Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
55801	Find the Absolute Max and Min over the Interval	f(t)=t- cube root of t , [-1,5]	$f (t) = t - \sqrt[3]{t}$ , $[- 1, 5]$
55802	Find the Absolute Max and Min over the Interval	f(x)=1/4(3x-1) , x<=3	$f (x) = \frac{1}{4} (3 x - 1)$ , $x \leq 3$
55803	Find the Absolute Max and Min over the Interval	f(x)=1/x+ natural log of x , 0.6<=x<=5	$f (x) = \frac{1}{x} + \ln (x)$ , $0.6 \leq x \leq 5$
55804	Find the Absolute Max and Min over the Interval	f(x)=7/9x+8 , 6<=x<=7	$f (x) = \frac{7}{9} x + 8$ , $6 \leq x \leq 7$
55805	Find the Absolute Max and Min over the Interval	f(x)=x/(x^2-x+9) , [0,9]	$f (x) = \frac{x}{x^{2} - x + 9}$ , $[0, 9]$
55806	Find the Absolute Max and Min over the Interval	T(t)=-0.2t^2+1.6t+98.6 , 0<=t<=8	$T (t) = - 0.2 t^{2} + 1.6 t + 98.6$ , $0 \leq t \leq 8$
55807	Find the Absolute Max and Min over the Interval	f(x)=x^4-2x^2+3 , [-2,3]	$f (x) = x^{4} - 2 x^{2} + 3$ , $[- 2, 3]$
55808	Find the Absolute Max and Min over the Interval	f(x)=x^4-32x^2-5 ; [-5,5]	$f (x) = x^{4} - 32 x^{2} - 5$ ; $[- 5, 5]$
55809	Find the Absolute Max and Min over the Interval	f(x)=x^3-2x^2-4x+6 ; [-1,0]	$f (x) = x^{3} - 2 x^{2} - 4 x + 6$ ; $[- 1, 0]$
55810	Find the Absolute Max and Min over the Interval	f(t)=2cos(t)+sin(2t) , [0,pi/2]	$f (t) = 2 \cos (t) + \sin (2 t)$ , $[0, \frac{π}{2}]$
55811	Find the Absolute Max and Min over the Interval	f(t)=3t^5-45t^3 ; -4<=t<=0	$f (t) = 3 t^{5} - 45 t^{3}$ ; $- 4 \leq t \leq 0$
55812	Find the Absolute Max and Min over the Interval	f(t)=3t^5-5t^3 ; -2<=t<=0	$f (t) = 3 t^{5} - 5 t^{3}$ ; $- 2 \leq t \leq 0$
55813	Find the Absolute Max and Min over the Interval	f(t)=4cos(t)+2sin(2t) , [0,pi/2]	$f (t) = 4 \cos (t) + 2 \sin (2 t)$ , $[0, \frac{π}{2}]$
55814	Find the Absolute Max and Min over the Interval	f(t)=4t^2-1 , [1,1.1]	$f (t) = 4 t^{2} - 1$ , $[1, 1.1]$
55815	Find the Absolute Max and Min over the Interval	f(t) = cube root of t(20-t) , [0,20]	$f (t) = \sqrt[3]{t} (20 - t)$ , $[0, 20]$
55816	Find the Absolute Max and Min over the Interval	f(x)=x^2e^(-x) ; [0,4]	$f (x) = x^{2} e^{- x}$ ; $[0, 4]$
55817	Find the Absolute Max and Min over the Interval	f(x)=x^2-2x-7 , [0,1]	$f (x) = x^{2} - 2 x - 7$ , $[0, 1]$
55818	Find the Absolute Max and Min over the Interval	f(x)=x^2-4x-2 , [0,2]	$f (x) = x^{2} - 4 x - 2$ , $[0, 2]$
55819	Find the Absolute Max and Min over the Interval	f(x)=x^2-6x-1 , [0,3]	$f (x) = x^{2} - 6 x - 1$ , $[0, 3]$
55820	Find the Absolute Max and Min over the Interval	f(x)=x(18-x) ; (negative infinity,infinity)	$f (x) = x (18 - x)$ ; $(- \infty, \infty)$
55821	Find the Absolute Max and Min over the Interval	f(x)=sin(x)+8 , 0<x<2pi	$f (x) = \sin (x) + 8$ , $0 < x < 2 π$
55822	Find the Absolute Max and Min over the Interval	f(x)=x^2 , [-7,4]	$f (x) = x^{2}$ , $[- 7, 4]$
55823	Find the Absolute Max and Min over the Interval	f(x)=-x+cos(3pix) , [0,pi/6]	$f (x) = - x + \cos (3 π x)$ , $[0, \frac{π}{6}]$
55824	Find the Absolute Max and Min over the Interval	f(x)=x+8cos(x) , [0,2pi]	$f (x) = x + 8 \cos (x)$ , $[0, 2 π]$
55825	Find the Absolute Max and Min over the Interval	f(x)=xe^(-5x) , 0<=x<=2	$f (x) = x e^{- 5 x}$ , $0 \leq x \leq 2$
55826	Find the Absolute Max and Min over the Interval	f(x)=x^4-18x^2+8 ; [-6,6]	$f (x) = x^{4} - 18 x^{2} + 8$ ; $[- 6, 6]$
55827	Find the Absolute Max and Min over the Interval	f(x)=x^3-9x^2+15x+6 , [-1,2]	$f (x) = x^{3} - 9 x^{2} + 15 x + 6$ , $[- 1, 2]$
55828	Find the Absolute Max and Min over the Interval	f(x)=x^4-32x^2+4 ; [-5,5]	$f (x) = x^{4} - 32 x^{2} + 4$ ; $[- 5, 5]$
55829	Find the Absolute Max and Min over the Interval	g(x)=-5sec(x) , -pi/2<x<(3pi)/2	$g (x) = - 5 \sec (x)$ , $- \frac{π}{2} < x < \frac{3 π}{2}$
55830	Find the Absolute Max and Min over the Interval	h(t)=t/(t-3) , [4,7]	$h (t) = \frac{t}{t - 3}$ , $[4, 7]$
55831	Convert to Polar Coordinates	(-8,4)	$(- 8, 4)$
55832	Convert to Polar Coordinates	(-3 square root of 2,3 square root of 2)	$(- 3 \sqrt{2}, 3 \sqrt{2})$
55833	Convert to Polar Coordinates	(-6,-4)	$(- 6, - 4)$
55834	Evaluate Using the Squeeze Theorem	limit as x approaches 0 of (1-sec(6x)^2)/((4x)^2)	$lim_{x \to 0} \frac{1 - \sec^{2} (6 x)}{{(4 x)}^{2}}$
55835	Evaluate Using the Squeeze Theorem	limit as x approaches 0 of square root of x^3+x^2sin(pi/x)	$lim_{x \to 0} \sqrt{x^{3} + x^{2}} \sin (\frac{π}{x})$
55836	Evaluate Using the Squeeze Theorem	limit as x approaches 0 of -x^3cos(2/x)	$lim_{x \to 0} - x^{3} \cos (\frac{2}{x})$
55837	Evaluate Using the Squeeze Theorem	limit as x approaches 0 of x^4cos(2/x)	$lim_{x \to 0} x^{4} \cos (\frac{2}{x})$
55838	Evaluate Using the Squeeze Theorem	limit as x approaches 0 of x^2cos(20pix)	$lim_{x \to 0} x^{2} \cos (20 π x)$
55839	Evaluate Using the Squeeze Theorem	limit as x approaches 2 of (x^2-4)/(x-2)	$lim_{x \to 2} \frac{x^{2} - 4}{x - 2}$
55840	Evaluate Using the Squeeze Theorem	limit as x approaches -2 of (x^2-4)/(x+2)	$lim_{x \to - 2} \frac{x^{2} - 4}{x + 2}$
55841	Evaluate Using the Squeeze Theorem	limit as x approaches infinity of arcsec(x/2)	$lim_{x \to \infty} arcsec (\frac{x}{2})$
55842	Evaluate Using the Squeeze Theorem	limit as x approaches infinity of (cos(x))/x	$lim_{x \to \infty} \frac{\cos (x)}{x}$
55843	Evaluate Using the Squeeze Theorem	limit as x approaches infinity of (e^x)/(e^x+1)	$lim_{x \to \infty} \frac{e^{x}}{e^{x} + 1}$
55844	Evaluate Using the Squeeze Theorem	limit as x approaches negative infinity of (3x)/( square root of 16x^2-9x)	$lim_{x \to - \infty} \frac{3 x}{\sqrt{16 x^{2} - 9 x}}$
55845	Evaluate Using the Squeeze Theorem	limit as x approaches infinity of (10sin(x)+15cos(x)+20)/x	$lim_{x \to \infty} \frac{10 \sin (x) + 15 \cos (x) + 20}{x}$
55846	Evaluate Using the Squeeze Theorem	limit as x approaches pi/2 of (sin(cos(pi-x))^2)/((pi/2-x)^2)	$lim_{x \to \frac{π}{2}} \frac{\sin^{2} (\cos (π - x))}{{(\frac{π}{2} - x)}^{2}}$
55847	Find the Median	0.8161 0.8193 0.8165 0.8176 0.7902 0.8143 0.8123	$0.8161$ $0.8193$ $0.8165$ $0.8176$ $0.7902$ $0.8143$ $0.8123$
55848	Find the Vertices	(y^2)/36-(x^2)/64=1	$\frac{y^{2}}{36} - \frac{x^{2}}{64} = 1$
55849	Find the Vertices	(x^2)/4+(y^2)/3=1	$\frac{x^{2}}{4} + \frac{y^{2}}{3} = 1$
55850	Find the Vertices	49x^2+16y^2+392x-224y+784=0	$49 x^{2} + 16 y^{2} + 392 x - 224 y + 784 = 0$
55851	Find the Vertices	36x^2+25y^2+360x-300y+900=0	$36 x^{2} + 25 y^{2} + 360 x - 300 y + 900 = 0$
55852	Find the Vertices	16x^2-9y^2=144	$16 x^{2} - 9 y^{2} = 144$
55853	Find the Vertices	5x^2+9y^2=45	$5 x^{2} + 9 y^{2} = 45$
55854	Find the Vertices	((y-1)^2)/16-((x-2)^2)/9=1	$\frac{{(y - 1)}^{2}}{16} - \frac{{(x - 2)}^{2}}{9} = 1$
55855	Find the Vertices	(x^2)/25+(y^2)/9=1	$\frac{x^{2}}{25} + \frac{y^{2}}{9} = 1$
55856	Identify the Zeros and Their Multiplicities	f(x)=3x^3-7x^2-75x+175	$f (x) = 3 x^{3} - 7 x^{2} - 75 x + 175$
55857	Identify the Zeros and Their Multiplicities	f(x)=x^3+9x^2-9x-81	$f (x) = x^{3} + 9 x^{2} - 9 x - 81$
55858	Identify the Zeros and Their Multiplicities	f(x)=x^3-5x^2-9x+45	$f (x) = x^{3} - 5 x^{2} - 9 x + 45$
55859	Find the Vertex	x^2=20y	$x^{2} = 20 y$
55860	Find the Vertex	y=(x-4)^2+5	$y = {(x - 4)}^{2} + 5$
55861	Find the Vertex	y=2x^2-4x+17	$y = 2 x^{2} - 4 x + 17$
55862	Find the Vertex	y=4x^2+16x-3	$y = 4 x^{2} + 16 x - 3$
55863	Find the Vertex	y=x-1/4x^2	$y = x - \frac{1}{4} x^{2}$
55864	Find the Vertex	y=x^2-8x-48	$y = x^{2} - 8 x - 48$
55865	Find dy/dx at (-1,5)	y=2x^2-3x ; (-1,5)	$y = 2 x^{2} - 3 x$ ; $(- 1, 5)$
55866	Find dx/dy at (5,5)	y^4=125x ; (5,5)	$y^{4} = 125 x$ ; $(5, 5)$
55867	Find dy/dx at (1,1)	2x^3+3y^2=5xy ; (1,1)	$2 x^{3} + 3 y^{2} = 5 x y$ ; $(1, 1)$
55868	Find dx/dy at (-1,5)	y=2x^2-3x ; (-1,5)	$y = 2 x^{2} - 3 x$ ; $(- 1, 5)$
55869	Find dy/dx at (5,5)	y^4=125x ; (5,5)	$y^{4} = 125 x$ ; $(5, 5)$
55870	Find dy/dx at (-3,-5)	6x^3y^2-2y^3=3 ; (-3,-5)	$6 x^{3} y^{2} - 2 y^{3} = 3$ ; $(- 3, - 5)$
55871	Find the Critical Points	c=8x+100000/x	$c = 8 x + \frac{100000}{x}$
55872	Find the Critical Points	f(theta)=6cos(theta)+3sin(theta)^2	$f (θ) = 6 \cos (θ) + 3 \sin^{2} (θ)$
55873	Find the Critical Points	f'(x)=(x+3)e^(-3x)	$f' (x) = (x + 3) e^{- 3 x}$
55874	Find the Critical Points	f'(x)=x^2-x-6	$f' (x) = x^{2} - x - 6$
55875	Find the Critical Points	g(theta)=20theta-5tan(theta)	$g (θ) = 20 θ - 5 \tan (θ)$
55876	Find the Critical Points	g(theta)=32theta-8tan(theta)	$g (θ) = 32 θ - 8 \tan (θ)$
55877	Find the Critical Points	h(x)=sin(2x)+cos(x)	$h (x) = \sin (2 x) + \cos (x)$
55878	Find the Critical Points	y=x/((x-9)^2)	$y = \frac{x}{{(x - 9)}^{2}}$
55879	Find the Critical Points	y=(x^2-143)e^x	$y = (x^{2} - 143) e^{x}$
55880	Find the Critical Points	y=2+3.6x+1.2x^2	$y = 2 + 3.6 x + 1.2 x^{2}$
55881	Find the Critical Points	y=2x^3-3x^2-12x	$y = 2 x^{3} - 3 x^{2} - 12 x$
55882	Find the Critical Points	y=2x^3-3x^2-9x	$y = 2 x^{3} - 3 x^{2} - 9 x$
55883	Find the Critical Points	y=2x^3-9x^2+12x	$y = 2 x^{3} - 9 x^{2} + 12 x$
55884	Find the Critical Points	y=2x^5+5x^4-16	$y = 2 x^{5} + 5 x^{4} - 16$
55885	Find the Critical Points	y=3x^3-18x^2+6	$y = 3 x^{3} - 18 x^{2} + 6$
55886	Find the Critical Points	y=4x^3-3x^2	$y = 4 x^{3} - 3 x^{2}$
55887	Find the Critical Points	y=7x^2-6x	$y = 7 x^{2} - 6 x$
55888	Find the Critical Points	y=x^(1/3)+1	$y = x^{\frac{1}{3}} + 1$
55889	Find the Critical Points	y=-x^3+4x^2+16x-1	$y = - x^{3} + 4 x^{2} + 16 x - 1$
55890	Find the Critical Points	y=x^3-12x+5	$y = x^{3} - 12 x + 5$
55891	Find the Critical Points	y=x^3-27x+7	$y = x^{3} - 27 x + 7$
55892	Find the Critical Points	y=x^4-2x^2-4	$y = x^{4} - 2 x^{2} - 4$
55893	Find the Critical Points	C=8x+100000/x	$C = 8 x + \frac{100000}{x}$
55894	Find dc/dq at (2,3)	c=0.3q^2+2q+54 , (2,3)	$c = 0.3 q^{2} + 2 q + 54$ , $(2, 3)$
55895	Find dq/dc at (2,3)	c=0.3q^2+2q+54 , (2,3)	$c = 0.3 q^{2} + 2 q + 54$ , $(2, 3)$
55896	Find dx/dy at (-1,1)	x^2y+xy^2=0 , (-1,1)	$x^{2} y + x y^{2} = 0$ , $(- 1, 1)$
55897	Find dx/dy at (2,3)	6x^2+5xy+2y^2=72 ; (2,3)	$6 x^{2} + 5 x y + 2 y^{2} = 72$ ; $(2, 3)$
55898	Find dx/dy at (2,-4)	x^2+y^2=20 , (2,-4)	$x^{2} + y^{2} = 20$ , $(2, - 4)$
55899	Find dx/dy at (-3,3)	y^2+4y+7x=0 ; (-3,3)	$y^{2} + 4 y + 7 x = 0$ ; $(- 3, 3)$
55900	Find dx/dy at (-3,-4)	x^2+y^2=25 , (-3,-4)	$x^{2} + y^{2} = 25$ , $(- 3, - 4)$