Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
101	Find the Asymptotes	f(x)=1/x	$f (x) = \frac{1}{x}$ $f (x) = \frac{1}{x}$
102	Use the Rational Roots Test to Find All Possible Roots	cos(2x)	$cos (2 x)$ $\cos (2 x)$
103	Use the Rational Roots Test to Find All Possible Roots	sin(2x)	$sin (2 x)$ $\sin (2 x)$
104	Find the Domain	1/x	$\frac{1}{x}$ $\frac{1}{x}$
105	Find the Value Using the Unit Circle	sin(15)	$sin (15)$ $\sin (15)$
106	Find the Domain	x^2+4	$x^{2} + 4$ $x^{2} + 4$
107	Find the Inverse	f(x)=(4^x)/(1+4^x)	$f (x) = \frac{4^{x}}{1 + 4^{x}}$ $f (x) = \frac{4^{x}}{1 + 4^{x}}$
108	Find the Domain and Range	f(x)=x^2+2x-3	$f (x) = x^{2} + 2 x - 3$ $f (x) = x^{2} + 2 x - 3$
109	Find the Vertex	x^2-2x-3	$x^{2} - 2 x - 3$ $x^{2} - 2 x - 3$
110	Use the Rational Roots Test to Find All Possible Roots	sin(x)	$sin (x)$ $\sin (x)$
111	Find the Asymptotes	f(x)=(x^2+2)/(x^2-1)	$f (x) = \frac{x^{2} + 2}{x^{2} - 1}$ $f (x) = \frac{x^{2} + 2}{x^{2} - 1}$
112	Solve for x	cos(2x)=( square root of 3)/2	$cos (2 x) = \frac{\sqrt{3}}{2}$ $\cos (2 x) = \frac{\sqrt{3}}{2}$
113	Solve for x	x^4-5x^2-4=0	$x^{4} - 5 x^{2} - 4 = 0$ $x^{4} - 5 x^{2} - 4 = 0$
114	Solve for x	log of 5x = log of 2x+9	$log (5 x) = log (2 x + 9)$ $\log (5 x) = \log (2 x + 9)$
115	Solve for x	10/(1+e^(-x))=2	$\frac{10}{1 + e^{- x}} = 2$ $\frac{10}{1 + e^{- x}} = 2$
116	Solve for ?	cos(3x)=-1	$cos (3 x) = - 1$ $\cos (3 x) = - 1$
117	Solve for x	x^5-2x^2=0	$x^{5} - 2 x^{2} = 0$ $x^{5} - 2 x^{2} = 0$
118	Solve for x	log base 4 of x=4	${log}_{4} (x) = 4$ $\log_{4} (x) = 4$
119	Solve for x	3x^2+6x-5=0	$3 x^{2} + 6 x - 5 = 0$ $3 x^{2} + 6 x - 5 = 0$
120	Solve for x	square root of 2x+1+1=x	$\sqrt{2 x + 1} + 1 = x$ $\sqrt{2 x + 1} + 1 = x$
121	Solve for x	-4\|x+2\|=x-8	$- 4 \| x + 2 \| = x - 8$ $- 4 \| x + 2 \| = x - 8$
122	Simplify	sec(x)^3-sec(x)^2-sec(x)+1	${sec}^{3} (x) - {sec}^{2} (x) - sec (x) + 1$ $\sec^{3} (x) - \sec^{2} (x) - \sec (x) + 1$
123	Simplify	1/(cot(x)^2)+sec(x)cos(x)	$\frac{1}{{cot}^{2} (x)} + sec (x) cos (x)$ $\frac{1}{\cot^{2} (x)} + \sec (x) \cos (x)$
124	Simplify	(2/(xy))^-3	${(\frac{2}{x y})}^{- 3}$ ${(\frac{2}{x y})}^{- 3}$
125	Solve for x	x/3+x/7<2	$\frac{x}{3} + \frac{x}{7} < 2$ $\frac{x}{3} + \frac{x}{7} < 2$
126	Find the Domain	f(x)=1/x+5/(x-3)	$f (x) = \frac{1}{x} + \frac{5}{x - 3}$ $f (x) = \frac{1}{x} + \frac{5}{x - 3}$
127	Find the Domain	f(x) = fourth root of x^2+3x	$f (x) = \sqrt[4]{x^{2} + 3 x}$ $f (x) = \sqrt[4]{x^{2} + 3 x}$
128	Find the Domain	1/(x+1)	$\frac{1}{x + 1}$ $\frac{1}{x + 1}$
129	Find the Domain	1/(x-2)	$\frac{1}{x - 2}$ $\frac{1}{x - 2}$
130	Simplify	arcsin((- square root of 2)/2)	$arcsin (\frac{- \sqrt{2}}{2})$ $\arcsin (\frac{- \sqrt{2}}{2})$
131	Simplify	sec(arcsin(-( square root of 3)/2))	$\sec (\arcsin (- \frac{\sqrt{3}}{2}))$
132	Simplify	square root of square root of 81x^4	$\sqrt{\sqrt{81 x^{4}}}$
133	Find the Exact Value	sin(285)	$\sin (285)$
134	Find the Exact Value	cos(60-45)	$\cos (60 - 45)$
135	Find Amplitude, Period, and Phase Shift	y=tan(2x)	$y = \tan (2 x)$
136	Convert from Degrees to Radians	-30	$- 30$
137	Find Amplitude, Period, and Phase Shift	d=2sin(pi/3t)	$d = 2 \sin (\frac{π}{3} t)$
138	Evaluate	log base 4 of 1/4	$\log_{4} (\frac{1}{4})$
139	Evaluate	log base 3 of 1/( square root of 3)	$\log_{3} (\frac{1}{\sqrt{3}})$
140	Find the Properties	x^2=8y	$x^{2} = 8 y$
141	Find the Properties	x^2+y^2=9	$x^{2} + y^{2} = 9$
142	Find the Properties	x^2+y^2=4	$x^{2} + y^{2} = 4$
143	Find the Center and Radius	x^2+y^2=36	$x^{2} + y^{2} = 36$
144	Graph	y=-tan(x)	$y = - \tan (x)$
145	Graph	y=tan(x-pi/4)	$y = \tan (x - \frac{π}{4})$
146	Graph	f(x)=2 log base 3 of x-1-3	$f (x) = 2 \log_{3} (x - 1) - 3$
147	Graph	f(x)=tan(x)	$f (x) = \tan (x)$
148	Find the Properties	(x^2)/9-(y^2)/4=1	$\frac{x^{2}}{9} - \frac{y^{2}}{4} = 1$
149	Find the Properties	x^2+4xy-2y^2-6=0	$x^{2} + 4 x y - 2 y^{2} - 6 = 0$
150	Expand the Trigonometric Expression	(x+1)^2	${(x + 1)}^{2}$
151	Find the Exact Value	sin(-225)	$\sin (- 225)$
152	Simplify	cube root of square root of 729x^6	$\sqrt[3]{\sqrt{729 x^{6}}}$
153	Simplify	square root of 49x^2+49	$\sqrt{49 x^{2} + 49}$
154	Split Using Partial Fraction Decomposition	(x^4+x^2+1)/(x^2(x^2+6)^2)	$\frac{x^{4} + x^{2} + 1}{x^{2} {(x^{2} + 6)}^{2}}$
155	Find the Domain	square root of x+7	$\sqrt{x + 7}$
156	Find the Domain	y=x	$y = x$
157	Find the Domain	f(x) = square root of x^2-16	$f (x) = \sqrt{x^{2} - 16}$
158	Simplify	cos(t)csc(t)	$\cos (t) \csc (t)$
159	Simplify	csc(x)-cos(x)cot(x)	$\csc (x) - \cos (x) \cot (x)$
160	Simplify	(2x+1)/(x+4)+(1-x)/(x-3)	$\frac{2 x + 1}{x + 4} + \frac{1 - x}{x - 3}$
161	Simplify	\|x^2\|+4	$\| x^{2} \| + 4$
162	Simplify	(x+y/x)/(y+x/y)	$\frac{x + \frac{y}{x}}{y + \frac{x}{y}}$
163	Simplify	(1+cos(y))/(1+sec(y))	$\frac{1 + \cos (y)}{1 + \sec (y)}$
164	Simplify	natural log of (x^4(x-4)^2)/( square root of x^2+1)	$\ln (\frac{x^{4} {(x - 4)}^{2}}{\sqrt{x^{2} + 1}})$
165	Solve for x	square root of x+ square root of 2x=1	$\sqrt{x} + \sqrt{2 x} = 1$
166	Solve for x	x^5-6x^2=0	$x^{5} - 6 x^{2} = 0$
167	Solve for x	3e^(-5x)=132	$3 e^{- 5 x} = 132$
168	Solve for ?	cot(x) = square root of 3	$\cot (x) = \sqrt{3}$
169	Solve for ?	2cos(x)^2-cos(x)-1=0	$2 \cos^{2} (x) - \cos (x) - 1 = 0$
170	Solve for t	cos(t)=0	$\cos (t) = 0$
171	Solve for x	(x+4)^2=144	${(x + 4)}^{2} = 144$
172	Solve for x	cos(2x)-cos(x)=0	$\cos (2 x) - \cos (x) = 0$
173	Solve for x	square root of x+20=x	$\sqrt{x + 20} = x$
174	Solve for x	sin(x)(sin(x)+1)=0	$\sin (x) (\sin (x) + 1) = 0$
175	Write as a Function of y	y=x^2	$y = x^{2}$
176	Find the Range	y=cos(x)	$y = \cos (x)$
177	Find the Vertex	f(x)=x^2-2x-3	$f (x) = x^{2} - 2 x - 3$
178	Find the Vertex	f(x)=x^2+4x+3	$f (x) = x^{2} + 4 x + 3$
179	Evaluate	(8pi)/3	$\frac{8 π}{3}$
180	Evaluate	tan(75)	$\tan (75)$
181	Evaluate	cos((3pi)/8)	$\cos (\frac{3 π}{8})$
182	Graph	y=2cos(1/2x)	$y = 2 \cos (\frac{1}{2} x)$
183	Graph	y=-2X	$y = - 2 X$
184	Determine if the Expression is a Perfect Square	-24xy^2	$- 24 x y^{2}$
185	Find the Slope	x=3	$x = 3$
186	Find the Domain	x^3	$x^{3}$
187	Find the Domain	f(x) = square root of x^2-9	$f (x) = \sqrt{x^{2} - 9}$
188	Find the Domain	f(x) = square root of x^2-4	$f (x) = \sqrt{x^{2} - 4}$
189	Find the Domain	square root of x^2-16	$\sqrt{x^{2} - 16}$
190	Find the Domain and Range	f(x)=2x^2+6x	$f (x) = 2 x^{2} + 6 x$
191	Use the Rational Roots Test to Find All Possible Roots	f(x)	$f (x)$
192	Convert to Interval Notation	(x+2)/(x+3)<(x-1)/(x-2)	$\frac{x + 2}{x + 3} < \frac{x - 1}{x - 2}$
193	Solve Using the Quadratic Formula	x^2+30x+200=0	$x^{2} + 30 x + 200 = 0$
194	Find the x and y Intercepts	x^2+y^2=4	$x^{2} + y^{2} = 4$
195	Divide	5/(3x-1)	$\frac{5}{3 x - 1}$
196	Find the Range	f(x)=(x-2)^2+2	$f (x) = {(x - 2)}^{2} + 2$
197	Find the Range	y=e^x	$y = e^{x}$
198	Find the Asymptotes	f(x)=2^x	$f (x) = 2^{x}$
199	Solve Using the Quadratic Formula	2x^2-3x+1=0	$2 x^{2} - 3 x + 1 = 0$
200	Factor	y^4(y+2)^3+y^5(y+2)^4	$y^{4} {(y + 2)}^{3} + y^{5} {(y + 2)}^{4}$