Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
82201	Find dy/dx	-x^2-y^2+3y=-5	$- x^{2} - y^{2} + 3 y = - 5$
82202	Find Where Increasing/Decreasing	f(x)=1/8(1/4)^(x-2)	$f (x) = \frac{1}{8} {(\frac{1}{4})}^{x - 2}$
82203	Evaluate the Limit	limit as x approaches 1 of ( square root of x- square root of 2x-1)/(x-1)	$lim_{x \to 1} \frac{\sqrt{x} - \sqrt{2 x - 1}}{x - 1}$
82204	Find dy/dx	x^3-y=4xy	$x^{3} - y = 4 x y$
82205	Find Where Increasing/Decreasing	g(x)=- cube root of x-2	$g (x) = - \sqrt[3]{x - 2}$
82206	Find the Derivative - d/dx	square root of e*x	$\sqrt{e} \cdot x$
82207	Integrate Using u-Substitution	integral of 5 square root of 5x-1 with respect to x	$\int 5 \sqrt{5 x - 1} d x$
82208	Find the Antiderivative	(x^2+2x+3)/(x+1)	$\frac{x^{2} + 2 x + 3}{x + 1}$
82209	Evaluate the Integral	integral from 1/18 to 1/6 of csc(3pit)cot(3pit) with respect to t	$\int_{\frac{1}{18}}^{\frac{1}{6}} \csc (3 π t) \cot (3 π t) d t$
82210	Evaluate the Integral	integral of (sin(x))/( square root of cos(x)) with respect to x	$\int \frac{\sin (x)}{\sqrt{\cos (x)}} d x$
82211	Find dy/dx	-5y^3=3+x+x^3	$- 5 y^{3} = 3 + x + x^{3}$
82212	Evaluate the Integral	integral from 4 to 6 of (x^2+2)/(x-2) with respect to x	$\int_{4}^{6} \frac{x^{2} + 2}{x - 2} d x$
82213	Find the Derivative - d/dx	(1/2)^(4x)	${(\frac{1}{2})}^{4 x}$
82214	Find the Percentage Rate of Change	y=575(1-0.6)^t	$y = 575 {(1 - 0.6)}^{t}$
82215	Find the Derivative - d/dh	V=1/3pir^2h	$V = \frac{1}{3} π r^{2} h$
82216	Evaluate the Summation	sum from i=1 to 7 of 840/i	$\sum_{i = 1}^{7} \frac{840}{i}$
82217	Find the Antiderivative	(sin(x))/(cos(x)^5)	$\frac{\sin (x)}{\cos^{5} (x)}$
82218	Evaluate the Limit	limit as x approaches 4 of 3x(x+5)	$lim_{x \to 4} 3 x (x + 5)$
82219	Find the Center and Radius	(x+2)^2-(y+2)^2=4^2	${(x + 2)}^{2} - {(y + 2)}^{2} = 4^{2}$
82220	Evaluate the Integral	integral of (5t^8-2t^4+t+3) with respect to x	$\int (5 t^{8} - 2 t^{4} + t + 3) d x$
82221	Evaluate the Limit	limit as x approaches -3 of 6/(9-x^2)-1/(x+3)	$lim_{x \to - 3} \frac{6}{9 - x^{2}} - \frac{1}{x + 3}$
82222	Find Where Increasing/Decreasing	f'(x)=x^3-18x^2+81x	$f' (x) = x^{3} - 18 x^{2} + 81 x$
82223	Evaluate the Integral	integral of (2e^(1/(x^2)))/(3x^3) with respect to x	$\int \frac{2 e^{\frac{1}{x^{2}}}}{3 x^{3}} d x$
82224	Find dy/dx	4x^3-3xy^2+y^3=28	$4 x^{3} - 3 x y^{2} + y^{3} = 28$
82225	Evaluate the Limit	limit as x approaches 0 of (tan(nx))/(sin(x))	$lim_{x \to 0} \frac{\tan (n x)}{\sin (x)}$
82226	Find the Derivative - d/dx	2^(1/x)	$2^{\frac{1}{x}}$
82227	Find the Concavity	f(x)=2/15x^6+x^5	$f (x) = \frac{2}{15} x^{6} + x^{5}$
82228	Find the Derivative - d/dx	d/(dx)( natural log of x^2+1)	$\frac{d}{d x} (\ln (x^{2} + 1))$
82229	Find the Maximum/Minimum Value	f(x)=-1/5x^5-2x^4-5x^3+9	$f (x) = - \frac{1}{5} x^{5} - 2 x^{4} - 5 x^{3} + 9$
82230	Find the Antiderivative	g(x)=5 cube root of x^2-1/(2 square root of x)+pi	$g (x) = 5 \sqrt[3]{x^{2}} - \frac{1}{2 \sqrt{x}} + π$
82231	Find the Percentage Rate of Change	y=(0.85)^x	$y = {(0.85)}^{x}$
82232	Find the Maximum/Minimum Value	y=-4cos(x+pi/4)	$y = - 4 \cos (x + \frac{π}{4})$
82233	Find the Skew	11 , 14 , 14 , 17 , 17 , 17 , 41 , 44 , 47 , 71 , 74 , 77	$11$ , $14$ , $14$ , $17$ , $17$ , $17$ , $41$ , $44$ , $47$ , $71$ , $74$ , $77$
82234	Find dy/dx	y=(3x-1)(2x+5)	$y = (3 x - 1) (2 x + 5)$
82235	Evaluate the Limit	limit as x approaches 9 of (3- square root of x)/(27- square root of x^3)	$lim_{x \to 9} \frac{3 - \sqrt{x}}{27 - \sqrt{x^{3}}}$
82236	Evaluate the Integral	integral of cos(x)-sin(x) with respect to x	$\int \cos (x) - \sin (x) d x$
82237	Evaluate the Limit	limit as x approaches infinity of (7x^3-5x^2+1)/(x^4-3)	$lim_{x \to \infty} \frac{7 x^{3} - 5 x^{2} + 1}{x^{4} - 3}$
82238	Find dy/dx	natural log of xy+5x=30	$\ln (x y) + 5 x = 30$
82239	Find the Derivative - d/dt	re^(rt)	$r e^{r t}$
82240	Evaluate the Integral	integral of (4x+2)/(x^2+x+5) with respect to x	$\int \frac{4 x + 2}{x^{2} + x + 5} d x$
82241	Find the Maximum/Minimum Value	y=(-x-1)^2+3	$y = {(- x - 1)}^{2} + 3$
82242	Find the Antiderivative	x^5+8x^3- square root of 5	$x^{5} + 8 x^{3} - \sqrt{5}$
82243	Evaluate the Integral	integral from 0 to 2 of x/((1+2x^2)^2) with respect to x	$\int_{0}^{2} \frac{x}{{(1 + 2 x^{2})}^{2}} d x$
82244	Find the Derivative - d/dt	y=t^2( natural log of t)^4	$y = t^{2} \ln^{4} (t)$
82245	Find the Derivative - d/dx	y=4cos(-5x^2)	$y = 4 \cos (- 5 x^{2})$
82246	Evaluate the Integral	integral from 0 to 3 of (1/4x^2)(2x^2)(3-x) with respect to x	$\int_{0}^{3} (\frac{1}{4} x^{2}) (2 x^{2}) (3 - x) d x$
82247	Find the Antiderivative	f(x)=5e^(2x+3)+4x^2	$f (x) = 5 e^{2 x + 3} + 4 x^{2}$
82248	Evaluate the Limit	limit as x approaches 7 of cube root of (2-8x)/(x-5)	$lim_{x \to 7} \sqrt[3]{\frac{2 - 8 x}{x - 5}}$
82249	Find the Inflection Points	1/10x^5-2x^4+12x^3	$\frac{1}{10} x^{5} - 2 x^{4} + 12 x^{3}$
82250	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (2 natural log of x+1+2x)/(4sin(x)-2x^3)	$lim_{x \to 0} \frac{2 \ln (x + 1) + 2 x}{4 \sin (x) - 2 x^{3}}$
82251	Find the Fourth Derivative	x^5-2/(x^3)-4x+2	$x^{5} - \frac{2}{x^{3}} - 4 x + 2$
82252	Find the Derivative - d/dy	x+y^2	$x + y^{2}$
82253	Find the Antiderivative	f(x)=4 cube root of x-6 square root of x	$f (x) = 4 \sqrt[3]{x} - 6 \sqrt{x}$
82254	Find the Maximum/Minimum Value	x^3-x	$x^{3} - x$
82255	Find the Derivative - d/dx	cos(x^2+1)	$\cos (x^{2} + 1)$
82256	Find the Percentage Rate of Change	f(t)=70(2/5)^t	$f (t) = 70 {(\frac{2}{5})}^{t}$
82257	Find the Maximum/Minimum Value	f(x)=-3/4x^4+x^3+45x^2+12	$f (x) = - \frac{3}{4} x^{4} + x^{3} + 45 x^{2} + 12$
82258	Find dy/dx	y=(x-1)(x+2)	$y = (x - 1) (x + 2)$
82259	Find the Derivative - d/dx	(2-3x)/(3+x^2)	$\frac{2 - 3 x}{3 + x^{2}}$
82260	Integrate Using u-Substitution	integral of cos(4x) with respect to x , u=4x	$\int \cos (4 x) d x$ , $u = 4 x$
82261	Find dy/dx	x+y-2x^3=2	$x + y - 2 x^{3} = 2$
82262	Evaluate the Integral	integral of 4x(2x-3)(3x+1) with respect to x	$\int 4 x (2 x - 3) (3 x + 1) d x$
82263	Evaluate the Integral	integral of e^x*2x with respect to x	$\int e^{x} \cdot 2 x d x$
82264	Find the Derivative - d/dt	y=(1+at)(ct)^-2	$y = (1 + a t) {(c t)}^{- 2}$
82265	Integrate Using Partial Fractions	integral of (2x^3+x^2-21x+24)/(x^2+2x-8) with respect to x	$\int \frac{2 x^{3} + x^{2} - 21 x + 24}{x^{2} + 2 x - 8} d x$
82266	Find the Antiderivative	sin(x)^2*cos(x)^3	$\sin^{2} (x) \cdot \cos^{3} (x)$
82267	Find Where Increasing/Decreasing	f(x)=x^4+4x^3-8x^2+1	$f (x) = x^{4} + 4 x^{3} - 8 x^{2} + 1$
82268	Find the Antiderivative	(x^2-2x+3)/(x+1)	$\frac{x^{2} - 2 x + 3}{x + 1}$
82269	Find dy/dx	y=(x^3+2x+1)^5	$y = {(x^{3} + 2 x + 1)}^{5}$
82270	Evaluate Using L'Hospital's Rule	limit as x approaches -3 of (4 natural log of -2-x)/(3e^(2x+6)-3)	$lim_{x \to - 3} \frac{4 \ln (- 2 - x)}{3 e^{2 x + 6} - 3}$
82271	Evaluate the Limit	limit as x approaches a of (2x-1)^5	$lim_{x \to a} {(2 x - 1)}^{5}$
82272	Evaluate the Integral	integral from -1 to 3 of [2y-(y^2-3)] with respect to y	$\int_{- 1}^{3} [2 y - (y^{2} - 3)] d y$
82273	Integrate Using u-Substitution	integral of sin(theta)^4cos(theta) with respect to theta , u=sin(theta)	$\int \sin^{4} (θ) \cos (θ) d θ$ , $u = \sin (θ)$
82274	Find dy/dx	3xy+3y+5=-3x	$3 x y + 3 y + 5 = - 3 x$
82275	Find the Derivative - d/dx	natural log of square root of 1+x^2	$\ln (\sqrt{1 + x^{2}})$
82276	Find Where Increasing/Decreasing	f(x)=(x+x^2)e^(-2x)	$f (x) = (x + x^{2}) e^{- 2 x}$
82277	Evaluate the Limit	limit as x approaches 7 of ( square root of x-6-1)/(7-x)	$lim_{x \to 7} \frac{\sqrt{x - 6} - 1}{7 - x}$
82278	Find the Derivative - d/dx	mx^(m-1)	$m x^{m - 1}$
82279	Evaluate the Integral	integral from 0 to 4 of 1/((x-2)^2) with respect to x	$\int_{0}^{4} \frac{1}{{(x - 2)}^{2}} d x$
82280	Evaluate the Integral	integral from 1 to 2 of (x/2-2/x) with respect to x	$\int_{1}^{2} (\frac{x}{2} - \frac{2}{x}) d x$
82281	Evaluate the Limit	limit as x approaches -4 of 4(x^3-8x^2+20x-16)tan(pix)	$lim_{x \to - 4} 4 (x^{3} - 8 x^{2} + 20 x - 16) \tan (π x)$
82282	Find the Derivative - d/dx	2/3x^(-1/3)	$\frac{2}{3} x^{- \frac{1}{3}}$
82283	Evaluate the Limit	limit as x approaches 0 of (1-cos(2x)^2)/((2x)^2)	$lim_{x \to 0} \frac{1 - \cos^{2} (2 x)}{{(2 x)}^{2}}$
82284	Evaluate the Limit	limit as x approaches 2 of 2/(x-2)-(x+6)/(x^2-4)	$lim_{x \to 2} \frac{2}{x - 2} - \frac{x + 6}{x^{2} - 4}$
82285	Find the Antiderivative	e^-1	$e^{- 1}$
82286	Find the Derivative - d/dy	y^(xy)	$y^{x y}$
82287	Find the Derivative - d/dx	arctan(4x^2-3)	$\arctan (4 x^{2} - 3)$
82288	Find the Antiderivative	x^2e^(x^3+1)	$x^{2} e^{x^{3} + 1}$
82289	Find the Maximum/Minimum Value	f(x)=-x^4+x^3+2x^2	$f (x) = - x^{4} + x^{3} + 2 x^{2}$
82290	Evaluate the Limit	limit as x approaches infinity of ( square root of x+5- square root of 5)/( square root of x- square root of 5)	$lim_{x \to \infty} \frac{\sqrt{x + 5} - \sqrt{5}}{\sqrt{x} - \sqrt{5}}$
82291	Find the Antiderivative	(20x^2-30x+7)/( square root of 2x-3)	$\frac{20 x^{2} - 30 x + 7}{\sqrt{2 x - 3}}$
82292	Find dy/dx	xy^2+4+y=-x^3	$x y^{2} + 4 + y = - x^{3}$
82293	Evaluate the Integral	integral of 3x(2x-1)^2 with respect to x	$\int 3 x {(2 x - 1)}^{2} d x$
82294	Evaluate the Integral	integral of 1/((1-x^2)^(3/2)) with respect to x	$\int \frac{1}{{(1 - x^{2})}^{\frac{3}{2}}} d x$
82295	Evaluate the Integral	integral of x^3 square root of 4+x^2 with respect to x	$\int x^{3} \sqrt{4 + x^{2}} d x$
82296	Find the Derivative - d/dx	y=(2x+3)^-3	$y = {(2 x + 3)}^{- 3}$
82297	Find Where Increasing/Decreasing	y=-1/2x^3	$y = - \frac{1}{2} x^{3}$
82298	Find dy/dx	-2+4y^3-4x^3=0	$- 2 + 4 y^{3} - 4 x^{3} = 0$
82299	Evaluate the Limit	limit as x approaches negative infinity of 3xe^x	$lim_{x \to - \infty} 3 x e^{x}$
82300	Evaluate the Limit	limit as x approaches 0 of (7+2x)/(cos(x))	$lim_{x \to 0} \frac{7 + 2 x}{\cos (x)}$