Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
61201	Find the Critical Points	x^4e^(-9x)	$x^{4} e^{- 9 x}$
61202	Find the Critical Points	x^(14/15)-x^(29/15)	$x^{\frac{14}{15}} - x^{\frac{29}{15}}$
61203	Find the Critical Points	x^2+2x+6	$x^{2} + 2 x + 6$
61204	Find the Critical Points	x^3-4x	$x^{3} - 4 x$
61205	Write in Standard Form	fourth root of x	$\sqrt[4]{x}$
61206	Evaluate from the Right	limit as x approaches 0 from the right of x^2 natural log of x	$lim_{x \to 0} x^{2} \ln (x)$
61207	Evaluate from the Right	limit as x approaches 1 of (x-1) natural log of x-1	$lim_{x \to 1} (x - 1) \ln (x - 1)$
61208	Evaluate from the Right	limit as x approaches 0 of sin(x) natural log of 2x	$lim_{x \to 0} \sin (x) \ln (2 x)$
61209	Convert to a Simplified Fraction	square root of 17	$\sqrt{17}$
61210	Solve by Factoring	x^2-2x+2=0	$x^{2} - 2 x + 2 = 0$
61211	Solve by Factoring	3x^2-4x-4=0	$3 x^{2} - 4 x - 4 = 0$
61212	Find the Tangent Line at the Point	xe^y+ye^x=4 , (0,4)	$x e^{y} + y e^{x} = 4$ , $(0, 4)$
61213	Find the Area Between the Curves	y=x^4-4x^2+3 , y=x^2-1	$y = x^{4} - 4 x^{2} + 3$ , $y = x^{2} - 1$
61214	Find the Area Between the Curves	y=x^4-4x^2 , y=x^2-4	$y = x^{4} - 4 x^{2}$ , $y = x^{2} - 4$
61215	Find the Domain and Range	y = square root of 4x	$y = \sqrt{4 x}$
61216	Find the Area Between the Curves	y=x^2 , y=0 , x=2	$y = x^{2}$ , $y = 0$ , $x = 2$
61217	Find the Area Between the Curves	y=x^2-32 , y=8-3x	$y = x^{2} - 32$ , $y = 8 - 3 x$
61218	Find the Area Between the Curves	y=-x^2-3x , -8<=x<=3	$y = - x^{2} - 3 x$ , $- 8 \leq x \leq 3$
61219	Find the Area Between the Curves	y=x^2-4x+3y=x-1	$y = x^{2} - 4 x + 3 y = x - 1$
61220	Find the Area Between the Curves	x=0 , x=-2 , y=e^x , y=0	$x = 0$ , $x = - 2$ , $y = e^{x}$ , $y = 0$
61221	Find the Area Between the Curves	x=-5 , x=2 , y=4x , y=x^2-5	$x = - 5$ , $x = 2$ , $y = 4 x$ , $y = x^{2} - 5$
61222	Find the Area Between the Curves	y=3x-x^2 , y=-6x	$y = 3 x - x^{2}$ , $y = - 6 x$
61223	Find the Area Between the Curves	y=4x , y=x^2-5	$y = 4 x$ , $y = x^{2} - 5$
61224	Find the Area Between the Curves	y=5x-x^2 , y=-6x	$y = 5 x - x^{2}$ , $y = - 6 x$
61225	Find the Area Between the Curves	y=5x-x^2 , y=-4x	$y = 5 x - x^{2}$ , $y = - 4 x$
61226	Find the Area Between the Curves	y=-6x-8 ; y=0 ; -1<=x<=2	$y = - 6 x - 8$ ; $y = 0$ ; $- 1 \leq x \leq 2$
61227	Find the Area Between the Curves	y=9-x^2	$y = 9 - x^{2}$
61228	Find the Area Between the Curves	y=x^2 y=3x	$y = x^{2}$ $y = 3 x$
61229	Find the Area Between the Curves	y=e^x , y=-3x^2-5x	$y = e^{x}$ , $y = - 3 x^{2} - 5 x$
61230	Find the Area Between the Curves	y = square root of 36-x^2 , y=0	$y = \sqrt{36 - x^{2}}$ , $y = 0$
61231	Find the Area Between the Curves	x=-5 , x=3 , y=6x , y=x^2-7	$x = - 5$ , $x = 3$ , $y = 6 x$ , $y = x^{2} - 7$
61232	Find the Area Between the Curves	x=y^2-8y , x=5y-y^2	$x = y^{2} - 8 y$ , $x = 5 y - y^{2}$
61233	Find the Area Between the Curves	y = cube root of x , y=1/x	$y = \sqrt[3]{x}$ , $y = \frac{1}{x}$
61234	Find the Area Between the Curves	y=2x^2-5x+10 ; y=x^2+7x-10	$y = 2 x^{2} - 5 x + 10$ ; $y = x^{2} + 7 x - 10$
61235	Find the Domain and Range	x^2-6	$x^{2} - 6$
61236	Find the Concavity	y=4x^2-x-5	$y = 4 x^{2} - x - 5$
61237	Find the Concavity	y=x^4-4x^3	$y = x^{4} - 4 x^{3}$
61238	Find the Derivative Using Product Rule - d/d@VAR	f(u) = square root of u(5-u^6)	$f (u) = \sqrt{u} (5 - u^{6})$
61239	Find the Absolute Max and Min over the Interval	f(x)=19+2x-x^2 , [0,5]	$f (x) = 19 + 2 x - x^{2}$ , $[0, 5]$
61240	Find the Absolute Max and Min over the Interval	f(x)=2x^3-3x^2-72x+5 , [-4,5]	$f (x) = 2 x^{3} - 3 x^{2} - 72 x + 5$ , $[- 4, 5]$
61241	Write in Exponential Form	log base 8 of 512=t	$\log_{8} (512) = t$
61242	Write in Exponential Form	4 = log base 6 of 1296	$4 = \log_{6} (1296)$
61243	Find the Second Derivative	y=x^5-5x	$y = x^{5} - 5 x$
61244	Find the Second Derivative	y=xe^(-2x)	$y = x e^{- 2 x}$
61245	Find the Second Derivative	xy-x+y=3	$x y - x + y = 3$
61246	Find the Second Derivative	r=1/(3s^2)-6/(5s^4)	$r = \frac{1}{3 s^{2}} - \frac{6}{5 s^{4}}$
61247	Find the Second Derivative	square root of x+ square root of y=1	$\sqrt{x} + \sqrt{y} = 1$
61248	Find the Second Derivative	y = square root of 5x^2+4	$y = \sqrt{5 x^{2} + 4}$
61249	Find the Second Derivative	y=(5x^4)/4-7x	$y = \frac{5 x^{4}}{4} - 7 x$
61250	Find the Second Derivative	y=10 root of x	$y = \sqrt[10]{x}$
61251	Find the x and y Intercepts	r=3cos(theta)	$r = 3 \cos (θ)$
61252	Find the x and y Intercepts	25x^2-9y^2=225	$25 x^{2} - 9 y^{2} = 225$
61253	Find the x and y Intercepts	y=81-x^2	$y = 81 - x^{2}$
61254	Find Amplitude, Period, and Phase Shift	y=-6sin(pitheta)	$y = - 6 \sin (π θ)$
61255	Find the Domain and Range	g(x)=3^x+2	$g (x) = 3^{x} + 2$
61256	Find Where Increasing/Decreasing Using Derivatives	y=x^3-2x^2-4x+3	$y = x^{3} - 2 x^{2} - 4 x + 3$
61257	Find Where Increasing/Decreasing Using Derivatives	y=x/(x^2+1)	$y = \frac{x}{x^{2} + 1}$
61258	Write in Standard Form	x^2-4y^2-2x+16y-31=0	$x^{2} - 4 y^{2} - 2 x + 16 y - 31 = 0$
61259	Find the Concavity	x+cos(x)	$x + \cos (x)$
61260	Find the Concavity	x^3-9x^2+24x-10	$x^{3} - 9 x^{2} + 24 x - 10$
61261	Find the Average Rate of Change	y=3/(x-2) , [4,7]	$y = \frac{3}{x - 2}$ , $[4, 7]$
61262	Find the Concavity	5x^3-60x+5	$5 x^{3} - 60 x + 5$
61263	Find the Concavity	-e^(-(x^2)/2)	$- e^{- \frac{x^{2}}{2}}$
61264	Find the Concavity	9 square root of xe^(-x)	$9 \sqrt{x} e^{- x}$
61265	Find the Concavity	natural log of x^2-2x+10	$\ln (x^{2} - 2 x + 10)$
61266	Find the Concavity	4/3x^3-12x^2+10x+1	$\frac{4}{3} x^{3} - 12 x^{2} + 10 x + 1$
61267	Identify the Sequence	1/2 , 2/3 , 3/4 , 4/5 , 5/6	$\frac{1}{2}$ , $\frac{2}{3}$ , $\frac{3}{4}$ , $\frac{4}{5}$ , $\frac{5}{6}$
61268	Identify the Sequence	1/8 , 1/4 , 1/2 , 1	$\frac{1}{8}$ , $\frac{1}{4}$ , $\frac{1}{2}$ , $1$
61269	Identify the Sequence	2/3 , 3/4 , 4/5 , 5/6	$\frac{2}{3}$ , $\frac{3}{4}$ , $\frac{4}{5}$ , $\frac{5}{6}$
61270	Identify the Sequence	-3 , 9 , -27 , 81	$- 3$ , $9$ , $- 27$ , $81$
61271	Identify the Sequence	4 , 12 , 36 , 108 , ...	$4$ , $12$ , $36$ , $108$ , $\dots$
61272	Find the Derivative of the Integral	integral from 0 to x^3 of e^(-4t) with respect to t	$\int_{0}^{x^{3}} e^{- 4 t} d t$
61273	Find the Derivative of the Integral	integral from x^2 to x^6 of (2t-1)^3 with respect to t	$\int_{x^{2}}^{x^{6}} {(2 t - 1)}^{3} d t$
61274	Find the Derivative of the Integral	integral from 3 to x of (tan(5t)sec(5t)-1) with respect to t	$\int_{3}^{x} (\tan (5 t) \sec (5 t) - 1) d t$
61275	Find the Derivative of the Integral	d/(dx) integral from 10 to x^3 of 1/(p^2) with respect to p	$\frac{d}{d x} \int_{10}^{x^{3}} \frac{1}{p^{2}} d p$
61276	Find the Derivative of the Integral	d/(dx) integral from 11 to x^3 of 1/(p^2) with respect to p	$\frac{d}{d x} \int_{11}^{x^{3}} \frac{1}{p^{2}} d p$
61277	Find the Derivative of the Integral	d/(dx) integral from 6 to x^3 of 1/(p^2) with respect to p	$\frac{d}{d x} \int_{6}^{x^{3}} \frac{1}{p^{2}} d p$
61278	Write as a Single Logarithm	log base 8 of square root of 80- log base 8 of square root of 5	$\log_{8} (\sqrt{80}) - \log_{8} (\sqrt{5})$
61279	Find the Derivative of the Integral	G(x) = integral from x to 6 of cos( square root of 9t) with respect to t	$G (x) = \int_{x}^{6} \cos (\sqrt{9 t}) d t$
61280	Find the Derivative of the Integral	h(x) = integral from 3 to x^2 of square root of 1+r^3 with respect to r	$h (x) = \int_{3}^{x^{2}} \sqrt{1 + r^{3}} d r$
61281	Find the Derivative of the Integral	g(x) = integral from 1 to x of 3/(t^3+3) with respect to t	$g (x) = \int_{1}^{x} \frac{3}{t^{3} + 3} d t$
61282	Find the Derivative of the Integral	g(x) = integral from 0 to x of f(t) with respect to t	$g (x) = \int_{0}^{x} f (t) d t$
61283	Find the Derivative of the Integral	g(s) = integral from 5 to s of (t-t^2)^8 with respect to t	$g (s) = \int_{5}^{s} {(t - t^{2})}^{8} d t$
61284	Write as a Single Logarithm	4 natural log of 2+ natural log of x+ natural log of 5	$4 \ln (2) + \ln (x) + \ln (5)$
61285	Write as a Single Logarithm	7 natural log of x+ natural log of y	$7 \ln (x) + \ln (y)$
61286	Find the Concavity	f(x)=x^3-12x+8	$f (x) = x^{3} - 12 x + 8$
61287	Find the Concavity	g(x)=150+8x^3+x^4	$g (x) = 150 + 8 x^{3} + x^{4}$
61288	Find the Concavity	f(x)=x^4-8x^2+1	$f (x) = x^{4} - 8 x^{2} + 1$
61289	Find the Concavity	h(x)=4/3x^3-12x^2+10x+1	$h (x) = \frac{4}{3} x^{3} - 12 x^{2} + 10 x + 1$
61290	Find the Concavity	f(x)=3x^4-30x^3+x-4	$f (x) = 3 x^{4} - 30 x^{3} + x - 4$
61291	Find the Concavity	f(x)=4x^3-48x-4	$f (x) = 4 x^{3} - 48 x - 4$
61292	Find the Concavity	f(x)=4x^6-5x^5	$f (x) = 4 x^{6} - 5 x^{5}$
61293	Find the Concavity	f(x)=5x^(2/3)-2x^(5/3)	$f (x) = 5 x^{\frac{2}{3}} - 2 x^{\frac{5}{3}}$
61294	Find the Concavity	f(x)=x^3	$f (x) = x^{3}$
61295	Find the Concavity	f(x)=x^2+3x-10	$f (x) = x^{2} + 3 x - 10$
61296	Find the Concavity	f(x)=e^(2x)+e^(-x)	$f (x) = e^{2 x} + e^{- x}$
61297	Find the Concavity	f(x) = natural log of x^2-2x+10	$f (x) = \ln (x^{2} - 2 x + 10)$
61298	Find the Concavity	f(x) = natural log of x^2-2x+17	$f (x) = \ln (x^{2} - 2 x + 17)$
61299	Find the Average Value of the Function	f(x)=-sin(x) , [0,pi]	$f (x) = - \sin (x)$ , $[0, π]$
61300	Find the Average Value of the Function	f(X)=x^2+x-9 ; [0,18]	$f (X) = x^{2} + x - 9$ ; $[0, 18]$