Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
70001	Evaluate Using L'Hospital's Rule	limit as x approaches 11 from the right of 110/(6x^2-102x+396)-(2x)/(6x-66)	$lim_{x \to 11^{+}} \frac{110}{6 x^{2} - 102 x + 396} - \frac{2 x}{6 x - 66}$
70002	Use Logarithmic Differentiation to Find the Derivative	y=x^(1/x)	$y = x^{\frac{1}{x}}$
70003	Evaluate the Limit	limit as x approaches infinity of x/(1+x^2)	$lim_{x \to \infty} \frac{x}{1 + x^{2}}$
70004	Evaluate the Integral	integral of (theta^8+sec(theta)^2) with respect to theta	$\int (θ^{8} + \sec^{2} (θ)) d θ$
70005	Evaluate the Integral	integral of 3x^2sec(x^3)^2 with respect to x	$\int 3 x^{2} \sec^{2} (x^{3}) d x$
70006	Find the Derivative - d/dx	cube root of (x^2-1)^2	$\sqrt[3]{{(x^{2} - 1)}^{2}}$
70007	Find the Maximum/Minimum Value	f(x)=2cos(1/3x)-2	$f (x) = 2 \cos (\frac{1}{3} x) - 2$
70008	Evaluate the Integral	integral from 5 to infinity of 1/((x-4)^(3/2)) with respect to x	$\int_{5}^{\infty} \frac{1}{{(x - 4)}^{\frac{3}{2}}} d x$
70009	Find dy/dx	y=tan(3x^2)	$y = \tan (3 x^{2})$
70010	Evaluate the Limit	limit as x approaches infinity of (x+1)/(2x^2+2x+1)	$lim_{x \to \infty} \frac{x + 1}{2 x^{2} + 2 x + 1}$
70011	Find dy/dx	x^2-3xy=10	$x^{2} - 3 x y = 10$
70012	Find dx/dy	(x^2)/(a^2)-(y^2)/(b^2)=1	$\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$
70013	Find dy/dx	y=(x^4)/( square root of 1-2x)	$y = \frac{x^{4}}{\sqrt{1 - 2 x}}$
70014	Find the Derivative - d/dx	d/(dx)(-4x^4-x^-2-5)	$\frac{d}{d x} (- 4 x^{4} - x^{- 2} - 5)$
70015	Find the Derivative - d/dx	x/((1-x)^2)	$\frac{x}{{(1 - x)}^{2}}$
70016	Find the Derivative - d/dx	cot(3x^4-2x^3-3)	$\cot (3 x^{4} - 2 x^{3} - 3)$
70017	Evaluate the Limit	limit as x approaches 1 of ( cube root of x-1)/(x-1)	$lim_{x \to 1} \frac{\sqrt[3]{x - 1}}{x - 1}$
70018	Find the Local Maxima and Minima	f(x)=x^(1/3)(x+3)^(2/3)	$f (x) = x^{\frac{1}{3}} {(x + 3)}^{\frac{2}{3}}$
70019	Find dy/dx	y=arccos(x^2)	$y = \arccos (x^{2})$
70020	Find dy/dx	xy+2x+3x^2=4	$x y + 2 x + 3 x^{2} = 4$
70021	Find the Derivative - d/dx	e^x+e^x	$e^{x} + e^{x}$
70022	Find the Derivative - d/dθ	3cos(theta)	$3 \cos (θ)$
70023	Integrate Using u-Substitution	integral of 1/(x natural log of x) with respect to x	$\int \frac{1}{x \ln (x)} d x$
70024	Find dy/dx	y=x^2-2x	$y = x^{2} - 2 x$
70025	Evaluate the Limit	limit as x approaches infinity of cos(1/x)-1^x	$lim_{x \to \infty} \cos (\frac{1}{x}) - 1^{x}$
70026	Evaluate the Limit	limit as x approaches negative infinity of -e^(-1/x)	$lim_{x \to - \infty} - e^{- \frac{1}{x}}$
70027	Find the Tangent Line at (7,4)	f(x)=((x+1)/(x-3))^2 , (7,4)	$f (x) = {(\frac{x + 1}{x - 3})}^{2}$ , $(7, 4)$
70028	Integrate Using u-Substitution	integral of x/( square root of 1-4x^2) with respect to x	$\int \frac{x}{\sqrt{1 - 4 x^{2}}} d x$
70029	Find dy/dx	y(x^2+4)=8	$y (x^{2} + 4) = 8$
70030	Find dz/dx	z=xy	$z = x y$
70031	Find the Derivative - d/dy	y^2x	$y^{2} x$
70032	Find the Integral	square root of x^2+1	$\sqrt{x^{2} + 1}$
70033	Find dy/dx	y=sin(3x)	$y = \sin (3 x)$
70034	Find the Derivative - d/dx	(cos(x))/( natural log of x)	$\frac{\cos (x)}{\ln (x)}$
70035	Find the Derivative - d/dx	x^2-1/2cos(x)	$x^{2} - \frac{1}{2} \cos (x)$
70036	Find the Derivative - d/dx	y=(x^2)/(3x-1)	$y = \frac{x^{2}}{3 x - 1}$
70037	Evaluate the Limit	limit as x approaches infinity of (x^3+5x)/(2x^3-x^2+4)	$lim_{x \to \infty} \frac{x^{3} + 5 x}{2 x^{3} - x^{2} + 4}$
70038	Find the Tangent Line at (0,3)	y=3e^x+x , (0,3)	$y = 3 e^{x} + x$ , $(0, 3)$
70039	Evaluate the Integral	integral of (sin(x)+7cos(x)-1) with respect to x	$\int (\sin (x) + 7 \cos (x) - 1) d x$
70040	Find the Derivative - d/dx	x^(1/2)y^(1/2)	$x^{\frac{1}{2}} y^{\frac{1}{2}}$
70041	Find the Derivative - d/dx	(x^2+mx+1)/(x+m)	$\frac{x^{2} + m x + 1}{x + m}$
70042	Evaluate the Integral	e^( integral of 3/x with respect to x)	$e^{\int \frac{3}{x} d x}$
70043	Evaluate the Limit	limit as w approaches a of (a^2-w^2)/(a-w)	$lim_{w \to a} \frac{a^{2} - w^{2}}{a - w}$
70044	Find the Derivative - d/dy	x natural log of y	$x \ln (y)$
70045	Evaluate the Limit	limit as x approaches 0 from the left of x^2-1/x	$lim_{x \to 0^{-}} x^{2} - \frac{1}{x}$
70046	Evaluate the Limit	limit as x approaches 2 of x^2f(x)	$lim_{x \to 2} x^{2} f (x)$
70047	Find the Tangent Line at (-2,-8)	f(x)=x^3 at (-2,-8)	$f (x) = x^{3}$ at $(- 2, - 8)$
70048	Evaluate the Integral	integral from 0 to 1 of (4x)/( square root of 1-x^4) with respect to x	$\int_{0}^{1} \frac{4 x}{\sqrt{1 - x^{4}}} d x$
70049	Find dy/dx	y = fifth root of (5x)/(3x-2)	$y = \sqrt[5]{\frac{5 x}{3 x - 2}}$
70050	Evaluate the Integral	integral of (e^(5x))/( square root of 1+e^(5x)) with respect to x	$\int \frac{e^{5 x}}{\sqrt{1 + e^{5 x}}} d x$
70051	Find the Derivative - d/dx	y=3x^(2/3)-4x^(1/2)-2	$y = 3 x^{\frac{2}{3}} - 4 x^{\frac{1}{2}} - 2$
70052	Find the Derivative - d/dx	e^x-e^(-x)-2x	$e^{x} - e^{- x} - 2 x$
70053	Find the Slope of the Tangent Line at (1,3)	y=4x-x^2 , (1,3)	$y = 4 x - x^{2}$ , $(1, 3)$
70054	Find the Derivative - d/dθ	1+sin(theta)	$1 + \sin (θ)$
70055	Find the Absolute Max and Min over the Interval	h(x)=e^(x^2-4) on -2 , 2	$h (x) = e^{x^{2} - 4}$ on $- 2$ , $2$
70056	Evaluate the Integral	integral from -4 to 4 of (16-x^2) with respect to x	$\int_{- 4}^{4} (16 - x^{2}) d x$
70057	Find the Derivative - d/dx	(3x^2-5x)e^x	$(3 x^{2} - 5 x) e^{x}$
70058	Evaluate the Integral	integral of ((x^6-5x)/(x^2)) with respect to x	$\int (\frac{x^{6} - 5 x}{x^{2}}) d x$
70059	Find Where Increasing/Decreasing	f(x)=x^3-1	$f (x) = x^{3} - 1$
70060	Evaluate the Integral	integral of (cos(x)+csc(x)^2) with respect to x	$\int (\cos (x) + \csc^{2} (x)) d x$
70061	Evaluate the Limit	limit as x approaches infinity of 100/(x^2+5)	$lim_{x \to \infty} \frac{100}{x^{2} + 5}$
70062	Find dy/dx	y=1/2x^(4/5)-3/(x^5)	$y = \frac{1}{2} x^{\frac{4}{5}} - \frac{3}{x^{5}}$
70063	Find the Maximum/Minimum Value	m(x)=1/2(x-2)^2	$m (x) = \frac{1}{2} {(x - 2)}^{2}$
70064	Find the Antiderivative	(x+1)(x-1)	$(x + 1) (x - 1)$
70065	Find dy/dx	9e^(x^3y^3)=y^2	$9 e^{x^{3} y^{3}} = y^{2}$
70066	Find dy/dx	y=(2-x)/(3x+1)	$y = \frac{2 - x}{3 x + 1}$
70067	Evaluate the Limit	limit as x approaches infinity of (3x^4-2x^2+7)/(5x^3+x-3)	$lim_{x \to \infty} \frac{3 x^{4} - 2 x^{2} + 7}{5 x^{3} + x - 3}$
70068	Find the Second Derivative	y=(x^2+x+1)^2	$y = {(x^{2} + x + 1)}^{2}$
70069	Find the Derivative - d/dt	tgx	$t g x$
70070	Evaluate the Integral	integral from a to b of coth(x) with respect to x	$\int_{a}^{b} \coth (x) d x$
70071	Solve the Differential Equation	y(dy)/(dx)=x	$y \frac{d y}{d x} = x$
70072	Integrate Using Partial Fractions	integral of (x+4)/(x^3+3x^2+2x) with respect to x	$\int \frac{x + 4}{x^{3} + 3 x^{2} + 2 x} d x$
70073	Find dx/dy	x^3-xy+y^2=7	$x^{3} - x y + y^{2} = 7$
70074	Evaluate the Limit	limit as x approaches infinity of (x^2)/(2x-1)-(x^2)/(2x+1)	$lim_{x \to \infty} \frac{x^{2}}{2 x - 1} - \frac{x^{2}}{2 x + 1}$
70075	Evaluate the Integral	integral from -2 to 0 of (x^2+x) with respect to x	$\int_{- 2}^{0} (x^{2} + x) d x$
70076	Find dy/dx	y+cos(y)=x+1	$y + \cos (y) = x + 1$
70077	Find dy/dt	y=te^(-t)	$y = t e^{- t}$
70078	Find the Derivative - d/dy	(dy)/y	$\frac{d y}{y}$
70079	Evaluate the Limit	limit as x approaches -3 from the left of (x+3)/(x^2+x-6)	$lim_{x \to {(- 3)}^{-}} \frac{x + 3}{x^{2} + x - 6}$
70080	Find the Tangent Line at (-2,-4)	h(x)=(x^2-2)(x^3-3x) , (-2,-4)	$h (x) = (x^{2} - 2) (x^{3} - 3 x)$ , $(- 2, - 4)$
70081	Find the Derivative - d/dx	cube root of (x^2+1)/(x^2-1)	$\sqrt[3]{\frac{x^{2} + 1}{x^{2} - 1}}$
70082	Evaluate the Limit	limit as x approaches c of f(x)g(x)	$lim_{x \to c} f (x) g (x)$
70083	Find the Tangent Line at (-1,1)	f(x)=-x^3 at (-1,1)	$f (x) = - x^{3}$ at $(- 1, 1)$
70084	Evaluate the Derivative at a=3	f(x) = square root of 5x+1 , a=3	$f (x) = \sqrt{5 x + 1}$ , $a = 3$
70085	Evaluate the Integral	integral from 0 to 3 of (5x^2-4x) with respect to x	$\int_{0}^{3} (5 x^{2} - 4 x) d x$
70086	Find the Derivative - d/dx	sin(x)*sin(x)	$\sin (x) \cdot \sin (x)$
70087	Find the Derivative - d/dx	y=xG(x)	$y = x G (x)$
70088	Evaluate the Integral	integral from -4 to 2 of [f(x)+2x+3] with respect to x	$\int_{- 4}^{2} [f (x) + 2 x + 3] d x$
70089	Evaluate the Limit	limit as x approaches 0 of ( square root of 1+x+x^2-1)/x	$lim_{x \to 0} \frac{\sqrt{1 + x + x^{2}} - 1}{x}$
70090	Evaluate the Integral	integral from negative infinity to infinity of 1/(x^2+1) with respect to x	$\int_{- \infty}^{\infty} \frac{1}{x^{2} + 1} d x$
70091	Find dy/dx	x^2+y^2=xy	$x^{2} + y^{2} = x y$
70092	Find the Derivative - d/dx	y=(5x)/3	$y = \frac{5 x}{3}$
70093	Find dy/dx	x^2+2xy+4y^2=12	$x^{2} + 2 x y + 4 y^{2} = 12$
70094	Evaluate the Integral	integral of 5^tsin(5^t) with respect to t	$\int 5^{t} \sin (5^{t}) d t$
70095	Evaluate the Limit	limit as x approaches 4 of (2/x+1/2)(x^2-4/x)	$lim_{x \to 4} (\frac{2}{x} + \frac{1}{2}) (x^{2} - \frac{4}{x})$
70096	Find the Derivative - d/dθ	(sin(theta))/theta	$\frac{\sin (θ)}{θ}$
70097	Solve the Differential Equation	xe^ydy+(x^2+1)/ydx=0	$x e^{y} d y + \frac{x^{2} + 1}{y} d x = 0$
70098	Evaluate the Limit	limit as r approaches 4 of (2/r+1/2)(r^2-4/r)	$lim_{r \to 4} (\frac{2}{r} + \frac{1}{2}) (r^{2} - \frac{4}{r})$
70099	Evaluate the Limit	limit as x approaches 5 of (3-x^2)/(2x+1)	$lim_{x \to 5} \frac{3 - x^{2}}{2 x + 1}$
70100	Integrate Using Trig Substitution	integral of 1/(x square root of x^2+36) with respect to x	$\int \frac{1}{x \sqrt{x^{2} + 36}} d x$