Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
5001	Find the Inflection Points	y=4x^3-48x-7	$y = 4 x^{3} - 48 x - 7$
5002	Find the Inflection Points	y=3x^3-36x-2	$y = 3 x^{3} - 36 x - 2$
5003	Find the Concavity	f(x)=x/(x^2-9)	$f (x) = \frac{x}{x^{2} - 9}$
5004	Find the Concavity	f(x)=x^3-3x^2-9x	$f (x) = x^{3} - 3 x^{2} - 9 x$
5005	Find the Concavity	f(x)=x^3-27x	$f (x) = x^{3} - 27 x$
5006	Find the Concavity	f(x)=x^3-3x^2-4x+5	$f (x) = x^{3} - 3 x^{2} - 4 x + 5$
5007	Find the Concavity	f(x)=x^3-6x^2	$f (x) = x^{3} - 6 x^{2}$
5008	Find the Concavity	f(x)=x^4-4x^3+2	$f (x) = x^{4} - 4 x^{3} + 2$
5009	Find the Concavity	f(x)=3/(x-5)	$f (x) = \frac{3}{x - 5}$
5010	Find the Concavity	f(x) = square root of 4-x	$f (x) = \sqrt{4 - x}$
5011	Find the Concavity	f(x) = square root of x	$f (x) = \sqrt{x}$
5012	Use the Limit Definition to Find the Derivative	g(x) = square root of 9-x	$g (x) = \sqrt{9 - x}$
5013	Use the Limit Definition to Find the Derivative	y = square root of x	$y = \sqrt{x}$
5014	Use the Limit Definition to Find the Derivative	f(x) = square root of x+1	$f (x) = \sqrt{x + 1}$
5015	Use the Limit Definition to Find the Derivative	f(x)=x/(x+1)	$f (x) = \frac{x}{x + 1}$
5016	Use the Limit Definition to Find the Derivative	f(x)=3x+2	$f (x) = 3 x + 2$
5017	Find the 2nd Derivative	y = square root of x+8	$y = \sqrt{x + 8}$
5018	Find the Arc Length	f(x)=x^2+2x , [0,7]	$f (x) = x^{2} + 2 x$ , $[0, 7]$
5019	Evaluate the Integral	integral from 0 to 2 of x^2+3 with respect to x	$\int_{0}^{2} x^{2} + 3 d x$
5020	Find the Derivative - d/dx	-6/(x^4)	$- \frac{6}{x^{4}}$
5021	Find the Derivative - d/d@VAR	f(x)=-1/3(x^-3-x^6)	$f (x) = - \frac{1}{3} (x^{- 3} - x^{6})$
5022	Evaluate the Summation	sum from n=1 to 12 of 2n+1	$\sum_{n = 1}^{12} 2 n + 1$
5023	Evaluate the Integral	integral from 0 to 10 of \|x-5\| with respect to x	$\int_{0}^{10} \| x - 5 \| d x$
5024	Find dy/dx	y=(4x-7)^2	$y = {(4 x - 7)}^{2}$
5025	Find the Derivative - d/d@VAR	g(x) = square root of 5x	$g (x) = \sqrt{5 x}$
5026	Evaluate the Integral	integral of 2x(1-x^-3) with respect to x	$\int 2 x (1 - x^{- 3}) d x$
5027	Evaluate the Integral	integral from -3 to 0 of -12x-x^2+x^3 with respect to x	$\int_{- 3}^{0} - 12 x - x^{2} + x^{3} d x$
5028	Evaluate the Integral	integral of tan(2x)^2 with respect to x	$\int \tan^{2} (2 x) d x$
5029	Evaluate the Limit	limit as x approaches 1 of (x^4-1)/(x^6-1)	$lim_{x \to 1} \frac{x^{4} - 1}{x^{6} - 1}$
5030	Evaluate the Integral	integral of x/( square root of 4-x^2) with respect to x	$\int \frac{x}{\sqrt{4 - x^{2}}} d x$
5031	Evaluate the Integral	integral of x^2sin(pix) with respect to x	$\int x^{2} \sin (π x) d x$
5032	Evaluate the Integral	integral of 1/(2x+1) with respect to x	$\int \frac{1}{2 x + 1} d x$
5033	Evaluate the Integral	integral of cos(x)^6 with respect to x	$\int \cos^{6} (x) d x$
5034	Evaluate the Integral	integral of (3x+4)^2 with respect to x	$\int {(3 x + 4)}^{2} d x$
5035	Find the Derivative - d/d@VAR	f(x) = square root of x+5	$f (x) = \sqrt{x + 5}$
5036	Evaluate the Integral	integral of 2/x+3e^x with respect to x	$\int \frac{2}{x} + 3 e^{x} d x$
5037	Evaluate the Limit	limit as x approaches -8 of (8-\|x\|)/(8+x)	$lim_{x \to - 8} \frac{8 - \| x \|}{8 + x}$
5038	Find the Derivative of the Integral	integral from 0 to 12 of square root of 144-x^2 with respect to x	$\int_{0}^{12} \sqrt{144 - x^{2}} d x$
5039	Find the Derivative of the Integral	integral of (arctan( square root of x))/( square root of x) with respect to x	$\int \frac{\arctan (\sqrt{x})}{\sqrt{x}} d x$
5040	Find the Derivative of the Integral	integral of (cos( square root of x))/( square root of x) with respect to x	$\int \frac{\cos (\sqrt{x})}{\sqrt{x}} d x$
5041	Find the Derivative of the Integral	integral of (arcsin(x))/( square root of 1-x^2) with respect to x	$\int \frac{\arcsin (x)}{\sqrt{1 - x^{2}}} d x$
5042	Find the Derivative of the Integral	integral of sec(x) with respect to x	$\int \sec (x) d x$
5043	Find the Derivative of the Integral	integral of xsin(x) with respect to x	$\int x \sin (x) d x$
5044	Find the Derivative of the Integral	integral of 3x with respect to x	$\int 3 x d x$
5045	Evaluate the Limit	limit as h approaches 0 of ((x+h)^3-x^3)/h	$lim_{h \to 0} \frac{({(x + h)}^{3} - x^{3})}{h}$
5046	Evaluate the Integral	integral of 11/x with respect to x	$\int \frac{11}{x} d x$
5047	Find the Derivative - d/dx	square root of 4x	$\sqrt{4 x}$
5048	Find the Derivative of the Integral	integral of 1/( square root of x square root of 1-x) with respect to x	$\int \frac{1}{\sqrt{x} \sqrt{1 - x}} d x$
5049	Evaluate the Integral	integral of xsin(1/3x) with respect to x	$\int x \sin (\frac{1}{3} x) d x$
5050	Evaluate the Integral	integral of xsin(1/8x) with respect to x	$\int x \sin (\frac{1}{8} x) d x$
5051	Evaluate	343/6	$\frac{343}{6}$
5052	Evaluate	3/2*(4)^2	$\frac{3}{2} \cdot {(4)}^{2}$
5053	Evaluate	(-128)^(3/7)	${(- 128)}^{\frac{3}{7}}$
5054	Evaluate	(1/16)^(-1/4)(27/64)^(-1/3)	${(\frac{1}{16})}^{- \frac{1}{4}} {(\frac{27}{64})}^{- \frac{1}{3}}$
5055	Evaluate	(9)^(3/2)	${(9)}^{\frac{3}{2}}$
5056	Evaluate	(8^(-2/3))/3	$\frac{8^{- \frac{2}{3}}}{3}$
5057	Evaluate the Integral	integral of 3x^2-6x with respect to x	$\int 3 x^{2} - 6 x d x$
5058	Evaluate the Integral	integral from 1 to 5 of x square root of 2x^2+7 with respect to x	$\int_{1}^{5} x \sqrt{2 x^{2} + 7} d x$
5059	Evaluate the Limit	limit as x approaches 1 of (2x-7)/(4x+5)	$lim_{x \to 1} \frac{2 x - 7}{4 x + 5}$
5060	Evaluate the Integral	integral from 1 to 8 of x^(-2/3) with respect to x	$\int_{1}^{8} x^{- \frac{2}{3}} d x$
5061	Evaluate the Integral	integral from 1 to 5e of 1/x with respect to x	$\int_{1}^{5 e} \frac{1}{x} d x$
5062	Evaluate the Integral	integral from 1 to 6 of -6/x with respect to x	$\int_{1}^{6} - \frac{6}{x} d x$
5063	Evaluate the Integral	integral of 10x^3 with respect to x	$\int 10 x^{3} d x$
5064	Evaluate the Integral	integral from 12 to 13 of x square root of x^2-144 with respect to x	$\int_{12}^{13} x \sqrt{x^{2} - 144} d x$
5065	Evaluate the Integral	integral from -10 to 0 of square root of 100-x^2 with respect to x	$\int_{- 10}^{0} \sqrt{100 - x^{2}} d x$
5066	Evaluate the Integral	integral from -10 to 10 of 100-x^2 with respect to x	$\int_{- 10}^{10} 100 - x^{2} d x$
5067	Evaluate the Integral	integral from 1 to 9 of 1/(2x) with respect to x	$\int_{1}^{9} \frac{1}{2 x} d x$
5068	Evaluate the Integral	integral from 1 to 9 of (u-9)/( square root of u) with respect to u	$\int_{1}^{9} \frac{u - 9}{\sqrt{u}} d u$
5069	Evaluate the Integral	integral from 1 to e of ( natural log of x)/(x^2) with respect to x	$\int_{1}^{e} \frac{\ln (x)}{x^{2}} d x$
5070	Evaluate the Integral	integral from 1 to e of ( natural log of x)^2 with respect to x	$\int_{1}^{e} \ln^{2} (x) d x$
5071	Evaluate the Integral	integral from 1 to x of 1/t with respect to t	$\int_{1}^{x} \frac{1}{t} d t$
5072	Evaluate the Integral	integral of 15x^2 with respect to x	$\int 15 x^{2} d x$
5073	Evaluate the Integral	integral of 16x natural log of 3x with respect to x	$\int 16 x \ln (3 x) d x$
5074	Evaluate the Integral	integral of 14x natural log of 2x with respect to x	$\int 14 x \ln (2 x) d x$
5075	Evaluate the Integral	integral of 18x with respect to x	$\int 18 x d x$
5076	Evaluate the Integral	integral from -2 to 0 of square root of 4-x^2 with respect to x	$\int_{- 2}^{0} \sqrt{4 - x^{2}} d x$
5077	Evaluate the Integral	integral from -2 to -1 of 2x(6-x^2)^3 with respect to x	$\int_{- 2}^{- 1} 2 x {(6 - x^{2})}^{3} d x$
5078	Evaluate the Integral	integral from 2 to 3 of x^2 with respect to x	$\int_{2}^{3} x^{2} d x$
5079	Evaluate the Integral	integral from -2 to 3 of x^2-3 with respect to x	$\int_{- 2}^{3} x^{2} - 3 d x$
5080	Evaluate the Integral	integral from 2 to 4 of 6x natural log of x with respect to x	$\int_{2}^{4} 6 x \ln (x) d x$
5081	Evaluate the Integral	integral from 1 to 4 of 10-4x with respect to x	$\int_{1}^{4} 10 - 4 x d x$
5082	Evaluate the Integral	integral from 1 to 32 of x^(-9/5) with respect to x	$\int_{1}^{32} x^{- \frac{9}{5}} d x$
5083	Evaluate the Integral	integral from 1 to 4 of x^2+ square root of x with respect to x	$\int_{1}^{4} x^{2} + \sqrt{x} d x$
5084	Evaluate the Integral	integral from 1 to 4 of 5-2x+3x^2 with respect to x	$\int_{1}^{4} 5 - 2 x + 3 x^{2} d x$
5085	Evaluate the Integral	integral from 1 to 4 of square root of x natural log of x with respect to x	$\int_{1}^{4} \sqrt{x} \ln (x) d x$
5086	Evaluate the Integral	integral from 1 to 4 of (u-2)/( square root of u) with respect to u	$\int_{1}^{4} \frac{u - 2}{\sqrt{u}} d u$
5087	Evaluate the Integral	integral from 1 to 4 of x^(5/2) with respect to x	$\int_{1}^{4} x^{\frac{5}{2}} d x$
5088	Evaluate the Integral	integral from 1 to 4 of square root of 5/x with respect to x	$\int_{1}^{4} \sqrt{\frac{5}{x}} d x$
5089	Evaluate the Integral	integral from 1 to 3 of xsin(pix^2) with respect to x	$\int_{1}^{3} x \sin (π x^{2}) d x$
5090	Evaluate the Integral	integral from 1 to 3 of r^3 natural log of r with respect to r	$\int_{1}^{3} r^{3} \ln (r) d r$
5091	Evaluate the Integral	integral from 1 to 2 of 2/x with respect to x	$\int_{1}^{2} \frac{2}{x} d x$
5092	Evaluate the Limit	limit as x approaches 3 of 1/(x-3)	$lim_{x \to 3} \frac{1}{x - 3}$
5093	Evaluate the Integral	integral from 1 to 2 of 1/((3-5x)^2) with respect to x	$\int_{1}^{2} \frac{1}{{(3 - 5 x)}^{2}} d x$
5094	Evaluate the Integral	integral from 1 to 2 of 2xe^(-x^2) with respect to x	$\int_{1}^{2} 2 x e^{- x^{2}} d x$
5095	Evaluate the Integral	integral from 1 to 2 of 4 square root of x-5/x with respect to x	$\int_{1}^{2} 4 \sqrt{x} - \frac{5}{x} d x$
5096	Evaluate the Integral	integral from 1 to 3 of 2e^x-1 with respect to x	$\int_{1}^{3} 2 e^{x} - 1 d x$
5097	Evaluate the Integral	integral from -1 to 2 of 4-x^2 with respect to x	$\int_{- 1}^{2} 4 - x^{2} d x$
5098	Evaluate the Integral	integral from -1 to 2 of 1-x with respect to x	$\int_{- 1}^{2} 1 - x d x$
5099	Evaluate the Integral	integral of 0 with respect to y	$\int 0 d y$
5100	Evaluate the Integral	integral from 0 to pi of 4sin(x) with respect to x	$\int_{0}^{π} 4 \sin (x) d x$