Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
23001	Evaluate the Limit	limit as x approaches -2 from the left of f(x)	$lim_{x \to - 2} f (x)$
23002	Evaluate the Integral	integral of cos(x)^2sin(x) with respect to x	$\int \cos^{2} (x) \sin (x) d x$
23003	Evaluate the Integral	integral of e^(3t) with respect to t	$\int e^{3 t} d t$
23004	Evaluate the Limit	limit as x approaches -2 of (2x^2-6x-20)/(x^2-4)	$lim_{x \to - 2} \frac{2 x^{2} - 6 x - 20}{x^{2} - 4}$
23005	Evaluate the Limit	limit as x approaches 2 of x/(2-x)	$lim_{x \to 2} \frac{x}{2 - x}$
23006	Evaluate the Limit	limit as x approaches 4 from the left of (\|x+4\|)/(x+4)	$lim_{x \to 4} \frac{\| x + 4 \|}{x + 4}$
23007	Evaluate the Limit	limit as x approaches 4 of (x-4)/(x^2-3x-4)	$lim_{x \to 4} \frac{x - 4}{x^{2} - 3 x - 4}$
23008	Find the Inflection Points	-3x^4+28x^3-60x^2	$- 3 x^{4} + 28 x^{3} - 60 x^{2}$
23009	Evaluate the Limit	limit as x approaches 4 of 3x-7	$lim_{x \to 4} 3 x - 7$
23010	Find the Critical Points	f(x)=x/(x^2+25)	$f (x) = \frac{x}{x^{2} + 25}$
23011	Evaluate the Limit	limit as x approaches 4 of 9x+6	$lim_{x \to 4} 9 x + 6$
23012	Find the Critical Points	f(x)=x^3-6x^2-36x	$f (x) = x^{3} - 6 x^{2} - 36 x$
23013	Evaluate the Limit	limit as x approaches 4 of ( square root of 13-x-3)/(12-3x)	$lim_{x \to 4} \frac{\sqrt{13 - x - 3}}{12 - 3 x}$
23014	Find the Critical Points	f(x)=x^2-8x	$f (x) = x^{2} - 8 x$
23015	Evaluate from the Right	limit as x approaches 3 of natural log of x^2-9	$lim_{x \to 3} \ln (x^{2} - 9)$
23016	Evaluate the Limit	limit as x approaches 4 of (5x^2-22x+8)/(2x^3-7x-4)	$lim_{x \to 4} \frac{5 x^{2} - 22 x + 8}{2 x^{3} - 7 x - 4}$
23017	Evaluate the Limit	limit as x approaches 5 of (3x^2-19x+20)/(x-5)	$lim_{x \to 5} \frac{3 x^{2} - 19 x + 20}{x - 5}$
23018	Evaluate the Limit	limit as x approaches 4 of (x-4)/(x^2-x-12)	$lim_{x \to 4} \frac{x - 4}{x^{2} - x - 12}$
23019	Evaluate the Limit	limit as x approaches 5 of 1/(x-5)-10/(x^2-25)	$lim_{x \to 5} \frac{1}{x - 5} - \frac{10}{x^{2} - 25}$
23020	Evaluate the Limit	limit as x approaches 144 of (x-144)/( square root of x-12)	$lim_{x \to 144} \frac{x - 144}{\sqrt{x} - 12}$
23021	Evaluate the Limit	limit as x approaches infinity of cos(2x)	$lim_{x \to \infty} \cos (2 x)$
23022	Evaluate the Limit	limit as x approaches 5 of (x^2-5x+6)/(x^2-8x+15)	$lim_{x \to 5} \frac{x^{2} - 5 x + 6}{x^{2} - 8 x + 15}$
23023	Solve the System of @WORD	x>0 , y>0	$x > 0$ , $y > 0$
23024	Determine if True	6^2=36	$6^{2} = 36$
23025	Solve the System of @WORD	y<-2x^2+4x , y>x^2-2x-8	$y < - 2 x^{2} + 4 x$ , $y > x^{2} - 2 x - 8$
23026	Graph	y=-3x^2+27	$y = - 3 x^{2} + 27$
23027	Graph	y=x^3-2x^2-15x+10	$y = x^{3} - 2 x^{2} - 15 x + 10$
23028	Graph	y=x^3-2x^2-3x	$y = x^{3} - 2 x^{2} - 3 x$
23029	Graph	y=4 log base 3 of x+1+1	$y = 4 \log_{3} (x + 1) + 1$
23030	Graph	3x^4-10x^3-12x^2+10x+9	$3 x^{4} - 10 x^{3} - 12 x^{2} + 10 x + 9$
23031	Graph	x^2+10x+24>0	$x^{2} + 10 x + 24 > 0$
23032	Graph	x^2(sin(1/x))	$x^{2} (\sin (\frac{1}{x}))$
23033	Graph	\|y-4\|=7	$\| y - 4 \| = 7$
23034	Graph	\|x\|+\|y\|=1+\|xy\|	$\| x \| + \| y \| = 1 + \| x y \|$
23035	Graph	2/(x-3)	$\frac{2}{x - 3}$
23036	Graph	(2x)/( square root of x^2-9)	$\frac{2 x}{\sqrt{x^{2} - 9}}$
23037	Graph	y = natural log of tan(x)^2	$y = \ln (\tan^{2} (x))$
23038	Graph	y=x^3-3x^2-105x	$y = x^{3} - 3 x^{2} - 105 x$
23039	Graph	x=3y^2-4y	$x = 3 y^{2} - 4 y$
23040	Graph	y=3/(x^2-4)	$y = \frac{3}{x^{2} - 4}$
23041	Graph	y = log base 5 of 4x-1+2	$y = \log_{5} (4 x - 1) + 2$
23042	Graph	y = log base 5 of x-1-1	$y = \log_{5} (x - 1) - 1$
23043	Graph	x+13y=1	$x + 13 y = 1$
23044	Graph	xy+9=0	$x y + 9 = 0$
23045	Graph	y=1/(x^2-16)	$y = \frac{1}{x^{2} - 16}$
23046	Evaluate the Limit	limit as x approaches infinity of (4x^2-9x-2)/(3x^2+x-7)	$lim_{x \to \infty} \frac{4 x^{2} - 9 x - 2}{3 x^{2} + x - 7}$
23047	Graph	h=-16t^2+64t+512	$h = - 16 t^{2} + 64 t + 512$
23048	Find dy/dt	y=t^7(t^5-6)^3	$y = t^{7} {(t^{5} - 6)}^{3}$
23049	Find dy/dx	y=2x	$y = 2 x$
23050	Graph	r=3csc(x)	$r = 3 \csc (x)$
23051	Graph	y=sin(x)^2e^(-2x)	$y = \sin^{2} (x) e^{- 2 x}$
23052	Graph	y=2cot(2x-5pi)+2	$y = 2 \cot (2 x - 5 π) + 2$
23053	Find the Derivative - d/d@VAR	f(x)=tan(x^5)^5	$f (x) = \tan^{5} (x^{5})$
23054	Graph	y=2x^3-3x^2-8x+9	$y = 2 x^{3} - 3 x^{2} - 8 x + 9$
23055	Graph	y=0.5x^2+5x+8	$y = 0.5 x^{2} + 5 x + 8$
23056	Graph	y=x^3-4x^2-16x+4	$y = x^{3} - 4 x^{2} - 16 x + 4$
23057	Find the Derivative - d/dx	y=e^(x/4)	$y = e^{\frac{x}{4}}$
23058	Find the Horizontal Tangent Line	y=2x^3+3x^2-12x+2	$y = 2 x^{3} + 3 x^{2} - 12 x + 2$
23059	Determine if Continuous	g(x)=(4x-9)/(3x^2-19x-14)	$g (x) = \frac{4 x - 9}{3 x^{2} - 19 x - 14}$
23060	Determine if Continuous	y=(5x-6)^(1/3)	$y = {(5 x - 6)}^{\frac{1}{3}}$
23061	Determine if Continuous	f(x) = square root of x/(x-2)	$f (x) = \sqrt{\frac{x}{x - 2}}$
23062	Determine if Continuous	h(x)=1/( square root of 7x^2+6)	$h (x) = \frac{1}{\sqrt{7 x^{2} + 6}}$
23063	Determine if Continuous	y=(5xtan(x))/(x^2+4)	$y = \frac{5 x \tan (x)}{x^{2} + 4}$
23064	Determine if Continuous	f(x)=5x^2-1	$f (x) = 5 x^{2} - 1$
23065	Determine if Continuous	f(x)=5x-5	$f (x) = 5 x - 5$
23066	Determine if Continuous	f(x)=6x-6	$f (x) = 6 x - 6$
23067	Determine if Continuous	f(x)=7x-4	$f (x) = 7 x - 4$
23068	Determine if Continuous	f(x)=2x-4	$f (x) = 2 x - 4$
23069	Determine if Continuous	f(x)=(x+2)/(x^2-3x-10)	$f (x) = \frac{x + 2}{x^{2} - 3 x - 10}$
23070	Determine if Continuous	f(x)=(x-2)/(x^2+2x-8)	$f (x) = \frac{x - 2}{x^{2} + 2 x - 8}$
23071	Determine if Continuous	f(x)=(x-3)/(x^2-9)	$f (x) = \frac{x - 3}{x^{2} - 9}$
23072	Determine if Continuous	f(x)=(x-4)/(x^2-16)	$f (x) = \frac{x - 4}{x^{2} - 16}$
23073	Determine if Continuous	f(x)=(x+2)/(x^2-4)	$f (x) = \frac{x + 2}{x^{2} - 4}$
23074	Determine if Continuous	f(x)=(x+2)/(x^2-x-6)	$f (x) = \frac{x + 2}{x^{2} - x - 6}$
23075	Determine if Continuous	f(x)=(x-1)/(x^2+x-2)	$f (x) = \frac{x - 1}{x^{2} + x - 2}$
23076	Determine if Continuous	f(x)=(x-1)/(x^2-1)	$f (x) = \frac{x - 1}{x^{2} - 1}$
23077	Determine if Continuous	f(x)=(x+3)/(x^2-3x-10)	$f (x) = \frac{x + 3}{x^{2} - 3 x - 10}$
23078	Determine if Continuous	f(x)=x/(x^2-9)	$f (x) = \frac{x}{x^{2} - 9}$
23079	Determine if Continuous	f(x)=x^2-9	$f (x) = x^{2} - 9$
23080	Determine if Continuous	f(x)=4/(x^2-25)	$f (x) = \frac{4}{x^{2} - 25}$
23081	Determine if Continuous	f(x)=3/(x-2)	$f (x) = \frac{3}{x - 2}$
23082	Determine if Continuous	f(x)=1/(4-x^2)	$f (x) = \frac{1}{4 - x^{2}}$
23083	Determine if Continuous	f(x)=1/(x^2-36)	$f (x) = \frac{1}{x^{2} - 36}$
23084	Determine if Continuous	f(x)=1/(x^2-4)	$f (x) = \frac{1}{x^{2} - 4}$
23085	Determine if Continuous	f(x)=(3x^2+x)/x	$f (x) = \frac{3 x^{2} + x}{x}$
23086	Determine if Continuous	f(x)=(x^2-5x-36)/(x^2-16)	$f (x) = \frac{x^{2} - 5 x - 36}{x^{2} - 16}$
23087	Determine if Continuous	f(x)=(x^2-64)/(x-8)	$f (x) = \frac{x^{2} - 64}{x - 8}$
23088	Determine if Continuous	f(x)=(x^2-81)/(x-9)	$f (x) = \frac{x^{2} - 81}{x - 9}$
23089	Determine if Continuous	f(x)=\|25-x^2\|	$f (x) = \| 25 - x^{2} \|$
23090	Determine if Continuous	f(x)=1/(x-2)	$f (x) = \frac{1}{x - 2}$
23091	Determine if Continuous	f(x) = square root of x^2-16	$f (x) = \sqrt{x^{2} - 16}$
23092	Determine if Continuous	f(x) = square root of x^2-25	$f (x) = \sqrt{x^{2} - 25}$
23093	Determine if Continuous	f(x) = square root of x^2-9	$f (x) = \sqrt{x^{2} - 9}$
23094	Determine if Continuous	f(x)=(4x)/(x^2+49)	$f (x) = \frac{4 x}{x^{2} + 49}$
23095	Determine if Continuous	f(x)=6/x	$f (x) = \frac{6}{x}$
23096	Determine if Continuous	f(x) = square root of x^2-4	$f (x) = \sqrt{x^{2} - 4}$
23097	Determine if Continuous	f(x) = square root of x-3	$f (x) = \sqrt{x - 3}$
23098	Determine if Continuous	f(x) = cube root of (x-2)(x+1)^2	$f (x) = \sqrt[3]{(x - 2) {(x + 1)}^{2}}$
23099	Determine if Continuous	f(x) = square root of 1-x^2	$f (x) = \sqrt{1 - x^{2}}$
23100	Determine if Continuous	f(x)=(x+2x^3)^4	$f (x) = {(x + 2 x^{3})}^{4}$