Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
70501	Evaluate the Limit	limit as x approaches -1/2 from the right of (6x^2+x-1)/(4x^2-4x-3)	$lim_{x \to {(- \frac{1}{2})}^{+}} \frac{6 x^{2} + x - 1}{4 x^{2} - 4 x - 3}$
70502	Integrate By Parts	integral of ( natural log of x)/x with respect to x	$\int \frac{\ln (x)}{x} d x$
70503	Evaluate the Limit	limit as x approaches c of 64/48	$lim_{x \to c} \frac{64}{48}$
70504	Find dx/dy	y=e^(-x)	$y = e^{- x}$
70505	Find the Third Derivative	y = square root of x	$y = \sqrt{x}$
70506	Find the Second Derivative	y = natural log of 3x^2+3x+6	$y = \ln (3 x^{2} + 3 x + 6)$
70507	Evaluate the Limit	limit as x approaches pi/4 of (2cos(x)^2-1)/(cos(x)-sin(x))	$lim_{x \to \frac{π}{4}} \frac{2 \cos^{2} (x) - 1}{\cos (x) - \sin (x)}$
70508	Find Where Increasing/Decreasing	f(x)=2	$f (x) = 2$
70509	Find the Derivative - d/dx	(d^2)/(dx^2)(10/(3x^3))	$\frac{d^{2}}{d x^{2}} (\frac{10}{3 x^{3}})$
70510	Evaluate the Limit	limit as x approaches 0 of (x^3)/x	$lim_{x \to 0} \frac{x^{3}}{x}$
70511	Evaluate the Integral	integral from 0 to pi/2 of cos(x)^3 with respect to x	$\int_{0}^{\frac{π}{2}} \cos^{3} (x) d x$
70512	Find the Derivative - d/da	square root of a^2-x^2	$\sqrt{a^{2} - x^{2}}$
70513	Find dy/dx	y=(2x+5) square root of 4x-1	$y = (2 x + 5) \sqrt{4 x - 1}$
70514	Evaluate the Limit	limit as x approaches infinity of (4x^2+1)/(5-x^2)	$lim_{x \to \infty} \frac{4 x^{2} + 1}{5 - x^{2}}$
70515	Evaluate the Integral	integral of (theta^6+sec(theta)^2) with respect to theta	$\int (θ^{6} + \sec^{2} (θ)) d θ$
70516	Find dθ/dy	y=e^(tan(theta))	$y = e^{\tan (θ)}$
70517	Find the Derivative of the Integral	integral from pi/3 to pi/2 of (cot(x))/( square root of 1+sin(x)^2) with respect to x	$\int_{\frac{π}{3}}^{\frac{π}{2}} \frac{\cot (x)}{\sqrt{1 + \sin^{2} (x)}} d x$
70518	Find dx/dy	y=x^2 natural log of x	$y = x^{2} \ln (x)$
70519	Evaluate the Integral	integral from 0 to 11 of 1/( cube root of 11-x) with respect to x	$\int_{0}^{11} \frac{1}{\sqrt[3]{11 - x}} d x$
70520	Evaluate the Limit	limit as x approaches 0 of (1-e^(2x))/(1-e^x)	$lim_{x \to 0} \frac{1 - e^{2 x}}{1 - e^{x}}$
70521	Find dy/dx	y^3-xy=2	$y^{3} - x y = 2$
70522	Find the Derivative - d/dx	y=sec(3x)	$y = \sec (3 x)$
70523	Find the Derivative - d/dx	1/(2 cube root of x^2)	$\frac{1}{2 \sqrt[3]{x^{2}}}$
70524	Find the Derivative - d/dx	tan(3x^2)^2	$\tan^{2} (3 x^{2})$
70525	Find the Derivative - d/dx	-6/5x^4cos(x)	$- \frac{6}{5} x^{4} \cos (x)$
70526	Evaluate the Integral	integral from 4 to infinity of 1/(x^2+x) with respect to x	$\int_{4}^{\infty} \frac{1}{x^{2} + x} d x$
70527	Integrate Using Trig Substitution	integral of x^3 square root of 9-x^2 with respect to x	$\int x^{3} \sqrt{9 - x^{2}} d x$
70528	Find the Derivative - d/dx	3^(x/y)	$3^{\frac{x}{y}}$
70529	Find the Tangent Line at x=3	f(x) = square root of x^2+16 , x=3	$f (x) = \sqrt{x^{2} + 16}$ , $x = 3$
70530	Evaluate the Integral	integral of (x^3+ square root of x) with respect to x	$\int (x^{3} + \sqrt{x}) d x$
70531	Find dy/dx	x^2+2y^2+5x-2y-1=0	$x^{2} + 2 y^{2} + 5 x - 2 y - 1 = 0$
70532	Evaluate the Integral	integral of ((1- cube root of x)/(x^2))^(1/3) with respect to x	$\int {(\frac{1 - \sqrt[3]{x}}{x^{2}})}^{\frac{1}{3}} d x$
70533	Evaluate the Integral	integral of (2x+1)(x^2+x+1) with respect to x	$\int (2 x + 1) (x^{2} + x + 1) d x$
70534	Find the Second Derivative	3x^2y	$3 x^{2} y$
70535	Find the Derivative - d/dx	6x^3 square root of xcsc(x)	$6 x^{3} \sqrt{x} \csc (x)$
70536	Evaluate the Integral	integral from -1 to 2 of (f(x)+6x) with respect to x=18	$\int_{- 1}^{2} (f (x) + 6 x) d x = 18$
70537	Integrate Using Trig Substitution	integral of 1/(x square root of 9x^2+4) with respect to x	$\int \frac{1}{x \sqrt{9 x^{2} + 4}} d x$
70538	Evaluate the Integral	integral of (3sec(4x)^2+3csc(4x)^2) with respect to x	$\int (3 \sec^{2} (4 x) + 3 \csc^{2} (4 x)) d x$
70539	Find dy/dx	y=(3x-1)/(2x+5)	$y = \frac{3 x - 1}{2 x + 5}$
70540	Find the Derivative - d/dx	3x square root of x	$3 x \sqrt{x}$
70541	Find the Slope	f(x)=x^2+1	$f (x) = x^{2} + 1$
70542	Evaluate the Limit	limit as theta approaches (3pi)/2 of sin(tan(cos(theta)))	$lim_{θ \to \frac{3 π}{2}} \sin (\tan (\cos (θ)))$
70543	Find the Relative Extrema	f(x)=x^2-6x	$f (x) = x^{2} - 6 x$
70544	Find the Antiderivative	x/( square root of x)	$\frac{x}{\sqrt{x}}$
70545	Find the Area Between the Curves	y=x^2 , y=2-x , y=0	$y = x^{2}$ , $y = 2 - x$ , $y = 0$
70546	Find the Normal Line at (0,5)	y=x^4+5e^x , (0,5)	$y = x^{4} + 5 e^{x}$ , $(0, 5)$
70547	Evaluate Using Summation Formulas	sum from k=1 to n of (6k(k-1))/(n^3)	$\sum_{k = 1}^{n} \frac{6 k (k - 1)}{n^{3}}$
70548	Find the Derivative - d/dx	sin(x)cos(y)	$\sin (x) \cos (y)$
70549	Find the Derivative - d/dθ	sin(theta/2)	$\sin (\frac{θ}{2})$
70550	Find dy/dx	(x+y)/(x-y)=x^2+y^2	$\frac{x + y}{x - y} = x^{2} + y^{2}$
70551	Solve the Differential Equation	(dy)/(dx)=3x^2y	$\frac{d y}{d x} = 3 x^{2} y$
70552	Evaluate the Integral	integral of (x^4+x+9) with respect to x	$\int (x^{4} + x + 9) d x$
70553	Find the Maximum/Minimum Value	y=sin(2x)	$y = \sin (2 x)$
70554	Find the Maximum/Minimum Value	f(x)=(x-2)^2-4	$f (x) = {(x - 2)}^{2} - 4$
70555	Evaluate the Limit	limit as x approaches infinity of (42x+5+49x^2)/(6x^3-9x^4)	$lim_{x \to \infty} \frac{42 x + 5 + 49 x^{2}}{6 x^{3} - 9 x^{4}}$
70556	Evaluate the Integral	integral of (x^2-2) square root of x^3-6x+3 with respect to x	$\int (x^{2} - 2) \sqrt{x^{3} - 6 x + 3} d x$
70557	Find the Derivative of the Integral	integral from a to b of (g(x))/(\|g(x)\| square root of (g(x))^2-1) with respect to x	$\int_{a}^{b} \frac{g (x)}{\| g (x) \| \sqrt{{(g (x))}^{2} - 1}} d x$
70558	Solve the Differential Equation	(dy)/(dx)=xe^(-y)	$\frac{d y}{d x} = x e^{- y}$
70559	Evaluate the Integral	integral of 1/(u square root of 3-u^2) with respect to u	$\int \frac{1}{u \sqrt{3 - u^{2}}} d u$
70560	Evaluate the Limit	limit as x approaches 0 from the right of x^(sin(x))	$lim_{x \to 0^{+}} x^{\sin (x)}$
70561	Find dy/dx	y=(x^2-4)/x	$y = \frac{x^{2} - 4}{x}$
70562	Find the Derivative - d/dx	y=1/(e^x)	$y = \frac{1}{e^{x}}$
70563	Find the Derivative - d/dx	y=(x/(1+x))^5	$y = {(\frac{x}{1 + x})}^{5}$
70564	Find the Tangent Line at x=1	f(x) = natural log of 4-x^2+2x^4 , x=1	$f (x) = \ln (4 - x^{2} + 2 x^{4})$ , $x = 1$
70565	Find the Maximum/Minimum Value	f(x)=(x^2-1)^2	$f (x) = {(x^{2} - 1)}^{2}$
70566	Evaluate the Limit	limit as x approaches infinity of 4/(4x^2-4x+5)	$lim_{x \to \infty} \frac{4}{4 x^{2} - 4 x + 5}$
70567	Evaluate the Integral	integral of 1/(4+(x-3)^2) with respect to x	$\int \frac{1}{4 + {(x - 3)}^{2}} d x$
70568	Find dx/dy	y = square root of 5x	$y = \sqrt{5 x}$
70569	Find dy/dx	y^2=(x^2-49)/(x^2+49)	$y^{2} = \frac{x^{2} - 49}{x^{2} + 49}$
70570	Find the Derivative - d/dθ	2sin(theta)^2	$2 \sin^{2} (θ)$
70571	Find the Second Derivative	x^2y-4x=5	$x^{2} y - 4 x = 5$
70572	Find the Inflection Points	f(x)=4xe^(3x)	$f (x) = 4 x e^{3 x}$
70573	Find the Upper and Lower Bounds	f(x)=2x^4-5x^2-45x-3	$f (x) = 2 x^{4} - 5 x^{2} - 45 x - 3$
70574	Find the Derivative - d/dx	e^(h(x))	$e^{h (x)}$
70575	Find the Derivative - d/dx	e^(-x^(1/2)+1/5x^(-3/5))	$e^{- x^{\frac{1}{2}} + \frac{1}{5} x^{- \frac{3}{5}}}$
70576	Find the Derivative - d/dx	arctanh(x)	$arctanh (x)$
70577	Find the Derivative - d/dx	y=ax^3+bx^2+cx+d	$y = a x^{3} + b x^{2} + c x + d$
70578	Evaluate the Integral	integral of (3x-2)e^(-x) with respect to x	$\int (3 x - 2) e^{- x} d x$
70579	Find the Derivative - d/dx	y=(x^2+5x-1)/(x^2)	$y = \frac{x^{2} + 5 x - 1}{x^{2}}$
70580	Find Where Increasing/Decreasing	f(x)=-3/4x^-5	$f (x) = - \frac{3}{4} x^{- 5}$
70581	Find the Derivative - d/dx	natural log of \|sec(x)\|	$\ln (\| \sec (x) \|)$
70582	Find the Second Derivative	x^(1/3)(x+3)^(2/3)	$x^{\frac{1}{3}} {(x + 3)}^{\frac{2}{3}}$
70583	Evaluate the Limit	limit as x approaches pi of (sin(x))/(x-pi)	$lim_{x \to π} \frac{\sin (x)}{x - π}$
70584	Find the Derivative - d/dx	y=(2/x-1/(x^2))^(1/2)	$y = {(\frac{2}{x} - \frac{1}{x^{2}})}^{\frac{1}{2}}$
70585	Solve the Differential Equation	(dy)/(dx)=4/(x^2-1)	$\frac{d y}{d x} = \frac{4}{x^{2} - 1}$
70586	Find the Derivative - d/dx	-2cot(x)+1/(x^4)	$- 2 \cot (x) + \frac{1}{x^{4}}$
70587	Find the Maximum/Minimum Value	y = cube root of x	$y = \sqrt[3]{x}$
70588	Find the Derivative - d/dx	-1/2x	$- \frac{1}{2} x$
70589	Find Where Increasing/Decreasing	f(x)=(x-4)/(x^2)	$f (x) = \frac{x - 4}{x^{2}}$
70590	Find the Slope of the Tangent Line at (1,1)	(x^2+y^2)^2=4x^2y , (1,1)	${(x^{2} + y^{2})}^{2} = 4 x^{2} y$ , $(1, 1)$
70591	Find dy/dx	e^ycos(x)=1+sin(xy)	$e^{y} \cos (x) = 1 + \sin (x y)$
70592	Evaluate the Limit	limit as x approaches infinity of (5x+5x^4)/(2x-3)	$lim_{x \to \infty} \frac{5 x + 5 x^{4}}{2 x - 3}$
70593	Evaluate the Limit	limit as x approaches -4 from the left of x^2+2/(x+4)	$lim_{x \to {(- 4)}^{-}} x^{2} + \frac{2}{x + 4}$
70594	Find the Antiderivative	f(x)=5e^(6x)+(-3x^6+4x)/(x^2)	$f (x) = 5 e^{6 x} + \frac{- 3 x^{6} + 4 x}{x^{2}}$
70595	Evaluate the Integral	integral of (3x^2)/(1+x^3) with respect to x	$\int \frac{3 x^{2}}{1 + x^{3}} d x$
70596	Find dy/dx	y=cos(x+y)	$y = \cos (x + y)$
70597	Find the Fourth Derivative	y=2e^(3x)	$y = 2 e^{3 x}$
70598	Find the Derivative - d/dx	y=4x(x-2)^2	$y = 4 x {(x - 2)}^{2}$
70599	Find the Center and Radius	((x-8)^2)/16+(y^2)/64=1	$\frac{{(x - 8)}^{2}}{16} + \frac{y^{2}}{64} = 1$
70600	Find the Derivative - d/dx	x^(2^x)	$x^{2^{x}}$