Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
68501	Evaluate the Limit	limit as x approaches infinity of (2x)/(x+2)	$lim_{x \to \infty} \frac{2 x}{x + 2}$
68502	Find the Derivative - d/dx	y = square root of 1-x^2-xarccos(x)	$y = \sqrt{1 - x^{2}} - x \arccos (x)$
68503	Find the Antiderivative	f(x)=1/((x/4+1)^5)	$f (x) = \frac{1}{{(\frac{x}{4} + 1)}^{5}}$
68504	Evaluate the Integral	integral of (sin(x)^2+cos(x)^2) with respect to x	$\int (\sin^{2} (x) + \cos^{2} (x)) d x$
68505	Find the Antiderivative	square root of xdx	$\sqrt{x} d x$
68506	Evaluate the Integral	integral of 7tan(x)^3sec(x) with respect to x	$\int 7 \tan^{3} (x) \sec (x) d x$
68507	Evaluate the Limit	limit as x approaches -4 of (-5x-35)/(x^2-4x)	$lim_{x \to - 4} \frac{- 5 x - 35}{x^{2} - 4 x}$
68508	Find dy/dx	y^2-x^3=22	$y^{2} - x^{3} = 22$
68509	Find the Derivative - d/dy	ye^y	$y e^{y}$
68510	Find dy/dx	x^2+3xy-y=7	$x^{2} + 3 x y - y = 7$
68511	Find the Antiderivative	-2/x	$- \frac{2}{x}$
68512	Evaluate the Limit	limit as x approaches 0 of (3x^2+5x^4)/(2x^2+6x^4-7x^8)	$lim_{x \to 0} \frac{3 x^{2} + 5 x^{4}}{2 x^{2} + 6 x^{4} - 7 x^{8}}$
68513	Find the Domain and Range	f(x)=-3x+4 if x<1; 4x-3 if x>=1	$f (x) = {\begin{cases} - 3 x + 4 & x < 1 \\ 4 x - 3 & x \geq 1 \end{cases}$
68514	Evaluate the Limit	limit as h approaches -3 of (h^2-3^2)/(2h^2+7h+3)	$lim_{h \to - 3} \frac{h^{2} - 3^{2}}{2 h^{2} + 7 h + 3}$
68515	Find dy/dx	y=arcsin(4x+1)	$y = \arcsin (4 x + 1)$
68516	Find the Derivative - d/dx	d/(dx)(x^6+3x^4+7x^2)	$\frac{d}{d x} (x^{6} + 3 x^{4} + 7 x^{2})$
68517	Find the Derivative - d/dx	e^(2sin(x))	$e^{2 \sin (x)}$
68518	Integrate Using u-Substitution	integral of e^(2x) with respect to x	$\int e^{2 x} d x$
68519	Find dy/dx	xsin(y)+ysin(x)=6	$x \sin (y) + y \sin (x) = 6$
68520	Evaluate the Integral	integral of (3-x) with respect to x	$\int (3 - x) d x$
68521	Find the Domain and Range	f(x)=-2x+5 if x<1; 4x-1 if x>=1	$f (x) = {\begin{cases} - 2 x + 5 & x < 1 \\ 4 x - 1 & x \geq 1 \end{cases}$
68522	Evaluate the Limit	limit as x approaches -3 of (-x^2-x+4)/(-x-1)	$lim_{x \to - 3} \frac{- x^{2} - x + 4}{- x - 1}$
68523	Find the Second Derivative	y=csc(x)	$y = \csc (x)$
68524	Find Where Increasing/Decreasing	F(x)=x square root of 9-x	$F (x) = x \sqrt{9 - x}$
68525	Find the Derivative - d/dx	arctan(x- square root of 1+x^2)	$\arctan (x - \sqrt{1 + x^{2}})$
68526	Evaluate the Limit	limit as x approaches 1/4 of 4x(x-3/8)	$lim_{x \to \frac{1}{4}} 4 x (x - \frac{3}{8})$
68527	Find dy/dx	y^2x-x^2y=y-2x	$y^{2} x - x^{2} y = y - 2 x$
68528	Find dy/dv	y=(5-v^2)/(5+v^2)	$y = \frac{5 - v^{2}}{5 + v^{2}}$
68529	Determine if Continuous	f(x)=cx^2+4x if x<5; x^3-cx if x>=5	$f (x) = {\begin{cases} c x^{2} + 4 x & x < 5 \\ x^{3} - c x & x \geq 5 \end{cases}$
68530	Find the Derivative - d/dx	sin(xdx)	$\sin (x d x)$
68531	Find the Derivative - d/dx	5 natural log of x+cos(x)	$5 \ln (x) + \cos (x)$
68532	Find the Derivative - d/dx	y=ax^2	$y = a x^{2}$
68533	Find dy/dx	y=arcsin(1/(9x+6))	$y = \arcsin (\frac{1}{9 x + 6})$
68534	Find the Derivative - d/dx	y=x/( square root of a^2-x^2)	$y = \frac{x}{\sqrt{a^{2} - x^{2}}}$
68535	Solve the Differential Equation	y natural log of x(dx)/(dy)=((y+1)/x)^2	$y \ln (x) \frac{d x}{d y} = {(\frac{y + 1}{x})}^{2}$
68536	Find the Derivative - d/dx	2sin(x)^3	$2 \sin^{3} (x)$
68537	Find the Derivative - d/dx	d/(dx)(-x^3+5x^2-8x)	$\frac{d}{d x} (- x^{3} + 5 x^{2} - 8 x)$
68538	Evaluate the Integral	integral of ( square root of x+1/(4 square root of x)) with respect to x	$\int (\sqrt{x} + \frac{1}{4 \sqrt{x}}) d x$
68539	Find the Maximum/Minimum Value	f(x)=x^3-x^2-x	$f (x) = x^{3} - x^{2} - x$
68540	Find the Slope	f(x)=2x-4	$f (x) = 2 x - 4$
68541	Find the Derivative - d/dx	d/(dx)((sin(x))/(x^2))	$\frac{d}{d x} (\frac{\sin (x)}{x^{2}})$
68542	Find the Derivative - d/dx	y=(2x^2+2)(x^2+3)	$y = (2 x^{2} + 2) (x^{2} + 3)$
68543	Find the Derivative - d/dx	3/(x^2)+1/x	$\frac{3}{x^{2}} + \frac{1}{x}$
68544	Find the Derivative - d/dx	4/(x^4)+1/x+2	$\frac{4}{x^{4}} + \frac{1}{x} + 2$
68545	Find the Center and Radius	11x^2-25y^2+22x+250y-889=0	$11 x^{2} - 25 y^{2} + 22 x + 250 y - 889 = 0$
68546	Find dy/dx	y^3+y=x^2	$y^{3} + y = x^{2}$
68547	Find the Derivative - d/dx	d/(dx)((x^2-x+5)/(4x-1))	$\frac{d}{d x} (\frac{x^{2} - x + 5}{4 x - 1})$
68548	Find dy/dx	3(x^2+y^2)^2=100(x^2-y^2)	$3 {(x^{2} + y^{2})}^{2} = 100 (x^{2} - y^{2})$
68549	Evaluate the Limit	limit as x approaches 1 from the right of (x^4-1)/(x-1)	$lim_{x \to 1^{+}} \frac{x^{4} - 1}{x - 1}$
68550	Evaluate the Integral	integral of (3/( square root of x)-(x square root of x)/4) with respect to x	$\int (\frac{3}{\sqrt{x}} - \frac{x \sqrt{x}}{4}) d x$
68551	Evaluate the Limit	limit as x approaches 7 of (x^2-49)/(-5x+35)	$lim_{x \to 7} \frac{x^{2} - 49}{- 5 x + 35}$
68552	Find the Derivative - d/dx	2e^x-5cos(x)+3	$2 e^{x} - 5 \cos (x) + 3$
68553	Evaluate the Limit	limit as x approaches pi/6 of -3cos(-x)-4tan(-x)	$lim_{x \to \frac{π}{6}} - 3 \cos (- x) - 4 \tan (- x)$
68554	Find the Integral	f(x)=3x^2	$f (x) = 3 x^{2}$
68555	Find dy/dx	cos(x+y)=x	$\cos (x + y) = x$
68556	Evaluate the Limit	limit as x approaches 1/3 of (3x-1)/(9x^2-1)	$lim_{x \to \frac{1}{3}} \frac{3 x - 1}{9 x^{2} - 1}$
68557	Evaluate the Limit	limit as x approaches 3 of (x-3)/(1+x)	$lim_{x \to 3} \frac{x - 3}{1 + x}$
68558	Find dy/dθ	y=sec(theta)tan(theta)	$y = \sec (θ) \tan (θ)$
68559	Find dy/dx	x^3+y^3=4	$x^{3} + y^{3} = 4$
68560	Find the Center and Radius	(x^2)/169+(y^2)/25=1	$\frac{x^{2}}{169} + \frac{y^{2}}{25} = 1$
68561	Find the Derivative - d/dx	y=(x^3-cos(x))^5	$y = {(x^{3} - \cos (x))}^{5}$
68562	Evaluate the Integral	integral of (6x^2-4x+5) with respect to x	$\int (6 x^{2} - 4 x + 5) d x$
68563	Find dy/dx	xsin(y)+ysin(x)=5	$x \sin (y) + y \sin (x) = 5$
68564	Evaluate the Integral	integral of ( square root of x^2+1)/x with respect to x	$\int \frac{\sqrt{x^{2} + 1}}{x} d x$
68565	Find the Derivative - d/dx	re^(rx)	$r e^{r x}$
68566	Find the Derivative - d/dx	y=sin(x/2)^2	$y = \sin^{2} (\frac{x}{2})$
68567	Evaluate the Integral	integral of ( cube root of x+1/( cube root of x)) with respect to x	$\int (\sqrt[3]{x} + \frac{1}{\sqrt[3]{x}}) d x$
68568	Evaluate the Integral	integral of (a-by)^4 with respect to y	$\int {(a - b y)}^{4} d y$
68569	Find the Derivative - d/dx	sinh(x^3-1)	$\sinh (x^{3} - 1)$
68570	Find dy/dx	y^5+x^2y^3=1+ye^(x^2)	$y^{5} + x^{2} y^{3} = 1 + y e^{x^{2}}$
68571	Find dy/dx	x^3+y^2=24	$x^{3} + y^{2} = 24$
68572	Find dx/dy	y=1/( square root of x)	$y = \frac{1}{\sqrt{x}}$
68573	Find dy/dx	(x+2)^2+(y-3)^2=37	${(x + 2)}^{2} + {(y - 3)}^{2} = 37$
68574	Find the Maximum/Minimum Value	f(x)=-0.5x^4+2.5x^3+x^2-6.5x	$f (x) = - 0.5 x^{4} + 2.5 x^{3} + x^{2} - 6.5 x$
68575	Evaluate the Integral	integral of (3x^2-4x+5) with respect to x	$\int (3 x^{2} - 4 x + 5) d x$
68576	Find the Derivative - d/dx	(1+x)^(1/2)	${(1 + x)}^{\frac{1}{2}}$
68577	Find dy/dx	y=x^2e^(-3x)	$y = x^{2} e^{- 3 x}$
68578	Use Logarithmic Differentiation to Find the Derivative	y=x^(2cos(x))	$y = x^{2 \cos (x)}$
68579	Find dy/dx	(x+y)^2=2x+2y	${(x + y)}^{2} = 2 x + 2 y$
68580	Find dy/dx	y = square root of x+1	$y = \sqrt{x + 1}$
68581	Find dy/dx	5y^2=2x^3-5y	$5 y^{2} = 2 x^{3} - 5 y$
68582	Find the Maximum/Minimum Value	f(x)=(x^2)/(x^2-4)	$f (x) = \frac{x^{2}}{x^{2} - 4}$
68583	Find dy/dx	y=arccos(x)+x square root of 1-x^2	$y = \arccos (x) + x \sqrt{1 - x^{2}}$
68584	Evaluate the Limit	limit as x approaches -1/2 from the right of (6x^2+x-1)/(4x^2-2x-2)	$lim_{x \to {(- \frac{1}{2})}^{+}} \frac{6 x^{2} + x - 1}{4 x^{2} - 2 x - 2}$
68585	Evaluate the Limit	limit as x approaches infinity of ((x-1)/(x+1))^x	$lim_{x \to \infty} {(\frac{x - 1}{x + 1})}^{x}$
68586	Find dy/dx	4y^2=(3x-5)/(3x+5)	$4 y^{2} = \frac{3 x - 5}{3 x + 5}$
68587	Evaluate the Integral	integral from 0 to a of 1/((1+x)^2) with respect to x=1/6	$\int_{0}^{a} \frac{1}{{(1 + x)}^{2}} d x = \frac{1}{6}$
68588	Evaluate the Limit	limit as x approaches -2 of (x^2-6x-16)/(4x-8)	$lim_{x \to - 2} \frac{x^{2} - 6 x - 16}{4 x - 8}$
68589	Evaluate the Integral	integral of (4/( cube root of x)-5/( fourth root of x)) with respect to x	$\int (\frac{4}{\sqrt[3]{x}} - \frac{5}{\sqrt[4]{x}}) d x$
68590	Find dy/dx	3x^2-2xy+5y^2=1	$3 x^{2} - 2 x y + 5 y^{2} = 1$
68591	Find the Maximum/Minimum Value	f(t)=5t+3/t	$f (t) = 5 t + \frac{3}{t}$
68592	Find the Derivative - d/dx	(2x)^2	${(2 x)}^{2}$
68593	Find the Derivative - d/dx	y=(1+x^2)/x	$y = \frac{1 + x^{2}}{x}$
68594	Find the Concavity	f(x)=4x^4-4x^2-8x-7	$f (x) = 4 x^{4} - 4 x^{2} - 8 x - 7$
68595	Evaluate the Limit	limit as x approaches 0 of x/(1-(x-1)^2)	$lim_{x \to 0} \frac{x}{1 - {(x - 1)}^{2}}$
68596	Evaluate the Integral	integral of t(2t-3 square root of t) with respect to t	$\int t (2 t - 3 \sqrt{t}) d t$
68597	Find the Derivative - d/dx	square root of x-x^2	$\sqrt{x - x^{2}}$
68598	Evaluate the Integral	integral from 0 to 1 of square root of x-x^2 with respect to x	$\int_{0}^{1} \sqrt{x - x^{2}} d x$
68599	Find the Maximum/Minimum Value	k(x)=3x^4+8x^3	$k (x) = 3 x^{4} + 8 x^{3}$
68600	Find dy/dx	y=(x-1)/(x+1)	$y = \frac{x - 1}{x + 1}$