Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
44701	Find the Local Maxima and Minima	x^3-4x^2-3x+3	$x^{3} - 4 x^{2} - 3 x + 3$
44702	Find the Local Maxima and Minima	3x^3-3x^2-3x+10	$3 x^{3} - 3 x^{2} - 3 x + 10$
44703	Find the Local Maxima and Minima	x^3-6x^2+7	$x^{3} - 6 x^{2} + 7$
44704	Find the Local Maxima and Minima	x^3-3x^2-9x+1	$x^{3} - 3 x^{2} - 9 x + 1$
44705	Find the Local Maxima and Minima	x^4-2x^2-4	$x^{4} - 2 x^{2} - 4$
44706	Find the Local Maxima and Minima	x^3-12x+1	$x^{3} - 12 x + 1$
44707	Find the Directrix	y^2-4x+2y-7=0	$y^{2} - 4 x + 2 y - 7 = 0$
44708	Find the Concavity	y=3x^4-16x^3+24x^2+48	$y = 3 x^{4} - 16 x^{3} + 24 x^{2} + 48$
44709	Find the Concavity	y=-x^3+9x^2-7	$y = - x^{3} + 9 x^{2} - 7$
44710	Find the Domain and Range	1/2x-1/10	$\frac{1}{2} x - \frac{1}{10}$
44711	Find the Local Maxima and Minima	f(x)=x^3-3x+10	$f (x) = x^{3} - 3 x + 10$
44712	Find the Local Maxima and Minima	f(x)=-5x^2+6x-4	$f (x) = - 5 x^{2} + 6 x - 4$
44713	Find the Local Maxima and Minima	f(x)=-125x^3+15x+5	$f (x) = - 125 x^{3} + 15 x + 5$
44714	Find the Local Maxima and Minima	f(x)=4x square root of 2-x	$f (x) = 4 x \sqrt{2 - x}$
44715	Find the Local Maxima and Minima	F(x)=x^3-12x+23	$F (x) = x^{3} - 12 x + 23$
44716	Find the Inflection Points	x^3-8x^2-12x+8	$x^{3} - 8 x^{2} - 12 x + 8$
44717	Find the Inflection Points	x^4-2x^3-36x+12	$x^{4} - 2 x^{3} - 36 x + 12$
44718	Find the Inflection Points	x^3-4x^2+4x	$x^{3} - 4 x^{2} + 4 x$
44719	Find the Inflection Points	x^3-6x+4	$x^{3} - 6 x + 4$
44720	Find the Inflection Points	(x+9)/(x^2-81)	$\frac{x + 9}{x^{2} - 81}$
44721	Find the Inflection Points	(x^5)/10+(x^4)/8+2	$\frac{x^{5}}{10} + \frac{x^{4}}{8} + 2$
44722	Find the Tangent Line at the Point	y=10xsin(x) , (pi/2,5pi)	$y = 10 x \sin (x)$ , $(\frac{π}{2}, 5 π)$
44723	Find the Tangent Line at the Point	square root of x+ square root of y=5 , (9,4)	$\sqrt{x} + \sqrt{y} = 5$ , $(9, 4)$
44724	Find the Tangent Line at the Point	y=4x-3x^2 , (2,-4)	$y = 4 x - 3 x^{2}$ , $(2, - 4)$
44725	Find the Tangent Line at the Point	y=x^4+4e^x , (0,4)	$y = x^{4} + 4 e^{x}$ , $(0, 4)$
44726	Find the Tangent Line at the Point	y=8xsin(x) , (pi/2,4pi)	$y = 8 x \sin (x)$ , $(\frac{π}{2}, 4 π)$
44727	Find the Tangent Line at the Point	y=x-x^3 , (1,0)	$y = x - x^{3}$ , $(1, 0)$
44728	Find the Tangent Line at the Point	y=x^3-4x , (-2,0)	$y = x^{3} - 4 x$ , $(- 2, 0)$
44729	Find the Tangent Line at the Point	x^2+y^2=(3x^2+2y^2-x)^2 , (0,0.5)	$x^{2} + y^{2} = {(3 x^{2} + 2 y^{2} - x)}^{2}$ , $(0, 0.5)$
44730	Find the Tangent Line at the Point	x^2y^2-9x^2-4y^2=0 , (4,2 square root of 3)	$x^{2} y^{2} - 9 x^{2} - 4 y^{2} = 0$ , $(4, 2 \sqrt{3})$
44731	Find the Tangent Line at the Point	y=(1+3x)^9 , (0,1)	$y = {(1 + 3 x)}^{9}$ , $(0, 1)$
44732	Find the Tangent Line at the Point	y=x^4+6e^x , (0,6)	$y = x^{4} + 6 e^{x}$ , $(0, 6)$
44733	Find the Second Derivative	3x^2+2y^2=12	$3 x^{2} + 2 y^{2} = 12$
44734	Find the Second Derivative	y=(4x^5)/5-2x	$y = \frac{4 x^{5}}{5} - 2 x$
44735	Find the Second Derivative	3xy+2y^2=12	$3 x y + 2 y^{2} = 12$
44736	Find the Second Derivative	y=2cos(x/2)	$y = 2 \cos (\frac{x}{2})$
44737	Find the Second Derivative	y=x^(8/9)+5x	$y = x^{\frac{8}{9}} + 5 x$
44738	Find the Second Derivative	y=(4x+1)/(2x-3)	$y = \frac{4 x + 1}{2 x - 3}$
44739	Find the Second Derivative	y=e^(14x)cos(x)	$y = e^{14 x} \cos (x)$
44740	Find the Second Derivative	y+sin(y)=x	$y + \sin (y) = x$
44741	Find the Third Derivative	y=sin(x)^2	$y = \sin^{2} (x)$
44742	Find the Third Derivative	y=x^-5+x^5	$y = x^{- 5} + x^{5}$
44743	Find the Third Derivative	3xy+2y^2=12	$3 x y + 2 y^{2} = 12$
44744	Find the Third Derivative	y=x/(2x+1)	$y = \frac{x}{2 x + 1}$
44745	Find the Fourth Derivative	y=7x^5	$y = 7 x^{5}$
44746	Find the Fourth Derivative	y=8x^5	$y = 8 x^{5}$
44747	Find the Second Derivative	xy+3e^y=3e	$x y + 3 e^{y} = 3 e$
44748	Find the Inflection Points	f(x)=1/2x^4-4x^3	$f (x) = \frac{1}{2} x^{4} - 4 x^{3}$
44749	Find the Inflection Points	f(x)=x^4-24x^2-20	$f (x) = x^{4} - 24 x^{2} - 20$
44750	Solve over the Interval	y=3x^(2/3)-2x , [-1,1]	$y = 3 x^{\frac{2}{3}} - 2 x$ , $[- 1, 1]$
44751	Evaluate from the Right	limit as x approaches (5pi)/2 from the right of e^(tan(x))	$lim_{x \to \frac{5 π}{2}} e^{\tan (x)}$
44752	Evaluate from the Right	limit as x approaches 0 of ( natural log of x)/x	$lim_{x \to 0} \frac{\ln (x)}{x}$
44753	Find Where Increasing/Decreasing Using Derivatives	f(x)=x^2+54/x-2	$f (x) = x^{2} + \frac{54}{x} - 2$
44754	Find Where Increasing/Decreasing Using Derivatives	f(x)=4x+4cos(x)	$f (x) = 4 x + 4 \cos (x)$
44755	Find Where Increasing/Decreasing Using Derivatives	f(x)=x^4-4x+7	$f (x) = x^{4} - 4 x + 7$
44756	Find Where Increasing/Decreasing Using Derivatives	c(x)=x^(1/7)(x+8)	$c (x) = x^{\frac{1}{7}} (x + 8)$
44757	Find Where Increasing/Decreasing Using Derivatives	f(x)=(x+3)/(x-1)	$f (x) = \frac{x + 3}{x - 1}$
44758	Evaluate from the Left	limit as x approaches pi from the left of cot(x)	$lim_{x \to π} \cot (x)$
44759	Expand Using Sum/Difference Formulas	tan(105 degrees )	$\tan (105 °)$
44760	Split Using Partial Fraction Decomposition	(t^4+t^2-9t-12)/(t^4+3t^2)	$\frac{t^{4} + t^{2} - 9 t - 12}{t^{4} + 3 t^{2}}$
44761	Split Using Partial Fraction Decomposition	y/(y^2-4y-5)	$\frac{y}{y^{2} - 4 y - 5}$
44762	Find the Second Derivative	f(x)=7e^(-x)-5e^(-7x)	$f (x) = 7 e^{- x} - 5 e^{- 7 x}$
44763	Find the Second Derivative	f(x)=8x^-4	$f (x) = 8 x^{- 4}$
44764	Find the Second Derivative	f(x)=thetacos(theta)	$f (x) = θ \cos (θ)$
44765	Find the Second Derivative	f(x)=sin(7x^2)	$f (x) = \sin (7 x^{2})$
44766	Find the Second Derivative	f(x)=sin(x)+cos(x)	$f (x) = \sin (x) + \cos (x)$
44767	Find the Second Derivative	s(t)=15t^2	$s (t) = 15 t^{2}$
44768	Find the Second Derivative	f(x)=x^(8/9)	$f (x) = x^{\frac{8}{9}}$
44769	Find the Roots/Zeros Using the Rational Roots Test	f(x)=7x^3+52x^2+22x+7	$f (x) = 7 x^{3} + 52 x^{2} + 22 x + 7$
44770	Find the Third Derivative	s(t)=15t^2	$s (t) = 15 t^{2}$
44771	Find the Third Derivative	f(x)=8x^-4	$f (x) = 8 x^{- 4}$
44772	Find the Third Derivative	f(x)=cot(x)	$f (x) = \cot (x)$
44773	Find the Fourth Derivative	f(x)=(4x)/(x-4)	$f (x) = \frac{4 x}{x - 4}$
44774	Find the Fourth Derivative	s(t)=15t^2	$s (t) = 15 t^{2}$
44775	Find the Roots (Zeros)	1+2cos(x)=0	$1 + 2 \cos (x) = 0$
44776	Convert to a Decimal	(1+(1/1000000))^1000000	${(1 + (\frac{1}{1000000}))}^{1000000}$
44777	Convert to a Decimal	(1+(1/10000))^10000	${(1 + (\frac{1}{10000}))}^{10000}$
44778	Convert to a Decimal	(1+(1/10000000))^10000000	${(1 + (\frac{1}{10000000}))}^{10000000}$
44779	Convert to a Decimal	(1+(1/100000))^100000	${(1 + (\frac{1}{100000}))}^{100000}$
44780	Find All Complex Solutions	3x^2+x+4=0	$3 x^{2} + x + 4 = 0$
44781	Find All Complex Solutions	2x^2-x+6=0	$2 x^{2} - x + 6 = 0$
44782	Convert to a Decimal	13/15	$\frac{13}{15}$
44783	Convert to a Decimal	15/25	$\frac{15}{25}$
44784	Convert to a Decimal	20/9	$\frac{20}{9}$
44785	Find the Value Using the Unit Circle	tan(165 degrees )	$\tan (165 °)$
44786	Evaluate the Summation	sum from i=3 to 10 of 2i-9	$\sum_{i = 3}^{10} 2 i - 9$
44787	Evaluate the Summation	sum from i=1 to 4 of (7i)/(4n-9)	$\sum_{i = 1}^{4} \frac{7 i}{4 n - 9}$
44788	Evaluate the Summation	sum from n=1 to infinity of e^(-n)	$\sum_{n = 1}^{\infty} e^{- n}$
44789	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of ( natural log of e^(3x)+x)/x	$lim_{x \to \infty} \frac{\ln (e^{3 x} + x)}{x}$
44790	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of (1+1/x)^(x/2)	$lim_{x \to \infty} {(1 + \frac{1}{x})}^{\frac{x}{2}}$
44791	Subtract	infinity+negative infinity	$\infty + - \infty$
44792	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of xe^(-x)	$lim_{x \to \infty} x e^{- x}$
44793	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of xsin((8pi)/x)	$lim_{x \to \infty} x \sin (\frac{8 π}{x})$
44794	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of xsin((7pi)/x)	$lim_{x \to \infty} x \sin (\frac{7 π}{x})$
44795	Evaluate Using L'Hospital's Rule	limit as x approaches pi/2 of cos(sin(x))	$lim_{x \to \frac{π}{2}} \cos (\sin (x))$
44796	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (e^x-e^(-x)-2x)/(x-sin(x))	$lim_{x \to 0} \frac{(e^{x} - e^{- x} - 2 x)}{x - \sin (x)}$
44797	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of (( natural log of x)^2)/(5x)	$lim_{x \to \infty} \frac{\ln^{2} (x)}{5 x}$
44798	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (3x-sin(3x))/(3x-tan(3x))	$lim_{x \to 0} \frac{3 x - \sin (3 x)}{3 x - \tan (3 x)}$
44799	Evaluate Using L'Hospital's Rule	limit as x approaches pi/4 of (cos(2x))/(cos(x)-sin(x))	$lim_{x \to \frac{π}{4}} \frac{\cos (2 x)}{\cos (x) - \sin (x)}$
44800	Evaluate Using L'Hospital's Rule	limit as x approaches pi/2 of (1-sin(x))/(1+cos(2x))	$lim_{x \to \frac{π}{2}} \frac{1 - \sin (x)}{1 + \cos (2 x)}$