Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
3001	Evaluate the Limit	limit as x approaches 0 of (sin(9x))/x	$lim_{x \to 0} \frac{\sin (9 x)}{x}$
3002	Evaluate the Limit	limit as x approaches 0 of (tan(x)-x)/(x^3)	$lim_{x \to 0} \frac{\tan (x) - x}{x^{3}}$
3003	Evaluate the Limit	limit as x approaches 0 of (tan(5x))/x	$lim_{x \to 0} \frac{\tan (5 x)}{x}$
3004	Evaluate the Limit	limit as x approaches 0 of e^(1/x)	$lim_{x \to 0} e^{\frac{1}{x}}$
3005	Evaluate the Limit	limit as x approaches 0 of 2/x	$lim_{x \to 0} \frac{2}{x}$
3006	Evaluate the Limit	limit as x approaches 0 of xcos(x)	$lim_{x \to 0} x \cos (x)$
3007	Evaluate the Limit	limit as x approaches 0 of (x-3)/(x^2-3x)	$lim_{x \to 0} \frac{x - 3}{x^{2} - 3 x}$
3008	Evaluate the Limit	limit as x approaches 0 of 3	$lim_{x \to 0} 3$
3009	Evaluate the Limit	limit as x approaches 0 of x^4cos(2/x)	$lim_{x \to 0} x^{4} \cos (\frac{2}{x})$
3010	Evaluate the Limit	limit as x approaches 0 of g(x)	$lim_{x \to 0} g (x)$
3011	Evaluate the Limit	limit as x approaches 196 of ( square root of x-14)/(x-196)	$lim_{x \to 196} \frac{\sqrt{x} - 14}{x - 196}$
3012	Evaluate the Limit	limit as x approaches 1 of 2/2*(16x-12)	$lim_{x \to 1} \frac{2}{2} \cdot (16 x - 12)$
3013	Evaluate the Limit	limit as x approaches 0 of ( square root of 9+x-3)/x	$lim_{x \to 0} \frac{\sqrt{9 + x} - 3}{x}$
3014	Evaluate the Limit	limit as x approaches 1 of 5	$lim_{x \to 1} 5$
3015	Evaluate the Limit	limit as x approaches 1 of g(x)	$lim_{x \to 1} g (x)$
3016	Evaluate the Limit	limit as x approaches 1 of x/(x-1)-1/( natural log of x)	$lim_{x \to 1} \frac{x}{x - 1} - \frac{1}{\ln (x)}$
3017	Evaluate the Limit	limit as x approaches -2 of (x^3+8)/(x^2+8x+12)	$lim_{x \to - 2} \frac{x^{3} + 8}{x^{2} + 8 x + 12}$
3018	Evaluate the Limit	limit as x approaches 1 of \|x-1\|	$lim_{x \to 1} \| x - 1 \|$
3019	Evaluate the Limit	limit as x approaches 7 of (x^2-7x)/(x^2-6x-7)	$lim_{x \to 7} \frac{x^{2} - 7 x}{x^{2} - 6 x - 7}$
3020	Evaluate the Limit	limit as x approaches -2 of (x^2+4x+4)/(x^4-16)	$lim_{x \to - 2} \frac{x^{2} + 4 x + 4}{x^{4} - 16}$
3021	Evaluate the Limit	limit as x approaches -2 of square root of 7x^4+x^2	$lim_{x \to - 2} \sqrt{7 x^{4} + x^{2}}$
3022	Evaluate the Limit	limit as x approaches 2 of natural log of x-2	$lim_{x \to 2} \ln (x - 2)$
3023	Evaluate the Limit	limit as x approaches 2 of 3x+2	$lim_{x \to 2} 3 x + 2$
3024	Evaluate the Limit	limit as x approaches -5 of (x^3+125)/(x+5)	$lim_{x \to - 5} \frac{x^{3} + 125}{x + 5}$
3025	Evaluate the Limit	limit as x approaches 2 of x^3+5x^2-7x+1	$lim_{x \to 2} x^{3} + 5 x^{2} - 7 x + 1$
3026	Evaluate the Limit	limit as x approaches -2 of 3x^5-3x^4+4x^3+x^2+5	$lim_{x \to - 2} 3 x^{5} - 3 x^{4} + 4 x^{3} + x^{2} + 5$
3027	Find the Area Between the Curves	y=4-x^2 , y=x+2	$y = 4 - x^{2}$ , $y = x + 2$
3028	Find the Area Between the Curves	y=4-x^2 , y=x-2	$y = 4 - x^{2}$ , $y = x - 2$
3029	Find the Area Between the Curves	y=x^(5/4) , y=3x^(1/4)	$y = x^{\frac{5}{4}}$ , $y = 3 x^{\frac{1}{4}}$
3030	Find the Volume	y=1-x^2 , y=0	$y = 1 - x^{2}$ , $y = 0$
3031	Find the Tangent Line at the Point	2x^2+y^2=12 , (2,-2)	$2 x^{2} + y^{2} = 12$ , $(2, - 2)$
3032	Find the Tangent Line at the Point	2x^2+y^2=57 , (-4,5)	$2 x^{2} + y^{2} = 57$ , $(- 4, 5)$
3033	Find the Tangent Line at the Point	y=(7x)/(x+4) , (3,3)	$y = \frac{7 x}{x + 4}$ , $(3, 3)$
3034	Find the Tangent Line at the Point	y=(7x)/(x-1) , (2,14)	$y = \frac{7 x}{x - 1}$ , $(2, 14)$
3035	Find the Tangent Line at the Point	y=(4x)/(x-5) , (7,14)	$y = \frac{4 x}{x - 5}$ , $(7, 14)$
3036	Find the Tangent Line at the Point	y = square root of 2x , (18,6)	$y = \sqrt{2 x}$ , $(18, 6)$
3037	Find the Tangent Line at the Point	y = square root of x , (1,1)	$y = \sqrt{x}$ , $(1, 1)$
3038	Evaluate the Limit	( limit as x approaches 0 of square root of 3+x- square root of 3)/x	$\frac{lim_{x \to 0} \sqrt{3 + x} - \sqrt{3}}{x}$
3039	Evaluate the Limit	( limit as x approaches 0 of (2+x)^3-8)/x	$\frac{lim_{x \to 0} {(2 + x)}^{3} - 8}{x}$
3040	Evaluate the Limit	( limit as x approaches 0 of x^3-6x+8)/(x-2)	$\frac{lim_{x \to 0} x^{3} - 6 x + 8}{x - 2}$
3041	Evaluate the Limit	( limit as x approaches 0 of 3(1-cos(x)))/x	$\frac{lim_{x \to 0} 3 (1 - \cos (x))}{x}$
3042	Evaluate the Limit	( limit as x approaches 0 of cos(x)-1)/x	$\frac{lim_{x \to 0} \cos (x) - 1}{x}$
3043	Evaluate the Limit	( limit as x approaches 0 of sin(x^2))/x	$\frac{lim_{x \to 0} \sin (x^{2})}{x}$
3044	Evaluate the Limit	( limit as x approaches 0 of sin(5x))/(2x)	$\frac{lim_{x \to 0} \sin (5 x)}{2 x}$
3045	Evaluate the Limit	( limit as a approaches 0 of sin(a))/a	$\frac{lim_{a \to 0} \sin (a)}{a}$
3046	Evaluate the Limit	( limit as x approaches 0 of tan(x)-x)/(x^3)	$\frac{lim_{x \to 0} \tan (x) - x}{x^{3}}$
3047	Evaluate the Limit	( limit as x approaches 0 of sin(x)cos(4x))/(x+xcos(5x))	$\frac{lim_{x \to 0} \sin (x) \cos (4 x)}{x + x \cos (5 x)}$
3048	Evaluate the Limit	( limit as x approaches 0 of tan(2x))/x	$\frac{lim_{x \to 0} \tan (2 x)}{x}$
3049	Find the Tangent Line at the Point	y=4x^3-4x , (-1,0)	$y = 4 x^{3} - 4 x$ , $(- 1, 0)$
3050	Find the Tangent Line at the Point	y=16 square root of x , (16,64)	$y = 16 \sqrt{x}$ , $(16, 64)$
3051	Graph	sin( natural log of x)	$\sin (\ln (x))$
3052	Graph	3x natural log of x	$3 x \ln (x)$
3053	Graph	cos( natural log of x)	$\cos (\ln (x))$
3054	Graph	natural log of 9x	$\ln (9 x)$
3055	Graph	natural log of sec(x)	$\ln (\sec (x))$
3056	Graph	natural log of 6x	$\ln (6 x)$
3057	Graph	1/(x natural log of x)	$\frac{1}{x \ln (x)}$
3058	Graph	x/( natural log of x)	$\frac{x}{\ln (x)}$
3059	Graph	natural log of (x)^3	$\ln ({(x)}^{3})$
3060	Evaluate	natural log of natural log of e^(e^8)	$\ln (\ln (e^{e^{8}}))$
3061	Evaluate	2 natural log of 3	$2 \ln (3)$
3062	Evaluate	natural log of 3e^2	$\ln (3 e^{2})$
3063	Solve the Function Operation	f(x)=x^2 , g(x)=2x+5 , h(x)=x^2-1 , f(g(x-1))	$f (x) = x^{2}$ , $g (x) = 2 x + 5$ , $h (x) = x^{2} - 1$ , $f (g (x - 1))$
3064	Find the Area Between the Curves	x=-2 , x=1 , y=2x , y=x^2-3	$x = - 2$ , $x = 1$ , $y = 2 x$ , $y = x^{2} - 3$
3065	Find the Derivative - d/dx	2^5	$2^{5}$
3066	Solve for ?	tan(x)=-4/5	$\tan (x) = - \frac{4}{5}$
3067	Solve for o	sin(o)=5/6	$\sin (o) = \frac{5}{6}$
3068	Solve for x	3x^2-4x-4=0	$3 x^{2} - 4 x - 4 = 0$
3069	Solve for x	4x-36/x=0	$4 x - \frac{36}{x} = 0$
3070	Solve for x	-12x^2+48x=0	$- 12 x^{2} + 48 x = 0$
3071	Solve for x	12x^2-120x+209=0	$12 x^{2} - 120 x + 209 = 0$
3072	Solve for x	12x^2-264x+989=0	$12 x^{2} - 264 x + 989 = 0$
3073	Solve for x	2x^-3=0	$2 x^{- 3} = 0$
3074	Solve for x	natural log of x- natural log of x^2+ natural log of 3=0	$\ln (x) - \ln (x^{2}) + \ln (3) = 0$
3075	Solve for x	natural log of x=0	$\ln (x) = 0$
3076	Solve for x	natural log of x^2+1-3 natural log of x = natural log of 2	$\ln (x^{2} + 1) - 3 \ln (x) = \ln (2)$
3077	Solve for x	6x^2-2x-4=0	$6 x^{2} - 2 x - 4 = 0$
3078	Simplify	e^(x^2)	$e^{x^{2}}$
3079	Simplify	(e^(1/x))/(x^2)	$\frac{e^{\frac{1}{x}}}{x^{2}}$
3080	Simplify	(x^(r/s))^(s/r)	${(x^{\frac{r}{s}})}^{\frac{s}{r}}$
3081	Simplify	(x^2-1)^3	${(x^{2} - 1)}^{3}$
3082	Simplify	(e^x+e^(-x))^2	${(e^{x} + e^{- x})}^{2}$
3083	Simplify	(e^x-e^(-x))^2	${(e^{x} - e^{- x})}^{2}$
3084	Simplify	(pi/2)^2	${(\frac{π}{2})}^{2}$
3085	Solve for x	cos(x)=x^4-x	$\cos (x) = x^{4} - x$
3086	Find dy/dx	x^3+y^3=12xy-8	$x^{3} + y^{3} = 12 x y - 8$
3087	Simplify	(tan(x))/x	$\frac{\tan (x)}{x}$
3088	Simplify	sec(0)^2	$\sec^{2} (0)$
3089	Simplify	x(99-x)(66-2x)	$x (99 - x) (66 - 2 x)$
3090	Simplify	x(27-x)(18-2x)	$x (27 - x) (18 - 2 x)$
3091	Find the Derivative - d/dx	(x^2+4)^5	${(x^{2} + 4)}^{5}$
3092	Find the Derivative - d/dx	(4x-5)^2	${(4 x - 5)}^{2}$
3093	Find the Derivative - d/dx	3e^xcos(x)	$3 e^{x} \cos (x)$
3094	Find the Derivative - d/dx	(x^3-8)^4	${(x^{3} - 8)}^{4}$
3095	Find the Derivative - d/dx	x square root of x-1	$x \sqrt{x - 1}$
3096	Find the Derivative - d/dx	square root of 16-x^2	$\sqrt{16 - x^{2}}$
3097	Find the Derivative - d/dt	1/t	$\frac{1}{t}$
3098	Find the Derivative - d/dt	699/((t+1)^0.94)	$\frac{699}{{(t + 1)}^{0.94}}$
3099	Find the Derivative - d/dt	cos(e^(cos(t)^2))^2	$\cos^{2} (e^{\cos^{2} (t)})$
3100	Find the Derivative - d/dt	860-326/( square root of t)	$860 - \frac{326}{\sqrt{t}}$