Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
47501	Split Using Partial Fraction Decomposition	(x^4-2x^3+x^2+3x-1)/(x^2-2x+1)	$\frac{x^{4} - 2 x^{3} + x^{2} + 3 x - 1}{x^{2} - 2 x + 1}$
47502	Split Using Partial Fraction Decomposition	(x+4)/(x^2+4x-12)	$\frac{x + 4}{x^{2} + 4 x - 12}$
47503	Split Using Partial Fraction Decomposition	(x^2)/(x^2+x+30)	$\frac{x^{2}}{x^{2} + x + 30}$
47504	Split Using Partial Fraction Decomposition	(-2x^2+19x-13)/(x^3-7x^2+11x-5)	$\frac{- 2 x^{2} + 19 x - 13}{x^{3} - 7 x^{2} + 11 x - 5}$
47505	Split Using Partial Fraction Decomposition	(x^4-2x^3+x^2+6x-5)/(x^2-2x+1)	$\frac{x^{4} - 2 x^{3} + x^{2} + 6 x - 5}{x^{2} - 2 x + 1}$
47506	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of 4x- square root of 16x^2-x	$lim_{x \to \infty} 4 x - \sqrt{16 x^{2} - x}$
47507	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (tan(6x))/(sin(7x))	$lim_{x \to 0} \frac{\tan (6 x)}{\sin (7 x)}$
47508	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (9x^2)/(cos(x)-1)	$lim_{x \to 0} \frac{9 x^{2}}{\cos (x) - 1}$
47509	Evaluate Using L'Hospital's Rule	limit as x approaches negative infinity of (9x^2+10x-1)/(8x^2-5x)	$lim_{x \to - \infty} \frac{9 x^{2} + 10 x - 1}{8 x^{2} - 5 x}$
47510	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (8x^2)/(cos(x)-1)	$lim_{x \to 0} \frac{8 x^{2}}{\cos (x) - 1}$
47511	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of (e^(2x)-e^(3x))/(e^(3x)-e^(2x))	$lim_{x \to \infty} \frac{e^{2 x} - e^{3 x}}{e^{3 x} - e^{2 x}}$
47512	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of x/(arctan(5x))	$lim_{x \to 0} \frac{x}{\arctan (5 x)}$
47513	Evaluate Using L'Hospital's Rule	limit as x approaches 9 of (x^2-x-72)/(x-9)	$lim_{x \to 9} \frac{x^{2} - x - 72}{x - 9}$
47514	Evaluate Using L'Hospital's Rule	limit as y approaches 0 of ( square root of 3y+16-4)/y	$lim_{y \to 0} \frac{\sqrt{3 y + 16} - 4}{y}$
47515	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of square root of 81x^2+x-9x	$lim_{x \to \infty} \sqrt{81 x^{2} + x} - 9 x$
47516	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (6x^2)/(cos(x)-1)	$lim_{x \to 0} \frac{6 x^{2}}{\cos (x) - 1}$
47517	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (sin(3x))/(sin(5x))	$lim_{x \to 0} \frac{\sin (3 x)}{\sin (5 x)}$
47518	Evaluate Using L'Hospital's Rule	limit as x approaches 1 of (x^3-1)/(4x^3-x-3)	$lim_{x \to 1} \frac{x^{3} - 1}{4 x^{3} - x - 3}$
47519	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of sin(9x)csc(7x)	$lim_{x \to 0} \sin (9 x) \csc (7 x)$
47520	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (sin(4x))/(sin(5x))	$lim_{x \to 0} \frac{\sin (4 x)}{\sin (5 x)}$
47521	Evaluate Using L'Hospital's Rule	limit as t approaches infinity of ( square root of t+t^2)/(9t-t^2)	$lim_{t \to \infty} \frac{\sqrt{t} + t^{2}}{9 t - t^{2}}$
47522	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (sin(5x))/(tan(9x))	$lim_{x \to 0} \frac{\sin (5 x)}{\tan (9 x)}$
47523	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of square root of 25x^2+x-5x	$lim_{x \to \infty} \sqrt{25 x^{2} + x} - 5 x$
47524	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of (e^x)/( natural log of x)	$lim_{x \to \infty} \frac{e^{x}}{\ln (x)}$
47525	Evaluate Using L'Hospital's Rule	limit as x approaches negative infinity of x/(e^x)	$lim_{x \to - \infty} \frac{x}{e^{x}}$
47526	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (e^(2x)-1)/(tan(x))	$lim_{x \to 0} \frac{e^{2 x} - 1}{\tan (x)}$
47527	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of xe^(-2x)	$lim_{x \to \infty} x e^{- 2 x}$
47528	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of xtan(5/x)	$lim_{x \to \infty} x \tan (\frac{5}{x})$
47529	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of (1+1/x)^( natural log of x)	$lim_{x \to \infty} {(1 + \frac{1}{x})}^{\ln (x)}$
47530	Evaluate Using L'Hospital's Rule	limit as x approaches 3 of (x^5-243)/(x-3)	$lim_{x \to 3} \frac{x^{5} - 243}{x - 3}$
47531	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (x^2)/(sin(x)^2)	$lim_{x \to 0} \frac{x^{2}}{\sin^{2} (x)}$
47532	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of ( natural log of x)/(e^x)	$lim_{x \to \infty} \frac{\ln (x)}{e^{x}}$
47533	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (e^(2x)-e^(-2x)-4x)/(x-sin(x))	$lim_{x \to 0} \frac{(e^{2 x} - e^{- 2 x} - 4 x)}{x - \sin (x)}$
47534	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (e^x+8x)^(1/x)	$lim_{x \to 0} {(e^{x} + 8 x)}^{\frac{1}{x}}$
47535	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of (x^9)/(e^(x^8))	$lim_{x \to \infty} \frac{x^{9}}{e^{x^{8}}}$
47536	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (1-cos(x))/((1-e^x)^2)	$lim_{x \to 0} \frac{(1 - \cos (x))}{{(1 - e^{x})}^{2}}$
47537	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of x/(arctan(9x))	$lim_{x \to 0} \frac{x}{\arctan (9 x)}$
47538	Subtract	(4d-6d^3+3d^2)-(10d^3+7d-2)	$(4 d - 6 d^{3} + 3 d^{2}) - (10 d^{3} + 7 d - 2)$
47539	Subtract	x-2x	$x - 2 x$
47540	Subtract	(2k)/(3k-7)-3/(8k)	$\frac{2 k}{3 k - 7} - \frac{3}{8 k}$
47541	Write as a Function of x	x+1000p=2500	$x + 1000 p = 2500$
47542	Write as a Function of t	(dv)/(dt)=9-v^2	$\frac{d v}{d t} = 9 - v^{2}$
47543	Write as a Function of v	(dv)/(dt)=9-v^2	$\frac{d v}{d t} = 9 - v^{2}$
47544	Write as a Function of p	x+1000p=2500	$x + 1000 p = 2500$
47545	Write as a Function of c1	y=x+c_1e^x+c_2e^(-2x)	$y = x + c_{1} e^{x} + c_{2} e^{- 2 x}$
47546	Write as a Function of w	c=14(w+2l)+5w	$c = 14 (w + 2 l) + 5 w$
47547	Find the Asymptotes	f(x)=(16x)/(20x-9)	$f (x) = \frac{16 x}{20 x - 9}$
47548	Find the Asymptotes	f(x)=-5/(x-6)	$f (x) = \frac{- 5}{x - 6}$
47549	Find the Asymptotes	f(x)=(x^2-3)/(x+6)	$f (x) = \frac{x^{2} - 3}{x + 6}$
47550	Find the Asymptotes	f(x)=(6x)/(15x-8)	$f (x) = \frac{6 x}{15 x - 8}$
47551	Find the Asymptotes	f(x)=(5x^2-26x+5)/(x^2-x-20)	$f (x) = \frac{5 x^{2} - 26 x + 5}{x^{2} - x - 20}$
47552	Find the Asymptotes	f(x)=(8x)/(12x-7)	$f (x) = \frac{8 x}{12 x - 7}$
47553	Find the Asymptotes	f(x)=3-4/x	$f (x) = 3 - \frac{4}{x}$
47554	Find the Asymptotes	g(t)=(t-3)/(t^2+9)	$g (t) = \frac{t - 3}{t^{2} + 9}$
47555	Find the Asymptotes	f(x)=( square root of 8x^2+9)/(10x+8)	$f (x) = \frac{\sqrt{8 x^{2} + 9}}{10 x + 8}$
47556	Find the Asymptotes	f(x)=(16x)/(20x-7)	$f (x) = \frac{16 x}{20 x - 7}$
47557	Find the Asymptotes	f(x)=(2x^2)/(x^2-2x-8)	$f (x) = \frac{2 x^{2}}{x^{2} - 2 x - 8}$
47558	Find the Asymptotes	f(x)=(2x-1)/(8x+4)	$f (x) = \frac{2 x - 1}{8 x + 4}$
47559	Find the Asymptotes	f(x)=(3 square root of x)/(x-12 square root of x+36)	$f (x) = \frac{3 \sqrt{x}}{x - 12 \sqrt{x} + 36}$
47560	Find the Asymptotes	f(x)=(3x^2+2x-5)/(x^2+8x-20)	$f (x) = \frac{3 x^{2} + 2 x - 5}{x^{2} + 8 x - 20}$
47561	Find the Asymptotes	f(x)=(4x)/(6x-5)	$f (x) = \frac{4 x}{6 x - 5}$
47562	Find the Asymptotes	f(x)=(6sin(x))/(sin(x)+1)	$f (x) = \frac{6 \sin (x)}{\sin (x) + 1}$
47563	Find the Asymptotes	f(x)=(6x-5)/(x-4)	$f (x) = \frac{6 x - 5}{x - 4}$
47564	Find the Asymptotes	f(x)=(7x)/(x+4)	$f (x) = \frac{7 x}{x + 4}$
47565	Find the Asymptotes	f(x)=(8sin(x))/(sin(x)+1)	$f (x) = \frac{8 \sin (x)}{\sin (x) + 1}$
47566	Find the Asymptotes	f(x)=(8x)/(10x-9)	$f (x) = \frac{8 x}{10 x - 9}$
47567	Find the Asymptotes	f(x)=(8x-9)/x	$f (x) = \frac{8 x - 9}{x}$
47568	Find the Asymptotes	f(x)=(cos(x)+8 square root of x)/( square root of x)	$f (x) = \frac{\cos (x) + 8 \sqrt{x}}{\sqrt{x}}$
47569	Find the Asymptotes	f(x)=( natural log of x)/x	$f (x) = \frac{\ln (x)}{x}$
47570	Find the Asymptotes	f(x)=(x^2-49)/(x^2-4x-21)	$f (x) = \frac{x^{2} - 49}{x^{2} - 4 x - 21}$
47571	Find the Asymptotes	f(x)=(x^2-6x-27)/(x^2-12x+27)	$f (x) = \frac{x^{2} - 6 x - 27}{x^{2} - 12 x + 27}$
47572	Find the Asymptotes	f(x)=(x^2-8x+15)/(x^2-9)	$f (x) = \frac{x^{2} - 8 x + 15}{x^{2} - 9}$
47573	Find the Asymptotes	f(x)=(x+2)/(x^2+7x+10)	$f (x) = \frac{x + 2}{x^{2} + 7 x + 10}$
47574	Find the Asymptotes	f(x)=(x+2)/(x^2+9x+14)	$f (x) = \frac{x + 2}{x^{2} + 9 x + 14}$
47575	Find the Asymptotes	f(x)=(x+6)/(x^2+14x+48)	$f (x) = \frac{x + 6}{x^{2} + 14 x + 48}$
47576	Find the Asymptotes	f(x)=7sec(1/4pix-1/2pi)	$f (x) = 7 \sec (\frac{1}{4} π x - \frac{1}{2} π)$
47577	Find the Maximum/Minimum Value	2x^3+3x^2-12x+5	$2 x^{3} + 3 x^{2} - 12 x + 5$
47578	Find the Maximum/Minimum Value	4x-48x^(1/3)	$4 x - 48 x^{\frac{1}{3}}$
47579	Find the Maximum/Minimum Value	x^2-6x-5	$x^{2} - 6 x - 5$
47580	Find the Maximum/Minimum Value	x^2-22x+6	$x^{2} - 22 x + 6$
47581	Find the Maximum/Minimum Value	x^3+3x^2-9x-3	$x^{3} + 3 x^{2} - 9 x - 3$
47582	Find the Maximum/Minimum Value	x/(25+x^2)	$\frac{x}{25 + x^{2}}$
47583	Find the Maximum/Minimum Value	x^2-18x+72	$x^{2} - 18 x + 72$
47584	Find the Maximum/Minimum Value	x^2-26x+2	$x^{2} - 26 x + 2$
47585	Find the Maximum/Minimum Value	x^2-2x+9	$x^{2} - 2 x + 9$
47586	Find the Maximum/Minimum Value	-x^3+5x^2+8x+2	$- x^{3} + 5 x^{2} + 8 x + 2$
47587	Find the Area Under the Curve	y=49-x^2 ; [-7,7]	$y = 49 - x^{2}$ ; $[- 7, 7]$
47588	Find the Area Under the Curve	y=x^2-6x+9 ; 2<=x<=4	$y = x^{2} - 6 x + 9$ ; $2 \leq x \leq 4$
47589	Find the Area Under the Curve	y=3x ; [1,3]	$y = 3 x$ ; $[1, 3]$
47590	Find Trig Functions Using Identities	cos(3theta)=1	$\cos (3 θ) = 1$
47591	Find Trig Functions Using Identities	cot(theta)=12/5 , sin(theta)<0	$\cot (θ) = \frac{12}{5}$ , $\sin (θ) < 0$
47592	Determine if Rational	- square root of 25	$- \sqrt{25}$
47593	Determine if Rational	6pi	$6 π$
47594	Find the Normal Line at @POINT	y=( square root of x)/(x+6) , (4,0.2)	$y = \frac{\sqrt{x}}{x + 6}$ , $(4, 0.2)$
47595	Find the Normal Line at @POINT	x^2+y^2=25 , (4,3)	$x^{2} + y^{2} = 25$ , $(4, 3)$
47596	Find the Normal Line at @POINT	x^2+y^2=25 , (-4,3)	$x^{2} + y^{2} = 25$ , $(- 4, 3)$
47597	Find the Horizontal Tangent Line	y=-0.025x^2+3x	$y = - 0.025 x^{2} + 3 x$
47598	Find the Horizontal Tangent Line	y=3+cot(x)-2csc(x)	$y = 3 + \cot (x) - 2 \csc (x)$
47599	Find the Horizontal Tangent Line	y=((3x-1)/(x^2+3))^2	$y = {(\frac{3 x - 1}{x^{2} + 3})}^{2}$
47600	Find the Horizontal Tangent Line	3x^2-xy+y^2=33	$3 x^{2} - x y + y^{2} = 33$