Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
4501	Simplify	x(x^2+1)^(-1/2)	$x {(x^{2} + 1)}^{- \frac{1}{2}}$
4502	Simplify	tan(x)csc(x)	$\tan (x) \csc (x)$
4503	Simplify	tan(x)sec(x)	$\tan (x) \sec (x)$
4504	Simplify	tan(pi/4)-tan(0)	$\tan (\frac{π}{4}) - \tan (0)$
4505	Solve for x	\|3x-4\|>-2	$\| 3 x - 4 \| > - 2$
4506	Solve for x	1/(x^4+4)+1/(x^4-4x^3+4x^2-4)-2/(x^4-4x^2-8x-4)=0	$\frac{1}{x^{4} + 4} + \frac{1}{x^{4} - 4 x^{3} + 4 x^{2} - 4} - \frac{2}{x^{4} - 4 x^{2} - 8 x - 4} = 0$
4507	Simplify	1+1/(x^2)	$1 + \frac{1}{x^{2}}$
4508	Simplify	(z+3)/(z^2+3z+2)-(z-1)/(z^2+z-2)	$\frac{z + 3}{z^{2} + 3 z + 2} - \frac{z - 1}{z^{2} + z - 2}$
4509	Simplify	(sin(x))/(2x)	$\frac{\sin (x)}{2 x}$
4510	Simplify	b^8(2b)^3	$b^{8} {(2 b)}^{3}$
4511	Simplify	b^8(2b)^6	$b^{8} {(2 b)}^{6}$
4512	Simplify	3x^(-1/2)	$3 x^{- \frac{1}{2}}$
4513	Simplify	3-6sin(pi/3)	$3 - 6 \sin (\frac{π}{3})$
4514	Solve for x	x-x-12=0	$x - x - 12 = 0$
4515	Evaluate the Limit	limit as x approaches 3 of (x-3)/(\|x-3\|)	$lim_{x \to 3} \frac{x - 3}{\| x - 3 \|}$
4516	Evaluate the Limit	limit as x approaches 7 of (x^2-5x-14)/(x-7)	$lim_{x \to 7} \frac{x^{2} - 5 x - 14}{x - 7}$
4517	Simplify	(1/2x^(-1/2))^2	${(\frac{1}{2} x^{- \frac{1}{2}})}^{2}$
4518	Simplify	(x^2-3)^2	${(x^{2} - 3)}^{2}$
4519	Simplify	(x+8)(36/x+8)	$(x + 8) (\frac{36}{x} + 8)$
4520	Simplify	(e^(2x))/(e^x)	$\frac{e^{2 x}}{e^{x}}$
4521	Simplify	(sec(x)^2)/(tan(x))	$\frac{\sec^{2} (x)}{\tan (x)}$
4522	Simplify	(x^(1/2))/(1/2)	$\frac{x^{\frac{1}{2}}}{\frac{1}{2}}$
4523	Simplify	(x+h)^(1/2)	${(x + h)}^{\frac{1}{2}}$
4524	Simplify	(3+h)^2	${(3 + h)}^{2}$
4525	Simplify	e^(-x^2)	$e^{- x^{2}}$
4526	Simplify	e^(e^x)	$e^{e^{x}}$
4527	Simplify	e^(2x)*e^(2x)	$e^{2 x} \cdot e^{2 x}$
4528	Find the Horizontal Tangent Line	y=x^2+7	$y = x^{2} + 7$
4529	Simplify	1/x-1/a	$\frac{1}{x} - \frac{1}{a}$
4530	Simplify	1/t-1/(t^2+t)	$\frac{1}{t} - \frac{1}{t^{2} + t}$
4531	Simplify	1/e	$\frac{1}{e}$
4532	Simplify	1/3x^(-2/3)	$\frac{1}{3} x^{- \frac{2}{3}}$
4533	Simplify	(2x)/(x^2-6x+9)-1/(x+1)-8/(x^2-2x-3)	$\frac{2 x}{x^{2} - 6 x + 9} - \frac{1}{x + 1} - \frac{8}{x^{2} - 2 x - 3}$
4534	Solve for x	V=(x)(22-2x)(22-2x)	$V = (x) (22 - 2 x) (22 - 2 x)$
4535	Solve for x	y=(e^x-e^(-x))/2	$y = \frac{e^{x} - e^{- x}}{2}$
4536	Solve for x	6x-14=0	$6 x - 14 = 0$
4537	Solve for x	6x-18=0	$6 x - 18 = 0$
4538	Solve for x	6x-8=0	$6 x - 8 = 0$
4539	Solve for x	9x^2-36=0	$9 x^{2} - 36 = 0$
4540	Solve for X	6X-6=0	$6 X - 6 = 0$
4541	Solve for x	natural log of x+ natural log of x+2=0	$\ln (x) + \ln (x + 2) = 0$
4542	Solve for x	2-200/(x^2)=0	$2 - \frac{200}{x^{2}} = 0$
4543	Solve for x	-2sin(2x)=0	$- 2 \sin (2 x) = 0$
4544	Solve for x	2cos(2x)=0	$2 \cos (2 x) = 0$
4545	Solve for x	12x^2-252x+902=0	$12 x^{2} - 252 x + 902 = 0$
4546	Solve for x	12x+6=0	$12 x + 6 = 0$
4547	Solve for x	log of x+3+ log of x+4 = log of 20	$\log (x + 3) + \log (x + 4) = \log (20)$
4548	Solve for x	1-x^2=0	$1 - x^{2} = 0$
4549	Solve for x	4x^3-4x=0	$4 x^{3} - 4 x = 0$
4550	Solve for X	4X^3-12X^2=0	$4 X^{3} - 12 X^{2} = 0$
4551	Solve for x	4x+2y=0	$4 x + 2 y = 0$
4552	Solve for x	2x-8/x=0	$2 x - \frac{8}{x} = 0$
4553	Solve for x	2x-250/(x^2)=0	$2 x - \frac{250}{x^{2}} = 0$
4554	Solve for x	3x^2-2x-6=0	$3 x^{2} - 2 x - 6 = 0$
4555	Solve for x	3x^2-6x+3=0	$3 x^{2} - 6 x + 3 = 0$
4556	Solve for y	24^2+y^2=625	$24^{2} + y^{2} = 625$
4557	Solve for y	0=(y(12-y))/((y^2-2y+12)^2)	$0 = \frac{y (12 - y)}{{(y^{2} - 2 y + 12)}^{2}}$
4558	Solve for x	3^(3x-4)=3^5	$3^{3 x - 4} = 3^{5}$
4559	Evaluate the Limit	limit as x approaches infinity of (x^2+2x-3)/(2x^2-2)	$lim_{x \to \infty} \frac{x^{2} + 2 x - 3}{2 x^{2} - 2}$
4560	Solve for x	natural log of 1-x+ natural log of 2-x = natural log of x+14	$\ln (1 - x) + \ln (2 - x) = \ln (x + 14)$
4561	Solve for x	log base 3 of x^2=2 log base 3 of 4-4 log base 3 of 5	$\log_{3} (x^{2}) = 2 \log_{3} (4) - 4 \log_{3} (5)$
4562	Solve for x	(dy)/(dx)=5x-4	$\frac{d y}{d x} = 5 x - 4$
4563	Solve for x	(4x)/(x^2+x+3)+(5x)/(x^2-5x+3)=-3/2	$\frac{4 x}{x^{2} + x + 3} + \frac{5 x}{x^{2} - 5 x + 3} = - \frac{3}{2}$
4564	Solve for x	3^(2x)-12*3^x+27=0	$3^{2 x} - 12 \cdot 3^{x} + 27 = 0$
4565	Solve for x	3^(x-x^2)=1/(9^x)	$3^{x - x^{2}} = \frac{1}{9^{x}}$
4566	Solve for x	4^(x-x^2)=1/(64^x)	$4^{x - x^{2}} = \frac{1}{64^{x}}$
4567	Solve for x	2/3x^(-1/3)=0	$\frac{2}{3} x^{- \frac{1}{3}} = 0$
4568	Solve for x	1/x=0	$\frac{1}{x} = 0$
4569	Solve for x	(x^2+1)^2=0	${(x^{2} + 1)}^{2} = 0$
4570	Solve for p	2p^2=-4p+1	$2 p^{2} = - 4 p + 1$
4571	Solve for t	e^(3t)=900	$e^{3 t} = 900$
4572	Solve for t	e^(3t)=1000	$e^{3 t} = 1000$
4573	Solve for t	3t^2-12t+9=0	$3 t^{2} - 12 t + 9 = 0$
4574	Solve for t	6000=3000e^((0.04)(t))	$6000 = 3000 e^{(0.04) (t)}$
4575	Solve for t	P=ae^(kt)	$P = a e^{k t}$
4576	Solve for a	6ax^5=18x^5	$6 a x^{5} = 18 x^{5}$
4577	Solve for b	log base b of 216=3	$\log_{b} (216) = 3$
4578	Solve for D	J=p*(D^4-(D-2w)^4)/32	$J = p \cdot \frac{D^{4} - {(D - 2 w)}^{4}}{32}$
4579	Find the Area Between the Curves	x=3t , y=3-t , t=5	$x = 3 t$ , $y = 3 - t$ , $t = 5$
4580	Find the Area Between the Curves	x=-5 , x=2 , y=x , y=x^2-2	$x = - 5$ , $x = 2$ , $y = x$ , $y = x^{2} - 2$
4581	Find the Area Between the Curves	x=-1 , x=2 , y=3e^(3x) , y=2e^(3x)+1	$x = - 1$ , $x = 2$ , $y = 3 e^{3 x}$ , $y = 2 e^{3 x} + 1$
4582	Evaluate	natural log of 2x	$\ln (2 x)$
4583	Evaluate	natural log of square root of e^6	$\ln (\sqrt{e^{6}})$
4584	Evaluate	natural log of 5/8	$\ln (\frac{5}{8})$
4585	Evaluate	4 natural log of 2	$4 \ln (2)$
4586	Evaluate	natural log of 1/3	$\ln (\frac{1}{3})$
4587	Evaluate	11 natural log of 12	$11 \ln (12)$
4588	Graph	natural log of 4x^2	$\ln (4 x^{2})$
4589	Graph	natural log of natural log of x^2	$\ln (\ln (x^{2}))$
4590	Graph	natural log of x^8	$\ln (x^{8})$
4591	Graph	natural log of (e^x)/(e^x-1)	$\ln (\frac{e^{x}}{e^{x} - 1})$
4592	Evaluate	e^(7 natural log of x)	$e^{7 \ln (x)}$
4593	Graph	x natural log of x-x	$x \ln (x) - x$
4594	Evaluate	e^(2 natural log of x)	$e^{2 \ln (x)}$
4595	Evaluate the Limit	( limit as h approaches 0 of (2+h)^2-4)/h	$\frac{lim_{h \to 0} {(2 + h)}^{2} - 4}{h}$
4596	Find the Tangent Line at the Point	y=x^3-5x , (2,-2)	$y = x^{3} - 5 x$ , $(2, - 2)$
4597	Find the Tangent Line at the Point	y=2x^3-4x , (1,-2)	$y = 2 x^{3} - 4 x$ , $(1, - 2)$
4598	Find the Tangent Line at the Point	y=5x^3-2x , (1,3)	$y = 5 x^{3} - 2 x$ , $(1, 3)$
4599	Find the Tangent Line at the Point	y=3x^3-2x , (1,1)	$y = 3 x^{3} - 2 x$ , $(1, 1)$
4600	Find the Tangent Line at the Point	y=3x^3-5x , (1,-2)	$y = 3 x^{3} - 5 x$ , $(1, - 2)$