Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
82601	Evaluate the Limit	limit as x approaches 1 of (x^3+x^2-2)/(x-1)	$lim_{x \to 1} \frac{x^{3} + x^{2} - 2}{x - 1}$
82602	Evaluate the Integral	integral of sin(x)(4csc(x)-cot(x)) with respect to x	$\int \sin (x) (4 \csc (x) - \cot (x)) d x$
82603	Find the Antiderivative	(4x+11)/(x^2+5x+6)	$\frac{4 x + 11}{x^{2} + 5 x + 6}$
82604	Find the Maximum/Minimum Value	f(x)=4/3x^3+7x^2-8x-42	$f (x) = \frac{4}{3} x^{3} + 7 x^{2} - 8 x - 42$
82605	Find the Derivative - d/dx	(e^x+x)^(1/x)	${(e^{x} + x)}^{\frac{1}{x}}$
82606	Find the Antiderivative	(2 square root of x)/x	$\frac{2 \sqrt{x}}{x}$
82607	Find the Derivative - d/dt	y=e^(cos(t))	$y = e^{\cos (t)}$
82608	Find the Antiderivative	1/x-2e^x	$\frac{1}{x} - 2 e^{x}$
82609	Find dy/dx	y-2xy=3x	$y - 2 x y = 3 x$
82610	Evaluate the Limit	limit as x approaches pi/(()/())*2 of 3sin(x)	$lim_{x \to \frac{π}{\frac{}{}} \cdot 2} 3 \sin (x)$
82611	Find the Percentage Rate of Change	y=7500(1+0.03)^x	$y = 7500 {(1 + 0.03)}^{x}$
82612	Find the Maximum/Minimum Value	h(x)=-3x^4+8x^3+18x^2	$h (x) = - 3 x^{4} + 8 x^{3} + 18 x^{2}$
82613	Find the Antiderivative	(e^x+e^(-x))^2	${(e^{x} + e^{- x})}^{2}$
82614	Find dy/dx	-2x^2+1+xy^2=-2y^3	$- 2 x^{2} + 1 + x y^{2} = - 2 y^{3}$
82615	Find the Antiderivative	e^0	$e^{0}$
82616	Evaluate the Limit	limit as x approaches infinity of 3/(2+e^(-x))	$lim_{x \to \infty} \frac{3}{2 + e^{- x}}$
82617	Find the Antiderivative	f(x)=x^6+3x^2	$f (x) = x^{6} + 3 x^{2}$
82618	Evaluate the Integral	integral of (4x^4+3)/(4x^5+15x+2) with respect to x	$\int \frac{4 x^{4} + 3}{4 x^{5} + 15 x + 2} d x$
82619	Find dy/dx	-y-4x^2=3y^3	$- y - 4 x^{2} = 3 y^{3}$
82620	Find the Derivative - d/dx	-2e^(3x)sin(2x)+3e^(3x)cos(2x)	$- 2 e^{3 x} \sin (2 x) + 3 e^{3 x} \cos (2 x)$
82621	Evaluate the Limit	limit as x approaches 1 of (x^3-x^2+x-1)/(x^2-1)	$lim_{x \to 1} \frac{x^{3} - x^{2} + x - 1}{x^{2} - 1}$
82622	Evaluate the Integral	integral from 1 to infinity of 4xe^(-x^2) with respect to x	$\int_{1}^{\infty} 4 x e^{- x^{2}} d x$
82623	Evaluate the Limit	limit as x approaches 2 of ((f(x))^2+f(x)-12)/(f(x)+4)	$lim_{x \to 2} \frac{{(f (x))}^{2} + f (x) - 12}{f (x) + 4}$
82624	Find dy/dx	x^4+4y=8xy	$x^{4} + 4 y = 8 x y$
82625	Evaluate the Limit	limit as x approaches 0 from the right of 8/x- natural log of x	$lim_{x \to 0^{+}} \frac{8}{x} - \ln (x)$
82626	Find the Antiderivative	sin(3x+pi/6)	$\sin (3 x + \frac{π}{6})$
82627	Evaluate the Integral	integral of 1/(x square root of 9x^2-7) with respect to x	$\int \frac{1}{x \sqrt{9 x^{2} - 7}} d x$
82628	Find the Skew	4 , 6 , 16	$4$ , $6$ , $16$
82629	Find the Derivative of the Integral	F(x) = integral from 2 to x of t^2-1 with respect to t	$F (x) = \int_{2}^{x} t^{2} - 1 d t$
82630	Evaluate the Limit	limit as x approaches -7 of (49-x^2)/(x^3+7x^2)	$lim_{x \to - 7} \frac{49 - x^{2}}{x^{3} + 7 x^{2}}$
82631	Find Where Increasing/Decreasing	f(x)=-x^4+x^3+2x^2	$f (x) = - x^{4} + x^{3} + 2 x^{2}$
82632	Find the Concavity	-1/5x^5-x^4	$- \frac{1}{5} x^{5} - x^{4}$
82633	Find Where Increasing/Decreasing	x^2e^x	$x^{2} e^{x}$
82634	Evaluate the Limit	limit as x approaches 0 of x^2=0	$lim_{x \to 0} x^{2} = 0$
82635	Evaluate the Integral	integral of (5cos(x)-2sec(x)^2) with respect to x	$\int (5 \cos (x) - 2 \sec^{2} (x)) d x$
82636	Find dy/dx	y=(1-2x^2)/(2x^2-5)	$y = \frac{1 - 2 x^{2}}{2 x^{2} - 5}$
82637	Evaluate Using L'Hospital's Rule	limit as x approaches 0 from the right of -x natural log of x	$lim_{x \to 0^{+}} - x \ln (x)$
82638	Evaluate the Integral	integral from 3 to 12 of square root of \|-2x-2\| with respect to x	$\int_{3}^{12} \sqrt{\| - 2 x - 2 \|} d x$
82639	Evaluate the Limit	limit as x approaches 0 of (2-e^(2x))^(1/x)	$lim_{x \to 0} {(2 - e^{2 x})}^{\frac{1}{x}}$
82640	Find the Derivative Using Product Rule - d/dx	x natural log of x	$x \ln (x)$
82641	Find the Tangent Line at (-1,2)	f(x)=-2x^3 at (-1,2)	$f (x) = - 2 x^{3}$ at $(- 1, 2)$
82642	Find the Derivative - d/dt	(80sin(0.6t))/t+15	$\frac{80 \sin (0.6 t)}{t} + 15$
82643	Find the Critical Points	f(x)=- square root of x-3+2	$f (x) = - \sqrt{x - 3} + 2$
82644	Find the Derivative - d/dx	y=1/3cos(2x)^3	$y = \frac{1}{3} \cos^{3} (2 x)$
82645	Evaluate the Integral	integral of (x^2)/(1-x) with respect to x	$\int \frac{x^{2}}{1 - x} d x$
82646	Find da/dr	a=pir^2	$a = π r^{2}$
82647	Find the Derivative - d/ds	d/(ds)((a^2-s^2)/( square root of a^2+s^2))	$\frac{d}{d s} (\frac{a^{2} - s^{2}}{\sqrt{a^{2} + s^{2}}})$
82648	Find the Antiderivative	f(x)=1/(x^2)-10x^4+3	$f (x) = \frac{1}{x^{2}} - 10 x^{4} + 3$
82649	Find the Derivative - d/dx	xe^(-x/2)	$x e^{- \frac{x}{2}}$
82650	Find dy/dx	-4y^3-y^2=3+5x^2	$- 4 y^{3} - y^{2} = 3 + 5 x^{2}$
82651	Find Where Increasing/Decreasing	-3/5x^5+9x^4-32x^3+49	$- \frac{3}{5} x^{5} + 9 x^{4} - 32 x^{3} + 49$
82652	Find dy/dx	y=sin(1/x)	$y = \sin (\frac{1}{x})$
82653	Find dy/dx	4x^2-y^2=7x-5	$4 x^{2} - y^{2} = 7 x - 5$
82654	Evaluate the Integral	integral of (x+3)/(4x+4) with respect to x	$\int \frac{x + 3}{4 x + 4} d x$
82655	Integrate Using u-Substitution	integral of (7x+e^(4x)) with respect to x	$\int (7 x + e^{4 x}) d x$
82656	Evaluate the Integral	integral of 5(tan(x)^2+tan(x)^4) with respect to x	$\int 5 (\tan^{2} (x) + \tan^{4} (x)) d x$
82657	Evaluate the Integral	integral of (tan(x))/( natural log of cos(x)) with respect to x	$\int \frac{\tan (x)}{\ln (\cos (x))} d x$
82658	Find the Derivative - d/dx	(-x)/2	$\frac{- x}{2}$
82659	Find the Derivative - d/dx	sin(x)^2-sin(x)	$\sin^{2} (x) - \sin (x)$
82660	Evaluate the Summation	sum from k=2 to 5 of -4k+3k^2	$\sum_{k = 2}^{5} - 4 k + 3 k^{2}$
82661	Find the Derivative - d/dx	y=sec(x^2+2)	$y = \sec (x^{2} + 2)$
82662	Find the Inflection Points	-1/6x^4+x^3+18x^2	$- \frac{1}{6} x^{4} + x^{3} + 18 x^{2}$
82663	Find the Absolute Max and Min over the Interval	f(x)=x-(x) , 0<=x<=1	$f (x) = x - (x)$ , $0 \leq x \leq 1$
82664	Find the Tangent Line at (1/2,16)	f(t)=t^-4 ;, (1/2,16)	$f (t) = t^{- 4}$ ;, $(\frac{1}{2}, 16)$
82665	Find the Derivative - d/dx	Derivar y=(5/(x^4)+3/(x^3))(2x^5-4x^2)	Derivar $y = (\frac{5}{x^{4}} + \frac{3}{x^{3}}) (2 x^{5} - 4 x^{2})$
82666	Find the Derivative of the Integral	integral from 0 to natural log of 4x of sin(2e^t) with respect to t	$\int_{0}^{\ln (4 x)} \sin (2 e^{t}) d t$
82667	Find dy/dx	-y-xy-5x^3=0	$- y - x y - 5 x^{3} = 0$
82668	Evaluate the Integral	integral of (5/x+e^x) with respect to x	$\int (\frac{5}{x} + e^{x}) d x$
82669	Evaluate the Integral	integral from 0 to pi/4 of xsin(2x) with respect to x	$\int_{0}^{\frac{π}{4}} x \sin (2 x) d x$
82670	Find the Antiderivative	f(x)=3/4x^2	$f (x) = \frac{3}{4} x^{2}$
82671	Find the Derivative - d/dx	d/(dx)( integral from 0 to x^3 of natural log of t^2+1 with respect to t)	$\frac{d}{d x} (\int_{0}^{x^{3}} \ln (t^{2} + 1) d t)$
82672	Find dy/dt	y=3t^7-6t^4+8t^3-12^t+18	$y = 3 t^{7} - 6 t^{4} + 8 t^{3} - 12^{t} + 18$
82673	Find the Antiderivative	1/(3 cube root of x)	$\frac{1}{3 \sqrt[3]{x}}$
82674	Find the Derivative - d/dx	(x^2)/(2y)+(3y^2)/x	$\frac{x^{2}}{2 y} + \frac{3 y^{2}}{x}$
82675	Find the Derivative - d/dx	y=2x^(1/3)	$y = 2 x^{\frac{1}{3}}$
82676	Integrate By Parts	integral of 1/x with respect to x	$\int \frac{1}{x} d x$
82677	Find the Derivative - d/dx	(x^2+y^2+z^2)^(-1/2)	${(x^{2} + y^{2} + z^{2})}^{- \frac{1}{2}}$
82678	Find the Antiderivative	f(x)=2x+e^(2x)	$f (x) = 2 x + e^{2 x}$
82679	Evaluate the Integral	integral of square root of x^3 natural log of x with respect to x	$\int \sqrt{x^{3}} \ln (x) d x$
82680	Evaluate the Limit	limit as x approaches 2 of (x+ square root of 2)/2	$lim_{x \to 2} \frac{x + \sqrt{2}}{2}$
82681	Find the Derivative - d/dx	((cos(2x))/x)^3	${(\frac{\cos (2 x)}{x})}^{3}$
82682	Evaluate the Integral	integral from 1/2 to 1 of (x^-3-5) with respect to x	$\int_{\frac{1}{2}}^{1} (x^{- 3} - 5) d x$
82683	Find dy/dx	-x^3+y^3-xy=0	$- x^{3} + y^{3} - x y = 0$
82684	Evaluate the Integral	integral of ((2x^3+3x)^2)/(x^2) with respect to x	$\int \frac{{(2 x^{3} + 3 x)}^{2}}{x^{2}} d x$
82685	Find dy/dx	y = square root of 9xcos(x)	$y = \sqrt{9 x} \cos (x)$
82686	Find the Antiderivative	f(x)=3cos(x)-x	$f (x) = 3 \cos (x) - x$
82687	Evaluate the Limit	limit as x approaches 0 of (x^4-4x^3+x^2)/(x^3+x^2+x)	$lim_{x \to 0} \frac{x^{4} - 4 x^{3} + x^{2}}{x^{3} + x^{2} + x}$
82688	Evaluate the Integral	integral of 6(sin(2x))/(sin(x)) with respect to x	$\int 6 \frac{\sin (2 x)}{\sin (x)} d x$
82689	Find Where Increasing/Decreasing	f(x)=(x^2-4)^(2/3)	$f (x) = {(x^{2} - 4)}^{\frac{2}{3}}$
82690	Evaluate the Limit	limit as x approaches infinity of 1+2x^2-x^3	$lim_{x \to \infty} 1 + 2 x^{2} - x^{3}$
82691	Find the Concavity	-2/5x^6+5x^4	$- \frac{2}{5} x^{6} + 5 x^{4}$
82692	Find the Local Maxima and Minima	f(x) = square root of x^3+3x^2	$f (x) = \sqrt{x^{3} + 3 x^{2}}$
82693	Evaluate the Integral	integral of (x^5-4x^-4-6x^3+2x) with respect to x	$\int (x^{5} - 4 x^{- 4} - 6 x^{3} + 2 x) d x$
82694	Evaluate the Integral	integral of (x^3 natural log of (2+x^4)^2)/(2+x^4) with respect to x	$\int \frac{x^{3} \ln ({(2 + x^{4})}^{2})}{2 + x^{4}} d x$
82695	Find the Derivative - d/dx	2(x^2-1)	$2 (x^{2} - 1)$
82696	Evaluate the Integral	integral from -4 to 4 of [(32-x^2)-(x^2)] with respect to x	$\int_{- 4}^{4} [(32 - x^{2}) - (x^{2})] d x$
82697	Find the Integral	(3x+4)^2dx	${(3 x + 4)}^{2} d x$
82698	Find the Inflection Points	f(x)=x^2+8/x	$f (x) = x^{2} + \frac{8}{x}$
82699	Find Where Increasing/Decreasing	f(x) = log base 5 of x-1-1	$f (x) = \log_{5} (x - 1) - 1$
82700	Find dy/dx	2x^3y-y-x^4=-1	$2 x^{3} y - y - x^{4} = - 1$