Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
48001	Find the Integral	square root of x^3+6	$\sqrt{x^{3} + 6}$
48002	Find the Integral	sec(xdx)^2	$\sec^{2} (x d x)$
48003	Find the Integral	1/3e^(3x)	$\frac{1}{3} e^{3 x}$
48004	Find the Integral	integral from negative infinity to infinity of xe^(-x^2) with respect to x	$\int_{- \infty}^{\infty} x e^{- x^{2}} d x$
48005	Find the Integral	-1/2cos(2x)	$- \frac{1}{2} \cos (2 x)$
48006	Find the Integral	10x^4	$10 x^{4}$
48007	Find the Integral	2cos(x)^2	$2 \cos^{2} (x)$
48008	Find the Integral	sec(2x)	$\sec (2 x)$
48009	Find the Integral	1/(3y)	$\frac{1}{3 y}$
48010	Convert to Interval Notation	-1<x<7	$- 1 < x < 7$
48011	Convert to Interval Notation	x^2-2x-24<=0	$x^{2} - 2 x - 24 \leq 0$
48012	Convert to Interval Notation	x^2-3x-18<=0	$x^{2} - 3 x - 18 \leq 0$
48013	Convert to Interval Notation	x^3+10x^2<0	$x^{3} + 10 x^{2} < 0$
48014	Convert to Interval Notation	x^2+9x+20>=0	$x^{2} + 9 x + 20 \geq 0$
48015	Convert to Interval Notation	x^2-x-30<=0	$x^{2} - x - 30 \leq 0$
48016	Convert to Interval Notation	(3x^2+2x-1)/(3x^2-12x-96)>=0	$\frac{3 x^{2} + 2 x - 1}{3 x^{2} - 12 x - 96} \geq 0$
48017	Convert to Interval Notation	-3(z-3)<=21	$- 3 (z - 3) \leq 21$
48018	Convert to Interval Notation	x^3+x^2-65x+63>=0	$x^{3} + x^{2} - 65 x + 63 \geq 0$
48019	Convert to Interval Notation	\|x\|<=1	$\| x \| \leq 1$
48020	Convert to Interval Notation	{x\|x<=-2}	${x \| x \leq - 2}$
48021	Convert to Trigonometric Form	sec(arcsin(u))	$\sec (\arcsin (u))$
48022	Convert to Interval Notation	{x\|x<=-2}	${x \| x \leq - 2}$
48023	Convert to Interval Notation	(x-1)/(x+5)<=0	$\frac{x - 1}{x + 5} \leq 0$
48024	Convert to Interval Notation	-6(z-1)<=48	$- 6 (z - 1) \leq 48$
48025	Convert to Interval Notation	5y<7-2y<8+y	$5 y < 7 - 2 y < 8 + y$
48026	Convert to Interval Notation	(x^2-25)/(x-7)<=0	$\frac{x^{2} - 25}{x - 7} \leq 0$
48027	Convert to Interval Notation	\|12-16x\|<-13	$\| 12 - 16 x \| < - 13$
48028	Convert to Interval Notation	x^2-x>=20	$x^{2} - x \geq 20$
48029	Convert to Interval Notation	\|x-2\|>3	$\| x - 2 \| > 3$
48030	Convert to Interval Notation	\|4x-3\|<=5	$\| 4 x - 3 \| \leq 5$
48031	Find the Integral	1/(1+9x^2)	$\frac{1}{1 + 9 x^{2}}$
48032	Find the Integral	2xdx	$2 x d x$
48033	Convert to a Simplified Fraction	30 degrees	$30 °$
48034	Convert to a Simplified Fraction	60 degrees	$60 °$
48035	Write in Standard Form	(-20+ square root of -75)/40	$\frac{- 20 + \sqrt{- 75}}{40}$
48036	Convert to Regular Notation	5.706*10^-9	$5.706 \cdot 10^{- 9}$
48037	Evaluate from the Right	limit as x approaches 5 of (x^2-25)/(x-5)	$lim_{x \to 5} \frac{x^{2} - 25}{x - 5}$
48038	Evaluate from the Right	limit as x approaches 0 of natural log of sin(x)	$lim_{x \to 0} \ln (\sin (x))$
48039	Evaluate from the Right	limit as x approaches 3 from the right of (\|x-3\|)/(x-3)	$lim_{x \to 3} \frac{\| x - 3 \|}{x - 3}$
48040	Evaluate from the Right	limit as x approaches 9 of (x-9)/( square root of x-9)	$lim_{x \to 9} \frac{x - 9}{\sqrt{x - 9}}$
48041	Evaluate from the Right	limit as x approaches pi/4 of tan(2x)	$lim_{x \to \frac{π}{4}} \tan (2 x)$
48042	Apply the Quadratic Formula	3t^2-16t+24	$3 t^{2} - 16 t + 24$
48043	Apply the Quadratic Formula	12x^2-84x+104	$12 x^{2} - 84 x + 104$
48044	Solve by Factoring	6x^2-12x=0	$6 x^{2} - 12 x = 0$
48045	Convert to a Simplified Fraction	0.99	$0.99$
48046	Convert to a Simplified Fraction	8.25	$8.25$
48047	Find Where Increasing/Decreasing Using Derivatives	y=(x^3)/32-6x	$y = \frac{x^{3}}{32} - 6 x$
48048	Find Where Increasing/Decreasing Using Derivatives	y=(x^3)/64-3x	$y = \frac{x^{3}}{64} - 3 x$
48049	Find Where Increasing/Decreasing Using Derivatives	y=4x^4-2x^3	$y = 4 x^{4} - 2 x^{3}$
48050	Find Where Increasing/Decreasing Using Derivatives	y=100x^(1/4)	$y = 100 x^{\frac{1}{4}}$
48051	Write in Standard Form	y=-x+1/3	$y = - x + \frac{1}{3}$
48052	Determine if the Point is on the Graph	f(x)=3x(2x-2) , (-2,7)	$f (x) = 3 x (2 x - 2)$ , $(- 2, 7)$
48053	Find the Domain and Range	G(t)=(1-3t)/(6+t)	$G (t) = \frac{1 - 3 t}{6 + t}$
48054	Find the Domain and Range	f(x)=1/4x-1/10	$f (x) = \frac{1}{4} x - \frac{1}{10}$
48055	Find the Domain and Range	f(x)=1/2x-1/9	$f (x) = \frac{1}{2} x - \frac{1}{9}$
48056	Find the Domain and Range	f(x) = square root of 6x-7	$f (x) = \sqrt{6 x - 7}$
48057	Find the Domain and Range	C(p)=36000/(100-p)	$C (p) = \frac{36000}{100 - p}$
48058	Find the Domain and Range	F(x) = natural log of x+2	$F (x) = \ln (x) + 2$
48059	Find the Domain and Range	f(t)=7t-9t^2	$f (t) = 7 t - 9 t^{2}$
48060	Find the Domain and Range	g(t)=(1-3t)/(2+t)	$g (t) = \frac{1 - 3 t}{2 + t}$
48061	Find the Domain and Range	f(x)=-x^2+8x-7	$f (x) = - x^{2} + 8 x - 7$
48062	Find the Domain and Range	g(t)=8	$g (t) = 8$
48063	Find the Domain and Range	g(x)=x^3-2	$g (x) = x^{3} - 2$
48064	Find the Domain and Range	f(x)=mx+n	$f (x) = m x + n$
48065	Write in Standard Form	x^2+y^2-2x-6y-26=0	$x^{2} + y^{2} - 2 x - 6 y - 26 = 0$
48066	Write in Standard Form	theta=pi/3	$θ = \frac{π}{3}$
48067	Write in Standard Form	y=2/3x+4	$y = \frac{2}{3} x + 4$
48068	Write in Standard Form	x^2+y^2-2x-8y-19=0	$x^{2} + y^{2} - 2 x - 8 y - 19 = 0$
48069	Find the Domain and Range	g(t)=(1-3t)/(6+t)	$g (t) = \frac{1 - 3 t}{6 + t}$
48070	Find the Domain and Range	f(x)=x^2+10x+24	$f (x) = x^{2} + 10 x + 24$
48071	Find Amplitude, Period, and Phase Shift	f(x)=240sin(35pix+pi/6)	$f (x) = 240 \sin (35 π x + \frac{π}{6})$
48072	Find the Maximum/Minimum Value	f(x)=10cos(x)+5sin(2x)	$f (x) = 10 \cos (x) + 5 \sin (2 x)$
48073	Find the Maximum/Minimum Value	f(x)=x^2+8x+9	$f (x) = x^{2} + 8 x + 9$
48074	Find the Maximum/Minimum Value	f(x)=10x^2-10x	$f (x) = 10 x^{2} - 10 x$
48075	Find the Maximum/Minimum Value	f(x)=x^2-10x-4	$f (x) = x^{2} - 10 x - 4$
48076	Find the Maximum/Minimum Value	f(x)=-x^2+6x-5	$f (x) = - x^{2} + 6 x - 5$
48077	Find the Maximum/Minimum Value	f(x)=2x^3-9x^2-24x+10	$f (x) = 2 x^{3} - 9 x^{2} - 24 x + 10$
48078	Find the Maximum/Minimum Value	f(x)=4x^2-96x+530	$f (x) = 4 x^{2} - 96 x + 530$
48079	Find the Maximum/Minimum Value	f(x)=-7x^3+21x+8	$f (x) = - 7 x^{3} + 21 x + 8$
48080	Divide Using Synthetic Division	(x^3-4x^2-47x+210)÷(x-5)	$(x^{3} - 4 x^{2} - 47 x + 210) \div (x - 5)$
48081	Divide Using Synthetic Division	(x^3+2x^2-5x-6)/(x-2)	$\frac{x^{3} + 2 x^{2} - 5 x - 6}{x - 2}$
48082	Find the Maximum/Minimum Value	f(x)=x^2-2x-15	$f (x) = x^{2} - 2 x - 15$
48083	Find the Maximum/Minimum Value	f(x)=2x^2-4x-6	$f (x) = 2 x^{2} - 4 x - 6$
48084	Find the Maximum/Minimum Value	f(x)=cos(pix) , [0,1/6]	$f (x) = \cos (π x)$ , $[0, \frac{1}{6}]$
48085	Find the Maximum/Minimum Value	f(x)=x^2+320/x	$f (x) = x^{2} + \frac{320}{x}$
48086	Find the Maximum/Minimum Value	f(x)=x^2+120/x	$f (x) = x^{2} + \frac{120}{x}$
48087	Find the Maximum/Minimum Value	f(x)=-5x^2+8x-3	$f (x) = - 5 x^{2} + 8 x - 3$
48088	Find the Maximum/Minimum Value	f(x)=-x^2+8x-20	$f (x) = - x^{2} + 8 x - 20$
48089	Find the Maximum/Minimum Value	h(x)=sin(x)^2+cos(x) , 0<x<2pi	$h (x) = \sin^{2} (x) + \cos (x)$ , $0 < x < 2 π$
48090	Find the Tangent Line at x=1	f(x) = natural log of 13-9x^2+2x^4 , x=1	$f (x) = \ln (13 - 9 x^{2} + 2 x^{4})$ , $x = 1$
48091	Find the Tangent Line at x=e	f(x)=2+ natural log of x^5 ; x=e	$f (x) = 2 + \ln (x^{5})$ ; $x = e$
48092	Find the Tangent Line at x=3	f(x)=27/x ; x=3	$f (x) = \frac{27}{x}$ ; $x = 3$
48093	Find the Tangent Line at x=3	f(x)=x^4 x=3	$f (x) = x^{4}$ $x = 3$
48094	Find the Tangent Line at x=-2	f(x)=x^4-20x^2+64 ; x=-2	$f (x) = x^{4} - 20 x^{2} + 64$ ; $x = - 2$
48095	Find the Tangent Line at x=2	f(x)=x^4-17x^2+16 ; x=2	$f (x) = x^{4} - 17 x^{2} + 16$ ; $x = 2$
48096	Find the Tangent Line at a=0	f(x)=1-x-x^2 , a=0	$f (x) = 1 - x - x^{2}$ , $a = 0$
48097	Find the Tangent Line at a=1/16	f(x)=1/( square root of x) , a=1/16	$f (x) = \frac{1}{\sqrt{x}}$ , $a = \frac{1}{16}$
48098	Find the Tangent Line at a=2	f(x)=2x^2-x-3 , a=2	$f (x) = 2 x^{2} - x - 3$ , $a = 2$
48099	Find the Tangent Line at a=7	f(x) = square root of 5x+1 , a=7	$f (x) = \sqrt{5 x + 1}$ , $a = 7$
48100	Find the Tangent Line at a=-2	f(x)=2x^2+x-1 , a=-2	$f (x) = 2 x^{2} + x - 1$ , $a = - 2$