Mathway | Recent Popular Problems

Recent Popular Problems

Rank	Topic	Problem	Formatted Problem
47701	Evaluate the Limit	limit as x approaches 4 from the left of (\|5x-20\|)/(x^2-5x+4)	$lim_{x \to 4^{-}} \frac{\| 5 x - 20 \|}{x^{2} - 5 x + 4}$
47702	Solve for y	2+10/y=3/4	$2 + \frac{10}{y} = \frac{3}{4}$
47703	Convert to a Decimal	csc(225)deg	$\csc (225)$ degrees
47704	Evaluate the Integral	integral of (x+4)/(2x+6) with respect to x	$\int \frac{x + 4}{2 x + 6} d x$
47705	Evaluate the Integral	integral of (x-2)/(3x+6) with respect to x	$\int \frac{x - 2}{3 x + 6} d x$
47706	Simplify	(2 square root of x)(2 square root of x)	$(2 \sqrt{x}) (2 \sqrt{x})$
47707	Graph	x<=-1 or x>=2	$x \leq - 1$ or $x \geq 2$
47708	Evaluate	35x-56=g(-5x+8)	$35 x - 56 = g (- 5 x + 8)$
47709	Simplify	-(20w^7)/(-4(w^-5)^3)	$- \frac{20 w^{7}}{- 4 {(w^{- 5})}^{3}}$
47710	Simplify	- square root of -4-3 square root of 9+ square root of -81	$- \sqrt{- 4} - 3 \sqrt{9} + \sqrt{- 81}$
47711	Add	2/3+2 1/6	$\frac{2}{3} + 2 \frac{1}{6}$
47712	Solve for y	-7(y-4)=-2(9+y)	$- 7 (y - 4) = - 2 (9 + y)$
47713	Evaluate	(x+3)^2-1	${(x + 3)}^{2} - 1$
47714	Simplify	cube root of 216-3 cube root of -729+3 square root of -49	$\sqrt[3]{216} - 3 \sqrt[3]{- 729} + 3 \sqrt{- 49}$
47715	Evaluate the Limit	limit as x approaches b of ((x-b)^30-4x+4b)/(x-b)	$lim_{x \to b} \frac{{(x - b)}^{30} - 4 x + 4 b}{x - b}$
47716	Simplify the Radical Expression	5 square root of 20*3 square root of 8	$5 \sqrt{20} \cdot 3 \sqrt{8}$
47717	Evaluate the Integral	integral of (3x-2)/( square root of x) with respect to x	$\int \frac{3 x - 2}{\sqrt{x}} d x$
47718	Evaluate the Integral	integral of (pi+e^(3x)) with respect to x	$\int (π + e^{3 x}) d x$
47719	Simplify	(5x-1)/(x^2-3x+2)+3/(2x-4)	$\frac{5 x - 1}{x^{2} - 3 x + 2} + \frac{3}{2 x - 4}$
47720	Graph	If two lines are parallel and they are defined by the equations, y=4x-5 and y=ax+2 ; what is the value of a ?	If two lines are parallel and they are defined by the equations, $y = 4 x - 5$ and $y = a x + 2$ ; what is the value of $a$ ?
47721	Simplify	( cube root of 32m^6)( cube root of 3125m^7)	$(\sqrt[3]{32 m^{6}}) (\sqrt[3]{3125 m^{7}})$
47722	Solve the Inequality for x	4\|x+5\|+1<=33	$4 \| x + 5 \| + 1 \leq 33$
47723	Solve for x	x+3 = square root of 2x-1+5	$x + 3 = \sqrt{2 x - 1 + 5}$
47724	Simplify	x/4+x/2+(3x)/4	$\frac{x}{4} + \frac{x}{2} + \frac{3 x}{4}$
47725	Find the Derivative - d/dx	(cos(-8x))	$(\cos (- 8 x))$
47726	Find All Complex Solutions	5(y+1)-y=4(y-1)+9	$5 (y + 1) - y = 4 (y - 1) + 9$
47727	Evaluate the Limit	limit as x approaches infinity of 3x^-2e^x	$lim_{x \to \infty} 3 x^{- 2} e^{x}$
47728	Find the Derivative - d/dx	((x+2)^5-32)/x	$\frac{{(x + 2)}^{5} - 32}{x}$
47729	Solve for t	t=2pi square root of l/9.8	$t = 2 π \sqrt{\frac{l}{9.8}}$
47730	Simplify	square root of x^5y^5*3 square root of 5x^13y^8	$\sqrt{x^{5} y^{5}} \cdot 3 \sqrt{5 x^{13} y^{8}}$
47731	Simplify	(y^2)/(8c^2d^2)-(3x)/(14c^4d)	$\frac{y^{2}}{8 c^{2} d^{2}} - \frac{3 x}{14 c^{4} d}$
47732	Solve the Inequality for x	-1/4>=8x-(6x+9)+6	$- \frac{1}{4} \geq 8 x - (6 x + 9) + 6$
47733	Find dy/dx	4-xy=y-4x^4	$4 - x y = y - 4 x^{4}$
47734	Evaluate the Integral	integral from 0 to a^(1/5) of x^9 square root of a^2-x^10 with respect to x	$\int_{0}^{a^{\frac{1}{5}}} x^{9} \sqrt{a^{2} - x^{10}} d x$
47735	Evaluate Using L'Hospital's Rule	limit as x approaches -3 of (e^(x+3)-x)/(3sin(x+3)+3x)	$lim_{x \to - 3} \frac{e^{x + 3} - x}{3 \sin (x + 3) + 3 x}$
47736	Evaluate Using the Given Value	8-5xy^3 for x=3 and y=-2	$8 - 5 x y^{3}$ for $x = 3$ and $y = - 2$
47737	Simplify	x^2+3x-7-4x^2+5x-2	$x^{2} + 3 x - 7 - 4 x^{2} + 5 x - 2$
47738	Simplify	3/( sixth root of 2x^4)	$\frac{3}{\sqrt[6]{2 x^{4}}}$
47739	Solve the System of Inequalities	x>-3 and x<2	$x > - 3$ and $x < 2$
47740	Evaluate	4-(6+(-5+(12-8)))	$4 - (6 + (- 5 + (12 - 8)))$
47741	Evaluate	3(1/21013)+(1/2108.7)	$3 (\frac{1}{2} \cdot 10 \cdot 13) + (\frac{1}{2} \cdot 10 \cdot 8.7)$
47742	Find the Reference Angle	tan(315 degrees )	$\tan (315 °)$
47743	Simplify	-6/(3 square root of 5)	$- \frac{6}{3 \sqrt{5}}$
47744	Solve for v	v^3-8=0	$v^{3} - 8 = 0$
47745	Simplify	(x+y)(x-y)(x+y)	$(x + y) (x - y) (x + y)$
47746	Convert from Degrees to Radians	35deg	$35$ degrees
47747	Find the Inverse	y=- square root of x+3	$y = - \sqrt{x + 3}$
47748	Evaluate Using the Remainder Theorem	f(x)=2x^4+6x^3-2x^2-x-14 , c=-3	$f (x) = 2 x^{4} + 6 x^{3} - 2 x^{2} - x - 14$ , $c = - 3$
47749	Solve the Inequality for z	-3(z-3)<=21	$- 3 (z - 3) \leq 21$
47750	Simplify	i(3-2i)+(1+4i)	$i (3 - 2 i) + (1 + 4 i)$
47751	Evaluate	\|3x-2\|+4=21	$\| 3 x - 2 \| + 4 = 21$
47752	Solve the System of Inequalities	3x-7<=5x+5 and -4x+8<5x-1	$3 x - 7 \leq 5 x + 5$ and $- 4 x + 8 < 5 x - 1$
47753	Simplify	12(2+2/3x)	$12 (2 + \frac{2}{3} x)$
47754	Simplify	((3m^2t^5)/(2m^3t^-1))^2	${(\frac{3 m^{2} t^{5}}{2 m^{3} t^{- 1}})}^{2}$
47755	Find the Derivative - d/dx	d/(dx) natural log of 2x	$\frac{d}{d x} \ln (2 x)$
47756	Find the Maximum/Minimum Value	y=-x^4+9x^2-20	$y = - x^{4} + 9 x^{2} - 20$
47757	Determine the Possible Number of Real Roots	3x^4-6x^3+2x+4=0	$3 x^{4} - 6 x^{3} + 2 x + 4 = 0$
47758	Write the Fraction in Simplest Form	(-3(q^-2a^5)^3)/(15q^8a^5)	$\frac{- 3 {(q^{- 2} a^{5})}^{3}}{15 q^{8} a^{5}}$
47759	Graph	y>=0 y<x x+y<6	$y \geq 0$ $y < x$ $x + y < 6$
47760	Find dy/dx	-xy+2x=1	$- x y + 2 x = 1$
47761	Simplify	3 square root of 5- square root of x+4 square root of 5+3 square root of x	$3 \sqrt{5} - \sqrt{x} + 4 \sqrt{5} + 3 \sqrt{x}$
47762	Find the Exact Value	cos((11pi)/12)cos(pi/6)+sin((11pi)/12)sin(pi/6)	$\cos (\frac{11 π}{12}) \cos (\frac{π}{6}) + \sin (\frac{11 π}{12}) \sin (\frac{π}{6})$
47763	Find the Slope	(3,4) and (5,8)	$(3, 4)$ and $(5, 8)$
47764	Solve for u	(cos(u)sec(u))/(tan(u))=(f(u))/(g(u))	$\frac{\cos (u) \sec (u)}{\tan (u)} = \frac{f (u)}{g (u)}$
47765	Solve for a	3(4-a)=2(a+6)	$3 (4 - a) = 2 (a + 6)$
47766	Simplify the Radical Expression	9^-2	$9^{- 2}$
47767	Find Where Increasing/Decreasing	f(x)=-2 log base 3 of x+8	$f (x) = - 2 \log_{3} (x + 8)$
47768	Simplify	(x^5+x^3+3x-2)+(x^4+9x^2-8)	$(x^{5} + x^{3} + 3 x - 2) + (x^{4} + 9 x^{2} - 8)$
47769	Simplify	(3a^4+2a^2-5a-10)-(4a^4+a^3+2a^2-5)	$(3 a^{4} + 2 a^{2} - 5 a - 10) - (4 a^{4} + a^{3} + 2 a^{2} - 5)$
47770	Simplify	square root of 99-2 square root of 27+4 square root of 3-6 square root of 176	$\sqrt{99} - 2 \sqrt{27} + 4 \sqrt{3} - 6 \sqrt{176}$
47771	Simplify	(x^-2y^-1)^-3	${(x^{- 2} y^{- 1})}^{- 3}$
47772	Simplify	(-(-8)+- square root of (-8)^2-42-1)/(2(2))	$\frac{- (- 8) + - \sqrt{{(- 8)}^{2} - 4 \cdot 2 \cdot - 1}}{2 (2)}$
47773	Solve for k	y=2pi-3picot((4pi)/k)(x-2)	$y = 2 π - 3 π \cot (\frac{4 π}{k}) (x - 2)$
47774	Find the End Behavior	p(x)=1/2x^2+3x-4x^3+6x^4-1	$p (x) = \frac{1}{2} x^{2} + 3 x - 4 x^{3} + 6 x^{4} - 1$
47775	Solve for x	x/(x^2-9)=3/(x^2-9)-4/(x+3)	$\frac{x}{x^{2} - 9} = \frac{3}{x^{2} - 9} - \frac{4}{x + 3}$
47776	Evaluate the Integral	integral of (-2x^3+4+2x^-3) with respect to x	$\int (- 2 x^{3} + 4 + 2 x^{- 3}) d x$
47777	Add	-7x^2-6x+9+-3x^2-x+7	$- 7 x^{2} - 6 x + 9 + - 3 x^{2} - x + 7$
47778	Factor	10x^5-4x^2y+15x^3y-6y^2	$10 x^{5} - 4 x^{2} y + 15 x^{3} y - 6 y^{2}$
47779	Simplify the Radical Expression	- square root of 25+ square root of -7- square root of 100- square root of -63	$- \sqrt{25} + \sqrt{- 7} - \sqrt{100} - \sqrt{- 63}$
47780	Simplify	ab-a^2+4^2-5ab+3a^2+10	$a b - a^{2} + 4^{2} - 5 a b + 3 a^{2} + 10$
47781	Solve in Terms of the Arbitrary Variable Sₙ	S_n=1512 , n=6 , r=2	$S_{n} = 1512$ , $n = 6$ , $r = 2$
47782	Solve for y	ax-3y=b	$a x - 3 y = b$
47783	Find the x and y Intercepts	f(x)=(2x^3+x^2-8x-4)/(x^2-3x+2)	$f (x) = \frac{2 x^{3} + x^{2} - 8 x - 4}{x^{2} - 3 x + 2}$
47784	Solve for m	4m-5+3m+3=180	$4 m - 5 + 3 m + 3 = 180$
47785	Add	7/(9x)+1/(3x)	$\frac{7}{9 x} + \frac{1}{3 x}$
47786	Solve Over the Interval	2sin(x)^2tan(x)=tan(x) , [0,2pi)	$2 \sin^{2} (x) \tan (x) = \tan (x)$ , $[0, 2 π)$
47787	Find the Reference Angle	csc(-pi/6)	$\csc (- \frac{π}{6})$
47788	Solve for y	(y-1)/4+1/3=7/12	$\frac{y - 1}{4} + \frac{1}{3} = \frac{7}{12}$
47789	Simplify	cot(x)cos(x)sin(x)+sin(x)^2	$\cot (x) \cos (x) \sin (x) + \sin^{2} (x)$
47790	Simplify	(3^25^5)/(35^2)	$\frac{3^{2} \cdot 5^{5}}{3 \cdot 5^{2}}$
47791	Verify the Identity	(cos(x)^2)/(1+sin(x))=1-1/(csc(x))	$\frac{\cos^{2} (x)}{1 + \sin (x)} = 1 - \frac{1}{\csc (x)}$
47792	Evaluate	(3a^3b^3)(4ab^2)^2	$(3 a^{3} b^{3}) {(4 a b^{2})}^{2}$
47793	Solve for B in Degrees	5tan(B)+ square root of 13=0	$5 \tan (B) + \sqrt{13} = 0$
47794	Solve for a	2(-7a+6)=-16-7a	$2 (- 7 a + 6) = - 16 - 7 a$
47795	Simplify	(2x^0y^3)/((x^0y^3)^4)	$\frac{2 x^{0} y^{3}}{{(x^{0} y^{3})}^{4}}$
47796	Find the Domain	(3x+5)/(2x-1)+(7x+3)/(1-2x)	$\frac{3 x + 5}{2 x - 1} + \frac{7 x + 3}{1 - 2 x}$
47797	Graph	Graph y=-5	Graph $y = - 5$
47798	Solve the Inequality for x	2+x<9x+6	$2 + x < 9 x + 6$
47799	Simplify	(8xy^2+6x^2y+17y^2)-(3x^2y-6y+3y^2)	$(8 x y^{2} + 6 x^{2} y + 17 y^{2}) - (3 x^{2} y - 6 y + 3 y^{2})$
47800	Solve for x	x^4+4x^3+3x^2+4x+4=0	$x^{4} + 4 x^{3} + 3 x^{2} + 4 x + 4 = 0$