Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
67901	Evaluate the Integral	integral from 0 to 1 of 12/(4x^2+5x+1) with respect to x	$\int_{0}^{1} \frac{12}{4 x^{2} + 5 x + 1} d x$
67902	Evaluate the Integral	integral of (x^2+1) with respect to x	$\int (x^{2} + 1) d x$
67903	Find dy/dx	y^2=x^2+2x	$y^{2} = x^{2} + 2 x$
67904	Evaluate the Limit	limit as x approaches -8 of ( square root of 1-x-3)/(2+ cube root of x)	$lim_{x \to - 8} \frac{\sqrt{1 - x} - 3}{2 + \sqrt[3]{x}}$
67905	Find the Derivative - d/dx	(1-x^2)	$(1 - x^{2})$
67906	Find the Derivative - d/dy	(xy)/(x-y)	$\frac{x y}{x - y}$
67907	Find the Derivative - d/dx	( square root of x)	$(\sqrt{x})$
67908	Evaluate the Limit	limit as x approaches 0 from the right of (1+x)^(cot(x))	$lim_{x \to 0^{+}} {(1 + x)}^{\cot (x)}$
67909	Find the Derivative - d/dx	e^x+x	$e^{x} + x$
67910	Find dy/dx	y^2-2xy=16	$y^{2} - 2 x y = 16$
67911	Integrate By Parts	integral of sec(x)^3 with respect to x	$\int \sec^{3} (x) d x$
67912	Evaluate the Integral	integral of (cos(x)-sin(x)) with respect to x	$\int (\cos (x) - \sin (x)) d x$
67913	Find the Derivative - d/dθ	1-cos(theta)	$1 - \cos (θ)$
67914	Find the Derivative - d/dθ	thetasin(theta)	$θ \sin (θ)$
67915	Solve the Differential Equation	(dP)/(dt)=P-P^2	$\frac{d P}{d t} = P - P^{2}$
67916	Find dy/dx	5x^3=-3xy+2	$5 x^{3} = - 3 x y + 2$
67917	Evaluate the Limit	limit as x approaches infinity of ( square root of x^2+1)/(x+1)	$lim_{x \to \infty} \frac{\sqrt{x^{2} + 1}}{x + 1}$
67918	Evaluate the Summation	sum from i=1 to 5 of (2-i)/4	$\sum_{i = 1}^{5} \frac{2 - i}{4}$
67919	Find the Derivative - d/dx	-(2x)/((1+x^2)^2)	$- \frac{2 x}{{(1 + x^{2})}^{2}}$
67920	Find dy/dx	y = square root of 15+x^2	$y = \sqrt{15 + x^{2}}$
67921	Find Where Increasing/Decreasing	f(x) = square root of 49-x^2	$f (x) = \sqrt{49 - x^{2}}$
67922	Find the Center and Radius	9y^2-25x^2-100x-108y-1=0	$9 y^{2} - 25 x^{2} - 100 x - 108 y - 1 = 0$
67923	Find the Derivative - d/dx	(xy)/(x+y)	$\frac{x y}{x + y}$
67924	Find ds/dt	s=4t^3-3t^4	$s = 4 t^{3} - 3 t^{4}$
67925	Find dy/dx	y=e^(x/4)	$y = e^{\frac{x}{4}}$
67926	Find the Derivative - d/dx	d/(dx)(sin(x)x^2)	$\frac{d}{d x} (\sin (x) x^{2})$
67927	Evaluate the Integral	integral of ( fourth root of x^3+1) with respect to x	$\int (\sqrt[4]{x^{3}} + 1) d x$
67928	Find dy/dx	y=x+1/x	$y = x + \frac{1}{x}$
67929	Evaluate from the Left	limit as x approaches 0 of x/(\|x\|)	$lim_{x \to 0} \frac{x}{\| x \|}$
67930	Find the Derivative - d/dx	d/(dx)(- natural log of x+x^2)	$\frac{d}{d x} (- \ln (x) + x^{2})$
67931	Solve the Differential Equation	(dy)/(dx)=(2y)/x	$\frac{d y}{d x} = \frac{2 y}{x}$
67932	Evaluate the Integral	integral of (3x^2+2x+1) with respect to x	$\int (3 x^{2} + 2 x + 1) d x$
67933	Evaluate the Limit	limit as x approaches 2 of (x^2-4)/(3- square root of x+7)	$lim_{x \to 2} \frac{x^{2} - 4}{3 - \sqrt{x + 7}}$
67934	Evaluate the Integral	integral from 1 to infinity of 1/( square root of x) with respect to x	$\int_{1}^{\infty} \frac{1}{\sqrt{x}} d x$
67935	Evaluate the Limit	limit as x approaches a of f(x)=L	$lim_{x \to a} f (x) = L$
67936	Find dy/dx	y=( natural log of x)/(x^5)	$y = \frac{\ln (x)}{x^{5}}$
67937	Find the Derivative - d/dx	x^2+y^2=(2x^2+2y^2-x)^2	$x^{2} + y^{2} = {(2 x^{2} + 2 y^{2} - x)}^{2}$
67938	Find the Antiderivative	f(x)=2e^x-8x	$f (x) = 2 e^{x} - 8 x$
67939	Evaluate Using L'Hospital's Rule	limit as X approaches 0 of (cos(x)-1+1/2x^2)/(2x^4)	$lim_{X \to 0} \frac{\cos (x) - 1 + \frac{1}{2} x^{2}}{2 x^{4}}$
67940	Evaluate the Integral	integral of (theta^2+sec(theta)^2) with respect to theta	$\int (θ^{2} + \sec^{2} (θ)) d θ$
67941	Find dx/dy	y=sin(x)^2	$y = \sin^{2} (x)$
67942	Evaluate the Integral	integral from 1 to 9 of (4+x^2)/( square root of x) with respect to x	$\int_{1}^{9} \frac{4 + x^{2}}{\sqrt{x}} d x$
67943	Find dy/dx	cos(4x-y)=x+y	$\cos (4 x - y) = x + y$
67944	Find dy/dx	x^2-xy+y^2=7	$x^{2} - x y + y^{2} = 7$
67945	Find the Derivative - d/dx	d/(dx)(x^-4)	$\frac{d}{d x} (x^{- 4})$
67946	Evaluate the Integral	integral from 3 to 6 of (x^2-2x) with respect to x	$\int_{3}^{6} (x^{2} - 2 x) d x$
67947	Find the Slope	f(x)=2x-3	$f (x) = 2 x - 3$
67948	Find the Center and Radius	4y^2-49x^2-392x+16y-964=0	$4 y^{2} - 49 x^{2} - 392 x + 16 y - 964 = 0$
67949	Find dy/dx	x/(y^3)=1	$\frac{x}{y^{3}} = 1$
67950	Evaluate the Integral	integral from 0 to 1/( square root of 3) of 2(t^2-1)/(t^4-1) with respect to t	$\int_{0}^{\frac{1}{\sqrt{3}}} 2 \frac{t^{2} - 1}{t^{4} - 1} d t$
67951	Evaluate the Limit	limit as h approaches 0 of ((x+h)^2+4(x+h)-x^2-4x)/h	$lim_{h \to 0} \frac{{(x + h)}^{2} + 4 (x + h) - x^{2} - 4 x}{h}$
67952	Find the Derivative - d/dx	d/(dx)(e^xcos(x))	$\frac{d}{d x} (e^{x} \cos (x))$
67953	Find the Tangent Line at (π,π)	y=x+sin(x) , (pi,pi)	$y = x + \sin (x)$ , $(π, π)$
67954	Evaluate the Limit	limit as x approaches infinity of (2 square root of 5x)/(5x)	$lim_{x \to \infty} \frac{2 \sqrt{5 x}}{5 x}$
67955	Find the Derivative - d/dθ	3sin(theta)	$3 \sin (θ)$
67956	Evaluate the Limit	limit as x approaches -5 of ((x+1)^2)/(8-x)	$lim_{x \to - 5} \frac{{(x + 1)}^{2}}{8 - x}$
67957	Find dθ/dy	y=sec(theta)tan(theta)	$y = \sec (θ) \tan (θ)$
67958	Evaluate the Integral	integral of (8x^5-5x^4-4x^3-6x^2-2x-3) with respect to x	$\int (8 x^{5} - 5 x^{4} - 4 x^{3} - 6 x^{2} - 2 x - 3) d x$
67959	Find the Antiderivative	g(x)=(x^3)/( square root of 1-x^4)	$g (x) = \frac{x^{3}}{\sqrt{1 - x^{4}}}$
67960	Find the Derivative - d/dx	(x^2+1)/(2x^2-3x)	$\frac{x^{2} + 1}{2 x^{2} - 3 x}$
67961	Integrate By Parts	integral of e^( square root of x) with respect to x	$\int e^{\sqrt{x}} d x$
67962	Find the Derivative - d/dx	y=(4x)/(e^x)	$y = \frac{4 x}{e^{x}}$
67963	Find the Derivative Using Chain Rule - d/dθ	y=e^(tan(theta))	$y = e^{\tan (θ)}$
67964	Evaluate the Limit	limit as x approaches a of (f(x))/(g(x))	$lim_{x \to a} \frac{f (x)}{g (x)}$
67965	Find the Derivative - d/dx	x( natural log of x)^2	$x \ln^{2} (x)$
67966	Integrate Using Trig Substitution	integral of (x^3)/( square root of x^2+9) with respect to x	$\int \frac{x^{3}}{\sqrt{x^{2} + 9}} d x$
67967	Find Where Increasing/Decreasing	e^(-x^2)	$e^{- x^{2}}$
67968	Evaluate the Integral	integral from 0 to ( square root of 2)/2 of 1/( square root of 1-r^2) with respect to r	$\int_{0}^{\frac{\sqrt{2}}{2}} \frac{1}{\sqrt{1 - r^{2}}} d r$
67969	Find the Derivative - d/dx	y=pix	$y = π x$
67970	Find Where Increasing/Decreasing	f(x)=xe^(-x)	$f (x) = x e^{- x}$
67971	Find dy/dx	y=x^2 natural log of x	$y = x^{2} \ln (x)$
67972	Evaluate the Integral	integral from -1 to 2 of (f(x)+6x) with respect to x=20	$\int_{- 1}^{2} (f (x) + 6 x) d x = 20$
67973	Find the Center and Radius	x^2+y^2=r^2	$x^{2} + y^{2} = r^{2}$
67974	Integrate Using u-Substitution	integral of (( natural log of x)^2)/x with respect to x	$\int \frac{\ln^{2} (x)}{x} d x$
67975	Find the Maximum/Minimum Value	f(x)=x(x+7)	$f (x) = x (x + 7)$
67976	Evaluate the Limit	limit as x approaches 0 of square root of x=0	$lim_{x \to 0} \sqrt{x} = 0$
67977	Evaluate the Limit	limit as x approaches infinity of (x^4+x^3)/(12x^3+128)	$lim_{x \to \infty} \frac{x^{4} + x^{3}}{12 x^{3} + 128}$
67978	Integrate By Parts	integral of sin(x)^2 with respect to x	$\int \sin^{2} (x) d x$
67979	Evaluate the Limit	limit as x approaches infinity of (2x+3)/(x+ cube root of x)	$lim_{x \to \infty} \frac{2 x + 3}{x + \sqrt[3]{x}}$
67980	Find the Derivative - d/dx	e^xf(x)	$e^{x} f (x)$
67981	Find the Derivative - d/dx	-1/( square root of x)	$- \frac{1}{\sqrt{x}}$
67982	Evaluate the Integral	integral of (3/4x^4+2x^2+1) with respect to x	$\int (\frac{3}{4} x^{4} + 2 x^{2} + 1) d x$
67983	Find the Center and Radius	-9x^2+4y^2-36x-16y-164=0	$- 9 x^{2} + 4 y^{2} - 36 x - 16 y - 164 = 0$
67984	Find the Derivative - d/dx	y=(3x-1)(2x+5)	$y = (3 x - 1) (2 x + 5)$
67985	Find the Derivative - d/dx	d/(dx)(ax^2+bx+c)	$\frac{d}{d x} (a x^{2} + b x + c)$
67986	Find dy/dx	3y-6=12x^2-6y^3	$3 y - 6 = 12 x^{2} - 6 y^{3}$
67987	Use Logarithmic Differentiation to Find the Derivative	y=sec(theta)tan(theta)	$y = \sec (θ) \tan (θ)$
67988	Find dy/dx	y=1/(x^4)	$y = \frac{1}{x^{4}}$
67989	Find dr/dh	a=pir square root of r^2+h^2	$a = π r \sqrt{r^{2} + h^{2}}$
67990	Evaluate the Summation	sum from i=1 to 15 of (i^2+2)^2	$\sum_{i = 1}^{15} {(i^{2} + 2)}^{2}$
67991	Find the Derivative - d/dx	y/(x^2+y^2)	$\frac{y}{x^{2} + y^{2}}$
67992	Evaluate the Limit	limit as x approaches 0 of (cos(4x)-1)/(xtan(2x))	$lim_{x \to 0} \frac{\cos (4 x) - 1}{x \tan (2 x)}$
67993	Find the Derivative - d/dx	d/(dx)(-1/(x^5)-1/(x^3)+1/x)	$\frac{d}{d x} (- \frac{1}{x^{5}} - \frac{1}{x^{3}} + \frac{1}{x})$
67994	Evaluate the Integral	integral of (5-x) with respect to x	$\int (5 - x) d x$
67995	Evaluate the Integral	integral of x^2(1-x^3) with respect to x	$\int x^{2} (1 - x^{3}) d x$
67996	Find the Center and Radius	x^2-25y^2-14x+100y-76=0	$x^{2} - 25 y^{2} - 14 x + 100 y - 76 = 0$
67997	Find dy/dx	y=e^(-2x)	$y = e^{- 2 x}$
67998	Find the Tangent Line at (2,3)	y=x^3-3x+1 , (2,3)	$y = x^{3} - 3 x + 1$ , $(2, 3)$
67999	Find the Derivative - d/dθ	sin(theta)cos(theta)	$\sin (θ) \cos (θ)$
68000	Find the Derivative - d/dv	y=(v^3-2v square root of v)/v	$y = \frac{v^{3} - 2 v \sqrt{v}}{v}$