Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
4001	Find the Maximum/Minimum Value	-x^2-3x+3	$- x^{2} - 3 x + 3$
4002	Find the Maximum Number of Real Roots	f(x)=x^3-3x	$f (x) = x^{3} - 3 x$
4003	Find the Upper and Lower Bounds	f(x)=2x-3	$f (x) = 2 x - 3$
4004	Find the Difference Quotient	f(x)=2/x	$f (x) = \frac{2}{x}$
4005	Find the Difference Quotient	f(x)=1/(2x)	$f (x) = \frac{1}{2 x}$
4006	Find the Difference Quotient	f(x)=6/(x+1)	$f (x) = \frac{6}{x + 1}$
4007	Find the Difference Quotient	f(x)=4x^2-2x	$f (x) = 4 x^{2} - 2 x$
4008	Find the Difference Quotient	f(x)=2x^2-x-3	$f (x) = 2 x^{2} - x - 3$
4009	Find the Difference Quotient	f(x)=2x+1	$f (x) = 2 x + 1$
4010	Find the Difference Quotient	f(x)=2x^2-3	$f (x) = 2 x^{2} - 3$
4011	Find the Difference Quotient	f(x)=x^3+3x	$f (x) = x^{3} + 3 x$
4012	Find the Difference Quotient	f(x)=x^3	$f (x) = x^{3}$
4013	Find the Difference Quotient	f(x)=3/x	$f (x) = \frac{3}{x}$
4014	Find the Difference Quotient	f(x)=e^x	$f (x) = e^{x}$
4015	Find the Difference Quotient	f(x)=1/(5x)	$f (x) = \frac{1}{5 x}$
4016	Find the Difference Quotient	f(x)=1/(x+1)	$f (x) = \frac{1}{x + 1}$
4017	Find the Difference Quotient	f(x)=1/(x+2)	$f (x) = \frac{1}{x + 2}$
4018	Find the Difference Quotient	f(x)=4/(x+4)	$f (x) = \frac{4}{x + 4}$
4019	Find the Difference Quotient	f(x)=x^2+5	$f (x) = x^{2} + 5$
4020	Find the Difference Quotient	f(x)=x^2+8x-9	$f (x) = x^{2} + 8 x - 9$
4021	Find the Difference Quotient	f(x)=x^2-1	$f (x) = x^{2} - 1$
4022	Find the Difference Quotient	f(x)=x^2-3x+4	$f (x) = x^{2} - 3 x + 4$
4023	Find the Difference Quotient	f(x)=4x^3	$f (x) = 4 x^{3}$
4024	Find the Difference Quotient	f(x)=5	$f (x) = 5$
4025	Find the Vertex	f(x)=(x-3)^2-1	$f (x) = {(x - 3)}^{2} - 1$
4026	Find the Vertex	f(x)=(x-2)^2-9	$f (x) = {(x - 2)}^{2} - 9$
4027	Find the Vertex	f(x)=(x-3)^2	$f (x) = {(x - 3)}^{2}$
4028	Find the Vertex	f(x)=(x+5)^2-6	$f (x) = {(x + 5)}^{2} - 6$
4029	Find the Vertex	f(x)=(x-1)^2-4	$f (x) = {(x - 1)}^{2} - 4$
4030	Find the Vertex	-4x^2+24x-41	$- 4 x^{2} + 24 x - 41$
4031	Find the Vertex	4x^2-6x-2	$4 x^{2} - 6 x - 2$
4032	Find the Vertex	4x^2-2x+6	$4 x^{2} - 2 x + 6$
4033	Find the Vertex	x^2-2x-8	$x^{2} - 2 x - 8$
4034	Find the Vertex	-2x^2+16x-24	$- 2 x^{2} + 16 x - 24$
4035	Find the Vertex	-2x^2+8x-5	$- 2 x^{2} + 8 x - 5$
4036	Solve by Addition/Elimination	x+4y=6 , x=8y	$x + 4 y = 6$ , $x = 8 y$
4037	Solve by Addition/Elimination	3x-3y+2z=9 , 3x+y-3z=-8 , 11x-y-2z=0	$3 x - 3 y + 2 z = 9$ , $3 x + y - 3 z = - 8$ , $11 x - y - 2 z = 0$
4038	Solve by Addition/Elimination	x-2y+3z=6 , 2x+y+z=2 , -2x+4y-6z=-12	$x - 2 y + 3 z = 6$ , $2 x + y + z = 2$ , $- 2 x + 4 y - 6 z = - 12$
4039	Solve by Addition/Elimination	5x-y=16 , 2x+3y=3	$5 x - y = 16$ , $2 x + 3 y = 3$
4040	Solve by Addition/Elimination	2x^2+y^2=17 , 3x^2-2y^2=-6	$2 x^{2} + y^{2} = 17$ , $3 x^{2} - 2 y^{2} = - 6$
4041	Solve by Addition/Elimination	2x^2-8y^3=19 , 4x^2+16y^3=34	$2 x^{2} - 8 y^{3} = 19$ , $4 x^{2} + 16 y^{3} = 34$
4042	Solve by Addition/Elimination	-2x+y-2z=-15 , -x+y-z=-11 , z=-5	$- 2 x + y - 2 z = - 15$ , $- x + y - z = - 11$ , $z = - 5$
4043	Solve by Substitution	xy=9 , x^2+y^2=82	$x y = 9$ , $x^{2} + y^{2} = 82$
4044	Solve by Substitution	y=x^2 , y=x+12	$y = x^{2}$ , $y = x + 12$
4045	Solve by Substitution	y=4-x^2 , y=x^2-4	$y = 4 - x^{2}$ , $y = x^{2} - 4$
4046	Solve by Substitution	y=5x-2 , y=-2x+5	$y = 5 x - 2$ , $y = - 2 x + 5$
4047	Solve by Substitution	8r-s+t=-42 , 3r+2s-3t=-32 , r-3s+2t=10	$8 r - s + t = - 42$ , $3 r + 2 s - 3 t = - 32$ , $r - 3 s + 2 t = 10$
4048	Solve by Substitution	ax+by=1 , bx+ay=1	$a x + b y = 1$ , $b x + a y = 1$
4049	Solve by Substitution	w-6z=-4 , x+y+3z=2	$w - 6 z = - 4$ , $x + y + 3 z = 2$
4050	Solve by Substitution	x+y+4z=1 , 3x+2y+11z=1 , x+3z=-1	$x + y + 4 z = 1$ , $3 x + 2 y + 11 z = 1$ , $x + 3 z = - 1$
4051	Solve by Substitution	x+y=2 , y=x^2-10	$x + y = 2$ , $y = x^{2} - 10$
4052	Solve by Substitution	x-2y+z=1 , y+2z=5 , x+y+3z=8	$x - 2 y + z = 1$ , $y + 2 z = 5$ , $x + y + 3 z = 8$
4053	Solve by Substitution	4x^2-3xy+9y^2=15 , 2x+3y=5	$4 x^{2} - 3 x y + 9 y^{2} = 15$ , $2 x + 3 y = 5$
4054	Solve by Substitution	3x+2y=-5 , 2x-5y=-16	$3 x + 2 y = - 5$ , $2 x - 5 y = - 16$
4055	Solve by Substitution	3x-2y=8 , 5x+3y=7	$3 x - 2 y = 8$ , $5 x + 3 y = 7$
4056	Solve by Substitution	4x-8y=16 , 3x-6y=12	$4 x - 8 y = 16$ , $3 x - 6 y = 12$
4057	Solve by Substitution	y^2+17y+x^2-3x-18=0 , y+17+(3x-18)/y=0	$y^{2} + 17 y + x^{2} - 3 x - 18 = 0$ , $y + 17 + \frac{3 x - 18}{y} = 0$
4058	Find the Distance Between Two Points	(-5,2) , (7,-3)	$(- 5, 2) (7, - 3)$
4059	Solve by Substitution	256x^2+16y^2=4096 , y=x^2-16	$256 x^{2} + 16 y^{2} = 4096$ , $y = x^{2} - 16$
4060	Solve by Substitution	11x-6y=494 , x+7y=-23	$11 x - 6 y = 494$ , $x + 7 y = - 23$
4061	Solve by Substitution	2x^2+xy-y^2=3 , x^2+2xy+y^2=3	$2 x^{2} + x y - y^{2} = 3$ , $x^{2} + 2 x y + y^{2} = 3$
4062	Solve by Substitution	3/2x-1/3y=1/2 , 2x-1/2y=-1/2	$\frac{3}{2} x - \frac{1}{3} y = \frac{1}{2}$ , $2 x - \frac{1}{2} y = - \frac{1}{2}$
4063	Solve by Substitution	x^2+y^2=169 , x^2-8y=104	$x^{2} + y^{2} = 169$ , $x^{2} - 8 y = 104$
4064	Solve by Substitution	x^2+2y^2=441 , x+y=21	$x^{2} + 2 y^{2} = 441$ , $x + y = 21$
4065	Solve by Substitution	x^2+y=0 , x^3-12x-y=0	$x^{2} + y = 0$ , $x^{3} - 12 x - y = 0$
4066	Solve by Substitution	x^2-4y=19 , x^2+y^2=16	$x^{2} - 4 y = 19$ , $x^{2} + y^{2} = 16$
4067	Find the Inverse	g(x)=x^3	$g (x) = x^{3}$
4068	Find the Inverse	f(x)=3x^2-7	$f (x) = 3 x^{2} - 7$
4069	Solve for x	(2x-1)^(2/3)=4	${(2 x - 1)}^{\frac{2}{3}} = 4$
4070	Find Where Increasing/Decreasing	x^2-2x-3	$x^{2} - 2 x - 3$
4071	Find Where Increasing/Decreasing	f(x)=x^2-2x-3	$f (x) = x^{2} - 2 x - 3$
4072	Find Where Increasing/Decreasing	cos(2x)	$\cos (2 x)$
4073	Evaluate Using Summation Formulas	sum from i=2 to 5 of 6i	$\sum_{i = 2}^{5} 6 i$
4074	Evaluate Using Summation Formulas	sum from i=1 to infinity of 12(-0.7)^(i-1)	$\sum_{i = 1}^{\infty} 12 {(- 0.7)}^{i - 1}$
4075	Find Where Increasing/Decreasing	y=x^3-3x	$y = x^{3} - 3 x$
4076	Evaluate Using Summation Formulas	sum from i=1 to 11 of 3*2^i	$\sum_{i = 1}^{11} 3 \cdot 2^{i}$
4077	Evaluate Using Summation Formulas	sum from 1 to 4 of 4n+1	$\sum_{1}^{4} 4 n + 1$
4078	Find Where Increasing/Decreasing	g(x)=4-(x-6)^2	$g (x) = 4 - {(x - 6)}^{2}$
4079	Find Where Increasing/Decreasing	sin(x)	$\sin (x)$
4080	Find Where Increasing/Decreasing	y=2^x	$y = 2^{x}$
4081	Find the Inverse	1/x	$\frac{1}{x}$
4082	Determine the Types of the Numbers	72 , 36 , 18 , 9	$72$ , $36$ , $18$ , $9$
4083	Find the Inverse	sin(x)^4	$\sin^{4} (x)$
4084	Find the Inverse	f(x)=(2-x^3)^5	$f (x) = {(2 - x^{3})}^{5}$
4085	Evaluate Using Summation Formulas	sum from K=1 to 5 of 2k	$\sum_{K = 1}^{5} 2 k$
4086	Evaluate Using Summation Formulas	sum from k=1 to 4 of 2k	$\sum_{k = 1}^{4} 2 k$
4087	Evaluate Using Summation Formulas	sum from k=1 to 4 of k^2	$\sum_{k = 1}^{4} k^{2}$
4088	Find Where Undefined/Discontinuous	natural log of ex	$\ln (e x)$
4089	Find Where Undefined/Discontinuous	(sin(y)^2)/(1-cos(y))	$\frac{\sin^{2} (y)}{1 - \cos (y)}$
4090	Apply the Quadratic Formula	x^2-6x+2	$x^{2} - 6 x + 2$
4091	Find the Axis of Symmetry	f(x)=x^2+12x+36	$f (x) = x^{2} + 12 x + 36$
4092	Find the Axis of Symmetry	f(x)=6x^2+12x-1	$f (x) = 6 x^{2} + 12 x - 1$
4093	Complete the Square	x^2+10x+11	$x^{2} + 10 x + 11$
4094	Find the Axis of Symmetry	f(x)=2x^2-4x-1	$f (x) = 2 x^{2} - 4 x - 1$
4095	Complete the Square	-x^2+4x	$- x^{2} + 4 x$
4096	Complete the Square	-x^2+6x+4	$- x^{2} + 6 x + 4$
4097	Complete the Square	x^2-18x-11	$x^{2} - 18 x - 11$
4098	Evaluate	1/(-1/3)	$\frac{1}{- \frac{1}{3}}$
4099	Evaluate	1/(-21/29)	$\frac{1}{- \frac{21}{29}}$
4100	Evaluate	1/(15/17)	$\frac{1}{\frac{15}{17}}$