Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
63201	Find the Critical Points	f(x)=5-8x^3-x^4	$f (x) = 5 - 8 x^{3} - x^{4}$
63202	Find the Critical Points	f(x)=5arctan(x)-3x^3	$f (x) = 5 \arctan (x) - 3 x^{3}$
63203	Find the Critical Points	F(x)=5x^2-3x+4	$F (x) = 5 x^{2} - 3 x + 4$
63204	Find the Critical Points	f(x)=4x^3-15x^2-18x+8	$f (x) = 4 x^{3} - 15 x^{2} - 18 x + 8$
63205	Find the Critical Points	f(x)=3x^5-5x^3	$f (x) = 3 x^{5} - 5 x^{3}$
63206	Find the Critical Points	f(x)=3x+27/x	$f (x) = 3 x + \frac{27}{x}$
63207	Find the Critical Points	f(x)=2x^4-4x^2+1	$f (x) = 2 x^{4} - 4 x^{2} + 1$
63208	Find the Critical Points	f(x)=2x^3-6x^2-144x-7	$f (x) = 2 x^{3} - 6 x^{2} - 144 x - 7$
63209	Find the Critical Points	f(x)=3x^4-24x^3+48x^2	$f (x) = 3 x^{4} - 24 x^{3} + 48 x^{2}$
63210	Find the Critical Points	f(x)=3x^3+9x^2-27x	$f (x) = 3 x^{3} + 9 x^{2} - 27 x$
63211	Find the Critical Points	f(x)=x^(1/3)(x+3)^(2/3)	$f (x) = x^{\frac{1}{3}} {(x + 3)}^{\frac{2}{3}}$
63212	Find the Critical Points	f(x)=sin(x)	$f (x) = \sin (x)$
63213	Find the Critical Points	f(x)=e^(3x)	$f (x) = e^{3 x}$
63214	Find the Critical Points	f(x)=e^x-x^3	$f (x) = e^{x} - x^{3}$
63215	Find the Critical Points	f(x)=8x^3-69x^2-36x+6	$f (x) = 8 x^{3} - 69 x^{2} - 36 x + 6$
63216	Find the Critical Points	f(x)=8x^3-90x^2-96x+1	$f (x) = 8 x^{3} - 90 x^{2} - 96 x + 1$
63217	Find the Critical Points	f(x)=e^(-2.5x^2)	$f (x) = e^{- 2.5 x^{2}}$
63218	Find the Critical Points	f(x)=8x^3-123x^2+60x-3	$f (x) = 8 x^{3} - 123 x^{2} + 60 x - 3$
63219	Find the Critical Points	f(x)=7x^3+21x^2-504x+21	$f (x) = 7 x^{3} + 21 x^{2} - 504 x + 21$
63220	Find the Critical Points	f(x)=x^3-3x+6	$f (x) = x^{3} - 3 x + 6$
63221	Find the Critical Points	f(x)=-x^3-4.5x^2+12x+4	$f (x) = - x^{3} - 4.5 x^{2} + 12 x + 4$
63222	Find the Critical Points	f(x)=x^3-6x^2+2	$f (x) = x^{3} - 6 x^{2} + 2$
63223	Find the Critical Points	f(x)=x^3-12x^2+36x	$f (x) = x^{3} - 12 x^{2} + 36 x$
63224	Find the Critical Points	f(x)=-x^3-15x^2	$f (x) = - x^{3} - 15 x^{2}$
63225	Find the Critical Points	f(x)=x^2-5	$f (x) = x^{2} - 5$
63226	Find the Critical Points	f(x)=x^2-x- natural log of x	$f (x) = x^{2} - x - \ln (x)$
63227	Find the Critical Points	f(x)=x^2-8x+8	$f (x) = x^{2} - 8 x + 8$
63228	Find the Critical Points	f(x)=x^2+5x-7	$f (x) = x^{2} + 5 x - 7$
63229	Find the Critical Points	f(x)=x^(4/5)(x-5)^2	$f (x) = x^{\frac{4}{5}} {(x - 5)}^{2}$
63230	Find the Critical Points	f(x)=x^4-4x^2-1	$f (x) = x^{4} - 4 x^{2} - 1$
63231	Find the Critical Points	f(x)=x^5-5x^4+1	$f (x) = x^{5} - 5 x^{4} + 1$
63232	Find the Critical Points	f(x)=x+cos(x) , 0<=x<=2pi	$f (x) = x + \cos (x)$ , $0 \leq x \leq 2 π$
63233	Find the Critical Points	f(x)=xe^(5x)	$f (x) = x e^{5 x}$
63234	Evaluate Using L'Hospital's Rule	limit as theta approaches pi/2 of tan(theta^(cos(theta)))	$lim_{θ \to \frac{π}{2}} \tan (θ^{\cos (θ)})$
63235	Evaluate Using L'Hospital's Rule	limit as theta approaches pi of (1+cos(theta))/(1-cos(theta))	$lim_{θ \to π} \frac{1 + \cos (θ)}{1 - \cos (θ)}$
63236	Evaluate Using L'Hospital's Rule	limit as n approaches infinity of 1/(n^2)((n(n+1))/2)	$lim_{n \to \infty} \frac{1}{n^{2}} (\frac{n (n + 1)}{2})$
63237	Evaluate Using L'Hospital's Rule	limit as t approaches 0 of (1+t-e^(-t))/( natural log of t+1)	$lim_{t \to 0} \frac{1 + t - e^{- t}}{\ln (t + 1)}$
63238	Write as a Function of n	sum from i=1 to n of (8i+3)/(n^2)	$\sum_{i = 1}^{n} \frac{8 i + 3}{n^{2}}$
63239	Write as a Function of y	(dy)/(dx)=1/3x(y-2)^2	$\frac{d y}{d x} = \frac{1}{3} x {(y - 2)}^{2}$
63240	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of xsin(1/x)	$lim_{x \to 0} x \sin (\frac{1}{x})$
63241	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (tan(3x))/(sin(2x))	$lim_{x \to 0} \frac{\tan (3 x)}{\sin (2 x)}$
63242	Evaluate Using L'Hospital's Rule	limit as x approaches 1 of (x^(7a)-7ax+7a-1)/((x-1)^2)	$lim_{x \to 1} \frac{x^{7 a} - 7 a x + 7 a - 1}{{(x - 1)}^{2}}$
63243	Evaluate Using L'Hospital's Rule	limit as x approaches 2 of (x^3-7x^2+10x)/(x^2+x-6)	$lim_{x \to 2} \frac{x^{3} - 7 x^{2} + 10 x}{x^{2} + x - 6}$
63244	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (sin(x))/x	$lim_{x \to 0} \frac{\sin (x)}{x}$
63245	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (e^x-x-1)/(cos(x)-1)	$lim_{x \to 0} \frac{e^{x} - x - 1}{\cos (x) - 1}$
63246	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (1-cos(15x))/(225x^2)	$lim_{x \to 0} \frac{1 - \cos (15 x)}{225 x^{2}}$
63247	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (1-cos(5x))/(25x^2)	$lim_{x \to 0} \frac{1 - \cos (5 x)}{25 x^{2}}$
63248	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (25e^(x/5)-25-5x-1/2x^2)/(x^3)	$lim_{x \to 0} \frac{25 e^{\frac{x}{5}} - 25 - 5 x - \frac{1}{2} x^{2}}{x^{3}}$
63249	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (tan(x))/x	$lim_{x \to 0} \frac{\tan (x)}{x}$
63250	Evaluate Using L'Hospital's Rule	limit as v approaches 8 of (v-2- square root of v^2-28)/(v-8)	$lim_{v \to 8} \frac{v - 2 - \sqrt{v^{2} - 28}}{v - 8}$
63251	Evaluate Using L'Hospital's Rule	limit as t approaches -3 of (t^3-4t+15)/(t^2-t-12)	$lim_{t \to - 3} \frac{t^{3} - 4 t + 15}{t^{2} - t - 12}$
63252	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of ((3x-2)/(3x+4))^(3x+1)	$lim_{x \to \infty} {(\frac{3 x - 2}{3 x + 4})}^{3 x + 1}$
63253	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of ( natural log of x)/( square root of x)	$lim_{x \to \infty} \frac{(\ln (x))}{\sqrt{x}}$
63254	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of (6x-1/(4x))/(3x+1/x)	$lim_{x \to \infty} \frac{6 x - \frac{1}{4 x}}{3 x + \frac{1}{x}}$
63255	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of (e^x)/2	$lim_{x \to \infty} \frac{e^{x}}{2}$
63256	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of (e^x)/(5x+200)	$lim_{x \to \infty} \frac{e^{x}}{5 x + 200}$
63257	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of ( square root of x^2-9)/(2x-6)	$lim_{x \to \infty} \frac{\sqrt{x^{2} - 9}}{2 x - 6}$
63258	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of ((sin(x))/x)^(1/(x^2))	$lim_{x \to 0} {(\frac{\sin (x)}{x})}^{\frac{1}{x^{2}}}$
63259	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of xtan(4/x)	$lim_{x \to \infty} x \tan (\frac{4}{x})$
63260	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of natural log of 4x- natural log of x+1	$lim_{x \to \infty} \ln (4 x) - \ln (x + 1)$
63261	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of x/( natural log of x)	$lim_{x \to \infty} \frac{x}{\ln (x)}$
63262	Evaluate Using L'Hospital's Rule	limit as x approaches negative infinity of (x^102)/(e^x)	$lim_{x \to - \infty} \frac{x^{102}}{e^{x}}$
63263	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of (x^6)/( natural log of x)	$lim_{x \to \infty} \frac{x^{6}}{\ln (x)}$
63264	Subtract	(x+6)/(4x+8)-(x-2)/(5x+10)	$\frac{x + 6}{4 x + 8} - \frac{x - 2}{5 x + 10}$
63265	Subtract	(11b-2)/(6b)-(7b)/(6b)	$\frac{11 b - 2}{6 b} - \frac{7 b}{6 b}$
63266	Evaluate Using L'Hospital's Rule	limit as x approaches -8 of (x^2+17x+72)/(-72-1x+x^2)	$lim_{x \to - 8} \frac{x^{2} + 17 x + 72}{- 72 - 1 x + x^{2}}$
63267	Evaluate Using L'Hospital's Rule	limit as x approaches -8 of (x^2+12x+32)/(-72-1x+x^2)	$lim_{x \to - 8} \frac{x^{2} + 12 x + 32}{- 72 - 1 x + x^{2}}$
63268	Evaluate Using L'Hospital's Rule	limit as y approaches 0 of ( square root of 5y+25-5)/y	$lim_{y \to 0} \frac{\sqrt{5 y + 25} - 5}{y}$
63269	Find the Focus	x^2=40y	$x^{2} = 40 y$
63270	Find the Focus	y^2=1/4x	$y^{2} = \frac{1}{4} x$
63271	Find the Focus	y^2=-10x	$y^{2} = - 10 x$
63272	Find the Focus	y^2-3y-x+3=0	$y^{2} - 3 y - x + 3 = 0$
63273	Find the Focus	y=1/20x^2	$y = \frac{1}{20} x^{2}$
63274	Expand the Trigonometric Expression	sin(2arccos(x))	$\sin (2 \arccos (x))$
63275	Find the Roots (Zeros)	3x^2+2x-8	$3 x^{2} + 2 x - 8$
63276	Find the Roots (Zeros)	3x^2-60x+225	$3 x^{2} - 60 x + 225$
63277	Find the Roots (Zeros)	6x(x^2-1)^2	$6 x {(x^{2} - 1)}^{2}$
63278	Find the Roots (Zeros)	4x^3-12x-8	$4 x^{3} - 12 x - 8$
63279	Find the Roots (Zeros)	12x^2-108x+170	$12 x^{2} - 108 x + 170$
63280	Find the Roots (Zeros)	12x^2-264x+989	$12 x^{2} - 264 x + 989$
63281	Find the Roots (Zeros)	2x^2-8	$2 x^{2} - 8$
63282	Find the Roots (Zeros)	3x^2+6x-9	$3 x^{2} + 6 x - 9$
63283	Find the Roots (Zeros)	3x^2+8x-3	$3 x^{2} + 8 x - 3$
63284	Find the Roots (Zeros)	3t^2-30t+72	$3 t^{2} - 30 t + 72$
63285	Find the Intersection of the Functions	f(x)=x^4-8x^3+21x^2 , g(x)=-14x+136	$f (x) = x^{4} - 8 x^{3} + 21 x^{2}$ , $g (x) = - 14 x + 136$
63286	Find the Antiderivative	2^x	$2^{x}$
63287	Find the Roots (Zeros)	x^4-8x^2+8	$x^{4} - 8 x^{2} + 8$
63288	Find the Roots (Zeros)	x^3-3x^2-33x+35	$x^{3} - 3 x^{2} - 33 x + 35$
63289	Find the Roots (Zeros)	x^3-3x^2+4	$x^{3} - 3 x^{2} + 4$
63290	Find the Roots (Zeros)	x^3-3x+1	$x^{3} - 3 x + 1$
63291	Find the Roots (Zeros)	x^3+3	$x^{3} + 3$
63292	Find the Roots (Zeros)	x^2-3x+5	$x^{2} - 3 x + 5$
63293	Find the Roots (Zeros)	x^2-12x+32	$x^{2} - 12 x + 32$
63294	Find the Derivative - d/dA	A=pir^2	$A = π r^{2}$
63295	Find the Derivative - d/da	ae^(-ax)	$a e^{- a x}$
63296	Find the Derivative - d/da	sin(a+b)	$\sin (a + b)$
63297	Find the Derivative - d/da	2600+530 natural log of a	$2600 + 530 \ln (a)$
63298	Find the Derivative - d/dn	4^n	$4^{n}$
63299	Find the Derivative - d/dn	nx^(n-1)	$n x^{n - 1}$
63300	Find the Derivative - d/dq	(10+sec(q))/(10-sec(q))	$\frac{10 + \sec (q)}{10 - \sec (q)}$