Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
66701	Find the Concavity	f(x)=x^2 natural log of x	$f (x) = x^{2} \ln (x)$
66702	Find the Concavity	f(x)=-x^3+6x^2-16	$f (x) = - x^{3} + 6 x^{2} - 16$
66703	Identify the Sequence	1 , 3 , 5	$1$ , $3$ , $5$
66704	Identify the Sequence	20 , 40 , 80 , 160	$20$ , $40$ , $80$ , $160$
66705	Identify the Sequence	-26 , -31 , -36 , -41	$- 26$ , $- 31$ , $- 36$ , $- 41$
66706	Find the Derivative of the Integral	integral from 0 to 1 of (3x^3-x^2+2x-4) with respect to x	$\int_{0}^{1} (3 x^{3} - x^{2} + 2 x - 4) d x$
66707	Identify the Sequence	5 , 15 , 45 , 135 , ...	$5$ , $15$ , $45$ , $135$ , $\dots$
66708	Find the Roots (Zeros)	square root of x^2+1	$\sqrt{x^{2} + 1}$
66709	Find the Roots (Zeros)	-3x^2+24x+144	$- 3 x^{2} + 24 x + 144$
66710	Find the Roots (Zeros)	3x^2+2x-5	$3 x^{2} + 2 x - 5$
66711	Find the Roots (Zeros)	3x^2-30x+72	$3 x^{2} - 30 x + 72$
66712	Find the Roots (Zeros)	-3x^3+21x^2-42x+24	$- 3 x^{3} + 21 x^{2} - 42 x + 24$
66713	Find the Roots (Zeros)	2x-128/(x^2)	$2 x - \frac{128}{x^{2}}$
66714	Find the Roots (Zeros)	4+5/(x^2+2)	$4 + \frac{5}{x^{2} + 2}$
66715	Find the Roots (Zeros)	6x^2+84x+288	$6 x^{2} + 84 x + 288$
66716	Find the Roots (Zeros)	x^2-9x+8	$x^{2} - 9 x + 8$
66717	Find the Roots (Zeros)	x^2+4x-1	$x^{2} + 4 x - 1$
66718	Find the Roots (Zeros)	x^3-x^2-x+1	$x^{3} - x^{2} - x + 1$
66719	Find the Roots (Zeros)	x^5+x-1	$x^{5} + x - 1$
66720	Find the Roots (Zeros)	x^3+x^2-26x+24	$x^{3} + x^{2} - 26 x + 24$
66721	Find Amplitude, Period, and Phase Shift	r=4+2sin(theta)	$r = 4 + 2 \sin (θ)$
66722	Find the x and y Intercepts	y=-10	$y = - 10$
66723	Find the x and y Intercepts	y=x/(x^2-9)	$y = \frac{x}{x^{2} - 9}$
66724	Find the x and y Intercepts	y^2=x^3-4x	$y^{2} = x^{3} - 4 x$
66725	Find the x and y Intercepts	-11x+2y=1	$- 11 x + 2 y = 1$
66726	Find the Next Term	-1 , -7 , -13 , -19 , -25 , -31 , -37 , -43 , -49	$- 1$ , $- 7$ , $- 13$ , $- 19$ , $- 25$ , $- 31$ , $- 37$ , $- 43$ , $- 49$
66727	Find the Vertical and Horizontal Intercept(s)	f(x)=x/( square root of 2x-1)	$f (x) = \frac{x}{\sqrt{2 x - 1}}$
66728	Find the Vertical and Horizontal Intercept(s)	F(x)=(x^2)/(x-3)	$F (x) = \frac{x^{2}}{x - 3}$
66729	Find the Derivative Using Chain Rule - d/d@VAR	g(x)=(3x-1)^7(2x+1)^5	$g (x) = {(3 x - 1)}^{7} {(2 x + 1)}^{5}$
66730	Find the Derivative Using Chain Rule - d/dx	xy^2	$x y^{2}$
66731	Find the Derivative Using Chain Rule - d/dx	integral from 0 to 1 of (3x^3-x^2+2x-4)/( square root of x^2-3x+2) with respect to x	$\int_{0}^{1} \frac{3 x^{3} - x^{2} + 2 x - 4}{\sqrt{x^{2}} - 3 x + 2} d x$
66732	Convert to Rectangular	z=4(cos(150 degrees )+isin(150 degrees ))	$z = 4 (\cos (150 °) + i \sin (150 °))$
66733	Convert to Rectangular	r^2=cos(theta)	$r^{2} = \cos (θ)$
66734	Find Where Increasing/Decreasing Using Derivatives	4x^3-12x	$4 x^{3} - 12 x$
66735	Find Where Increasing/Decreasing Using Derivatives	x^3-3x+2	$x^{3} - 3 x + 2$
66736	Find Where Increasing/Decreasing Using Derivatives	x^3+6x^2+9x+3	$x^{3} + 6 x^{2} + 9 x + 3$
66737	Find Where Increasing/Decreasing Using Derivatives	-x^3+6x^2-18	$- x^{3} + 6 x^{2} - 18$
66738	Find Where Increasing/Decreasing Using Derivatives	x^4-12x^3+48x^2-64x	$x^{4} - 12 x^{3} + 48 x^{2} - 64 x$
66739	Find Where Increasing/Decreasing Using Derivatives	x^4-4x^3+5	$x^{4} - 4 x^{3} + 5$
66740	Find Where Increasing/Decreasing Using Derivatives	x+10/x	$x + \frac{10}{x}$
66741	Find Where Increasing/Decreasing Using Derivatives	x+6/x	$x + \frac{6}{x}$
66742	Find Where Increasing/Decreasing Using Derivatives	x^3-6x^2-63x	$x^{3} - 6 x^{2} - 63 x$
66743	Find Where Increasing/Decreasing Using Derivatives	2x^3-24x	$2 x^{3} - 24 x$
66744	Find Where Increasing/Decreasing Using Derivatives	(x+6)/(x-6)	$\frac{x + 6}{x - 6}$
66745	Find Where Increasing/Decreasing Using Derivatives	(x-3)/(x+4)	$\frac{x - 3}{x + 4}$
66746	Find Where Increasing/Decreasing Using Derivatives	(x-9)(x^2-18x-162)	$(x - 9) (x^{2} - 18 x - 162)$
66747	Find Where Increasing/Decreasing Using Derivatives	(1-x)e^x	$(1 - x) e^{x}$
66748	Find Where Increasing/Decreasing Using Derivatives	(2-2x)e^x	$(2 - 2 x) e^{x}$
66749	Find Where Increasing/Decreasing Using Derivatives	-(2x)/((x^2+1)^2)	$- \frac{2 x}{{(x^{2} + 1)}^{2}}$
66750	Find Where Increasing/Decreasing Using Derivatives	6/(x^2-16)	$\frac{6}{x^{2} - 16}$
66751	Find the Absolute Max and Min over the Interval	f(x)=5+x-x^2 ; [0,4]	$f (x) = 5 + x - x^{2}$ ; $[0, 4]$
66752	Evaluate Using the Squeeze Theorem	limit as x approaches 0 of (1+x)^(1/x)	$lim_{x \to 0} {(1 + x)}^{\frac{1}{x}}$
66753	Find the Absolute Max and Min over the Interval	f(x)=x^4-18x^2+9 ; [-6,6]	$f (x) = x^{4} - 18 x^{2} + 9$ ; $[- 6, 6]$
66754	Convert to Polar Coordinates	(6,6 square root of 3)	$(6, 6 \sqrt{3})$
66755	Convert to Polar Coordinates	(5,6)	$(5, 6)$
66756	Convert to Polar Coordinates	(-3,60 degrees )	$(- 3, 60 °)$
66757	Convert to Polar Coordinates	(3,8)	$(3, 8)$
66758	Convert to Polar Coordinates	(4,(7pi)/6)	$(4, \frac{7 π}{6})$
66759	Convert to Polar Coordinates	(1,(5pi)/3)	$(1, \frac{5 π}{3})$
66760	Find the Inverse	log of x-3	$\log (x - 3)$
66761	Find the Inverse	integral from 0 to 1 of (3x^3-x^2+2x-4)/( square root of x^2-3x+2) with respect to x	$\int_{0}^{1} \frac{3 x^{3} - x^{2} + 2 x - 4}{\sqrt{x^{2} - 3 x + 2}} d x$
66762	Find the Second Derivative	f(x)=(x^2+1)^9	$f (x) = {(x^{2} + 1)}^{9}$
66763	Find the Second Derivative	f(x)=(x^2)/(3+8x)	$f (x) = \frac{x^{2}}{3 + 8 x}$
66764	Find the Second Derivative	f(x)=(x^2)/(5+2x)	$f (x) = \frac{x^{2}}{5 + 2 x}$
66765	Find the Second Derivative	f(x)=(x+1)/(x-1)	$f (x) = \frac{x + 1}{x - 1}$
66766	Find the Second Derivative	f(x)=(x-3)/x	$f (x) = \frac{x - 3}{x}$
66767	Find the Second Derivative	f(x) = square root of x+ fifth root of x	$f (x) = \sqrt{x} + \sqrt[5]{x}$
66768	Find the Second Derivative	f(x)=(x^2+9)^6	$f (x) = {(x^{2} + 9)}^{6}$
66769	Find the Second Derivative	f(x)=(x^2+7)^7	$f (x) = {(x^{2} + 7)}^{7}$
66770	Find the Second Derivative	f(x)=(e^x)/x	$f (x) = \frac{e^{x}}{x}$
66771	Find the Second Derivative	f(x)=(2x)/(1+x^2)	$f (x) = \frac{2 x}{1 + x^{2}}$
66772	Find the Second Derivative	f(x)=(3x^2+5x-4)/x	$f (x) = \frac{3 x^{2} + 5 x - 4}{x}$
66773	Solve by Substitution	y=x-5y=x^2-2x-9	$y = x - 5 y = x^{2} - 2 x - 9$
66774	Find the Fourth Derivative	f(x)=2x^2-x^3	$f (x) = 2 x^{2} - x^{3}$
66775	Find the Fourth Derivative	f(x)=x^2	$f (x) = x^{2}$
66776	Split Using Partial Fraction Decomposition	6/(x(x^2+6)^2)	$\frac{6}{x {(x^{2} + 6)}^{2}}$
66777	Split Using Partial Fraction Decomposition	16/(x^2-4)	$\frac{16}{x^{2} - 4}$
66778	Find the Third Derivative	f(x)=14e^x	$f (x) = 14 e^{x}$
66779	Find the Third Derivative	f(x)=2x^2-x^3	$f (x) = 2 x^{2} - x^{3}$
66780	Find the Third Derivative	f(x)=1/(x^7)	$f (x) = \frac{1}{x^{7}}$
66781	Find the Third Derivative	f(x)=2/(x^2)	$f (x) = \frac{2}{x^{2}}$
66782	Find the Third Derivative	f(x)=x^2e^(2x)	$f (x) = x^{2} e^{2 x}$
66783	Find the Second Derivative	f(x)=x^(4/5)	$f (x) = x^{\frac{4}{5}}$
66784	Find the Second Derivative	f(x)=x^3+5x^2-10x+15	$f (x) = x^{3} + 5 x^{2} - 10 x + 15$
66785	Find the Second Derivative	f(x)=2x^2	$f (x) = 2 x^{2}$
66786	Find the Tangent Line at (1,1)	square root of x , (1,1)	$\sqrt{x}$ , $(1, 1)$
66787	Find the Tangent Line at (1,6)	y=7x-x^2 , (1,6)	$y = 7 x - x^{2}$ , $(1, 6)$
66788	Find the Tangent Line at (3,0)	y = natural log of x^2-8 , (3,0)	$y = \ln (x^{2} - 8)$ , $(3, 0)$
66789	Solve Using the Quadratic Formula	x^2-8x=10	$x^{2} - 8 x = 10$
66790	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of 8x^2e^(-x)	$lim_{x \to \infty} 8 x^{2} e^{- x}$
66791	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of square root of x^2+8x+1-x	$lim_{x \to \infty} \sqrt{x^{2} + 8 x + 1} - x$
66792	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (e^x-1)/(sin(6x))	$lim_{x \to 0} \frac{e^{x} - 1}{\sin (6 x)}$
66793	Evaluate Using L'Hospital's Rule	limit as x approaches 1 of (4^x-4)/(x^2-1)	$lim_{x \to 1} \frac{4^{x} - 4}{x^{2} - 1}$
66794	Evaluate Using L'Hospital's Rule	limit as x approaches 1 of ( natural log of x)/(20x-x^2-19)	$lim_{x \to 1} \frac{\ln (x)}{20 x - x^{2} - 19}$
66795	Find the Area Between the Curves	y = square root of 2xy=x-4	$y = \sqrt{2 x} y = x - 4$
66796	Find the Area Between the Curves	x=4-y^2 , x=y-2	$x = 4 - y^{2}$ , $x = y - 2$
66797	Find the Area Between the Curves	y = square root of 1-x^2 , y=0	$y = \sqrt{1 - x^{2}}$ , $y = 0$
66798	Find the Domain and Range	y = square root of 25-x^2	$y = \sqrt{25 - x^{2}}$
66799	Find the Area Between the Curves	y=\|x-16\| , y=x/3	$y = \| x - 16 \|$ , $y = \frac{x}{3}$
66800	Find the Area Between the Curves	y=2x^2 , y=x^3	$y = 2 x^{2}$ , $y = x^{3}$