
44576	Find the Second Derivative	(2x)/(16x^2-9)	$\frac{2 x}{16 x^{2} - 9}$
44577	Find the Second Derivative	7csc(x)	$7 \csc (x)$
44578	Find the Second Derivative	8x^-7	$8 x^{- 7}$
44579	Find the Second Derivative	cos(8x^2)	$\cos (8 x^{2})$
44580	Find the Second Derivative	cos(2x+pi/6)	$\cos (2 x + \frac{π}{6})$
44581	Find the Second Derivative	8xsin(x^2)	$8 x \sin (x^{2})$
44582	Find the Area Between the Curves	y=x^3 , y=x	$y = x^{3}$ , $y = x$
44583	Find the Maximum/Minimum Value	x^2+6x+16	$x^{2} + 6 x + 16$
44584	Find the Maximum/Minimum Value	x-2sin(x)	$x - 2 \sin (x)$
44585	Find the Asymptotes	f(x)=(x^2+9)/(x^2-9)	$f (x) = \frac{x^{2} + 9}{x^{2} - 9}$
44586	Find the Asymptotes	f(x)=(x+4)/(x^2+13x+36)	$f (x) = \frac{x + 4}{x^{2} + 13 x + 36}$
44587	Find the Asymptotes	f(x)=(8x^2+26x+15)/(2x^2-x-15)	$f (x) = \frac{8 x^{2} + 26 x + 15}{2 x^{2} - x - 15}$
44588	Find the Asymptotes	f(x)=(2x)/(x^2-5x)	$f (x) = \frac{2 x}{x^{2} - 5 x}$
44589	Find the Derivative Using Chain Rule - d/dx	(d^87)/(dx^87)(sin(x))	$\frac{d^{87}}{d x^{87}} (\sin (x))$
44590	Find the Derivative Using Chain Rule - d/dx	y=sin(9cos(x))	$y = \sin (9 \cos (x))$
44591	Find the Derivative Using Chain Rule - d/dx	y=sin(4cos(x))	$y = \sin (4 \cos (x))$
44592	Find the Derivative Using Chain Rule - d/dx	y=cos(9sin(x))	$y = \cos (9 \sin (x))$
44593	Find the Derivative Using Chain Rule - d/dx	y=tan(6x^2)	$y = \tan (6 x^{2})$
44594	Find Where Increasing/Decreasing Using Derivatives	2x^3-24x-2	$2 x^{3} - 24 x - 2$
44595	Find Where Increasing/Decreasing Using Derivatives	(6t)/(t^2+1)	$\frac{6 t}{t^{2} + 1}$
44596	Find Where Increasing/Decreasing Using Derivatives	(x^2+12)(144-x^2)	$(x^{2} + 12) (144 - x^{2})$
44597	Find the Derivative Using Chain Rule - d/dx	y=(6x+5)^11	$y = {(6 x + 5)}^{11}$
44598	Find the Derivative Using Chain Rule - d/dx	y=(csc(x)+cot(x))^8	$y = {(\csc (x) + \cot (x))}^{8}$
44599	Find the Derivative Using Chain Rule - d/dx	y=cos(3sin(x))	$y = \cos (3 \sin (x))$
44600	Find the Derivative Using Chain Rule - d/dd	(d^87)/(dx^87)(sin(x))	$\frac{d^{87}}{d x^{87}} (\sin (x))$