Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
5501	Find the Derivative - d/dx	arccos(x^2)	$\arccos (x^{2})$
5502	Find the Derivative - d/dx	4x^3-80x^2+400x	$4 x^{3} - 80 x^{2} + 400 x$
5503	Find the Derivative - d/dx	3x+1	$3 x + 1$
5504	Find the Derivative - d/dx	4e^(-x^2)	$4 e^{- x^{2}}$
5505	Find the Derivative - d/dx	3sin(4x)	$3 \sin (4 x)$
5506	Find the Derivative - d/dx	2x-2	$2 x - 2$
5507	Find the Derivative - d/dt	(e^(-t)+e^t)^3	${(e^{- t} + e^{t})}^{3}$
5508	Find the Derivative - d/dt	150000/((4t+75)^2)	$\frac{150000}{{(4 t + 75)}^{2}}$
5509	Find the Derivative - d/dt	cos(t)^2	$\cos^{2} (t)$
5510	Find the Derivative - d/dd	d/(dt)(at^2+bt+c)	$\frac{d}{d t} (a t^{2} + b t + c)$
5511	Find the Derivative - d/dt	sec(t)	$\sec (t)$
5512	Find the Derivative - d/dx	(x^2-4)^2	${(x^{2} - 4)}^{2}$
5513	Find the Derivative - d/dx	(2x+1)^3	${(2 x + 1)}^{3}$
5514	Find the Derivative - d/dx	(ax+b)/(cx+d)	$\frac{a x + b}{c x + d}$
5515	Find the Derivative - d/dx	x/4	$\frac{x}{4}$
5516	Find the Derivative - d/dx	x/5	$\frac{x}{5}$
5517	Find the Derivative - d/dx	x/y	$\frac{x}{y}$
5518	Find the Derivative - d/dx	x^(4/3)	$x^{\frac{4}{3}}$
5519	Find the Derivative - d/dx	x^2+4x^3	$x^{2} + 4 x^{3}$
5520	Find the Derivative - d/dx	(cos(x))/(1-sin(x))	$\frac{\cos (x)}{1 - \sin (x)}$
5521	Find the Derivative - d/dx	cos(3x)^2	$\cos^{2} (3 x)$
5522	Find the Derivative - d/dx	e^x-1	$e^{x} - 1$
5523	Find the Derivative - d/dx	e^(-5x)	$e^{- 5 x}$
5524	Find the Derivative - d/dx	e^(6x)	$e^{6 x}$
5525	Find the Derivative - d/dx	e^(7x)	$e^{7 x}$
5526	Find the Derivative - d/dx	e^(-4x)	$e^{- 4 x}$
5527	Evaluate the Limit	limit as x approaches 5 of 2/2*(25x-25)	$lim_{x \to 5} \frac{2}{2} \cdot (25 x - 25)$
5528	Evaluate the Limit	limit as x approaches 5 of 6/(x-5)	$lim_{x \to 5} \frac{6}{x - 5}$
5529	Evaluate the Limit	limit as x approaches 4 of 3/4*(4x-6)	$lim_{x \to 4} \frac{3}{4} \cdot (4 x - 6)$
5530	Evaluate the Limit	limit as x approaches 4 of square root of x^2-7	$lim_{x \to 4} \sqrt{x^{2} - 7}$
5531	Find the Derivative - d/d@VAR	f(x)=x^9cos(x)	$f (x) = x^{9} \cos (x)$
5532	Find dy/dx	x^3-3x^2y+3xy^2-y^3=10	$x^{3} - 3 x^{2} y + 3 x y^{2} - y^{3} = 10$
5533	Evaluate the Integral	integral of x^7e^(x^8) with respect to x	$\int x^{7} e^{x^{8}} d x$
5534	Evaluate the Limit	limit as x approaches 1 of 5/((x-1)^2)	$lim_{x \to 1} \frac{5}{{(x - 1)}^{2}}$
5535	Evaluate the Limit	limit as x approaches -1 of -f(x)	$lim_{x \to - 1} - f (x)$
5536	Find the Derivative - d/dt	5t^2+4/(t^2)-18	$5 t^{2} + \frac{4}{t^{2}} - 18$
5537	Evaluate the Limit	limit as x approaches 0 of (tan(6x))/(sin(3x))	$lim_{x \to 0} \frac{\tan (6 x)}{\sin (3 x)}$
5538	Evaluate the Limit	limit as x approaches pi of tan(x/3)	$lim_{x \to π} \tan (\frac{x}{3})$
5539	Evaluate the Limit	limit as y approaches -3 of (5-y)^(4/3)	$lim_{y \to - 3} {(5 - y)}^{\frac{4}{3}}$
5540	Evaluate the Limit	limit as x approaches pi of xcos(x)	$lim_{x \to π} x \cos (x)$
5541	Evaluate the Limit	limit as z approaches 2 of (z^3-8)/(z-2)	$lim_{z \to 2} \frac{z^{3} - 8}{z - 2}$
5542	Evaluate the Limit	limit as x approaches pi of 5sin(x+sin(x))	$lim_{x \to π} 5 \sin (x + \sin (x))$
5543	Evaluate the Limit	limit as x approaches pi of 2cot(x)	$lim_{x \to π} 2 \cot (x)$
5544	Evaluate the Limit	limit as x approaches pi of cos(7x)	$lim_{x \to π} \cos (7 x)$
5545	Evaluate the Limit	limit as x approaches pi of natural log of sin(x)	$lim_{x \to π} \ln (\sin (x))$
5546	Evaluate the Limit	( limit as h approaches 0 of square root of 1+h-1)/h	$\frac{lim_{h \to 0} \sqrt{1 + h} - 1}{h}$
5547	Evaluate the Limit	( limit as x approaches 0 of square root of 2x+9-3)/x	$\frac{lim_{x \to 0} \sqrt{2 x + 9} - 3}{x}$
5548	Evaluate the Limit	( limit as t approaches 0 of square root of t^2+9-3)/(t^2)	$\frac{lim_{t \to 0} \sqrt{t^{2} + 9} - 3}{t^{2}}$
5549	Evaluate the Limit	( limit as x approaches 1 of cube root of x-1)/( square root of x-1)	$\frac{lim_{x \to 1} \sqrt[3]{x} - 1}{\sqrt{x} - 1}$
5550	Evaluate the Limit	limit as x approaches 3 of (9-x^2)/(x-3)	$lim_{x \to 3} \frac{9 - x^{2}}{x - 3}$
5551	Evaluate the Limit	( limit as x approaches 1 of x^4-1)/(x^3-1)	$\frac{lim_{x \to 1} x^{4} - 1}{x^{3} - 1}$
5552	Evaluate the Function	f(theta)=cos(theta^2)	$f (θ) = \cos (θ^{2})$
5553	Evaluate the Limit	( limit as x approaches 7 of square root of x+2-3)/(x-7)	$\frac{lim_{x \to 7} \sqrt{x + 2} - 3}{x - 7}$
5554	Evaluate the Limit	( limit as x approaches 9 of x^2-81)/(x-9)	$\frac{lim_{x \to 9} x^{2} - 81}{x - 9}$
5555	Evaluate Using the Squeeze Theorem	limit as x approaches infinity of arctan(e^x)	$lim_{x \to \infty} \arctan (e^{x})$
5556	Find the Derivative - d/d?	cos(theta)	$\cos (θ)$
5557	Find the Derivative - d/d@VAR	f(x)=-4x^2-4cos(x)	$f (x) = - 4 x^{2} - 4 \cos (x)$
5558	Evaluate the Limit	limit as x approaches 0 of (1-cos(x))/(tan(x)^2)	$lim_{x \to 0} \frac{1 - \cos (x)}{\tan^{2} (x)}$
5559	Find the Derivative - d/d@VAR	f(x) = fifth root of (2x^2-3x+1)^3	$f (x) = \sqrt[5]{{(2 x^{2} - 3 x + 1)}^{3}}$
5560	Evaluate the Limit	limit as x approaches 0 of (1+x)^(cot(x))	$lim_{x \to 0} {(1 + x)}^{\cot (x)}$
5561	Evaluate the Summation	sum from i=1 to 5 of 3*4^(i-1)	$\sum_{i = 1}^{5} 3 {(4)}^{i - 1}$
5562	Evaluate the Limit	limit as x approaches 8 of x/(x-5)	$lim_{x \to 8} \frac{x}{x - 5}$
5563	Evaluate the Limit	limit as x approaches 8 of x^2sin(1/x)	$lim_{x \to 8} x^{2} \sin (\frac{1}{x})$
5564	Evaluate the Limit	limit as x approaches 8 of x^5e^(-x^4)	$lim_{x \to 8} x^{5} e^{- x^{4}}$
5565	Evaluate the Limit	limit as x approaches 8 of xe^x	$lim_{x \to 8} x e^{x}$
5566	Evaluate the Limit	limit as x approaches -8 of 2xe^(2x)	$lim_{x \to - 8} 2 x e^{2 x}$
5567	Evaluate the Limit	limit as x approaches 8 of 7cos(7/(3x))	$lim_{x \to 8} 7 \cos (\frac{7}{3 x})$
5568	Evaluate the Limit	limit as x approaches infinity of (1-x)/(2x)	$lim_{x \to \infty} \frac{1 - x}{2 x}$
5569	Evaluate the Limit	limit as x approaches -1 of (x^2-7x)/(x^2-6x-7)	$lim_{x \to - 1} \frac{x^{2} - 7 x}{x^{2} - 6 x - 7}$
5570	Evaluate the Limit	limit as x approaches 8 of ( natural log of natural log of x)/x	$lim_{x \to 8} \frac{\ln (\ln (x))}{x}$
5571	Evaluate the Limit	limit as x approaches 2 of 1/(x-2)	$lim_{x \to 2} \frac{1}{x - 2}$
5572	Evaluate the Limit	limit as x approaches 8 of xtan(3/x)	$lim_{x \to 8} x \tan (\frac{3}{x})$
5573	Evaluate the Limit	limit as x approaches 8 of arccos((1+x^2)/(1+2x^2))	$lim_{x \to 8} \arccos (\frac{1 + x^{2}}{1 + 2 x^{2}})$
5574	Evaluate the Limit	limit as x approaches 8 of arcsin(x/(1-2x))	$lim_{x \to 8} \arcsin (\frac{x}{1 - 2 x})$
5575	Evaluate the Limit	limit as x approaches 1 of 4/(x^2-2x+1)	$lim_{x \to 1} \frac{4}{x^{2} - 2 x + 1}$
5576	Evaluate the Limit	limit as x approaches -9 of (8- square root of x^2-17)/(x+9)	$lim_{x \to - 9} \frac{8 - \sqrt{x^{2} - 17}}{x + 9}$
5577	Evaluate the Limit	limit as x approaches 9 of (x^2-4x-45)/(x-9)	$lim_{x \to 9} \frac{x^{2} - 4 x - 45}{x - 9}$
5578	Evaluate the Limit	limit as x approaches 49 of (x-49)/( square root of x-7)	$lim_{x \to 49} \frac{x - 49}{\sqrt{x} - 7}$
5579	Evaluate the Limit	limit as x approaches 0 of (6x^2-7x)/x	$lim_{x \to 0} \frac{6 x^{2} - 7 x}{x}$
5580	Evaluate the Limit	limit as x approaches infinity of (x^2)/(x^2+1)	$lim_{x \to \infty} \frac{x^{2}}{x^{2} + 1}$
5581	Evaluate the Limit	limit as x approaches 8 of ((2x-1)(3-x))/((x-1)(x+3))	$lim_{x \to 8} \frac{(2 x - 1) (3 - x)}{(x - 1) (x + 3)}$
5582	Evaluate the Limit	limit as h approaches 0 of ((2+h)^3-8)/h	$lim_{h \to 0} \frac{{(2 + h)}^{3} - 8}{h}$
5583	Evaluate the Limit	limit as x approaches -3 of (3-\|x\|)/(3+x)	$lim_{x \to - 3} \frac{3 - \| x \|}{3 + x}$
5584	Evaluate the Limit	limit as x approaches -8 of ((1-x^4)/(x^2+5x))^7	$lim_{x \to - 8} {(\frac{1 - x^{4}}{x^{2} + 5 x})}^{7}$
5585	Evaluate the Limit	limit as x approaches 8 of (e^x+1)^(2/x)	$lim_{x \to 8} {(e^{x} + 1)}^{\frac{2}{x}}$
5586	Evaluate the Limit	limit as x approaches 8 of (1.001)^x	$lim_{x \to 8} {(1.001)}^{x}$
5587	Evaluate the Limit	limit as x approaches -1 of ((2x-1)^2-9)/(x+1)	$lim_{x \to - 1} \frac{{(2 x - 1)}^{2} - 9}{x + 1}$
5588	Evaluate the Limit	limit as x approaches 8 of (x^2-64)/(x+8)	$lim_{x \to 8} \frac{x^{2} - 64}{x + 8}$
5589	Evaluate the Limit	limit as x approaches infinity of x	$lim_{x \to \infty} x$
5590	Evaluate the Limit	limit as x approaches infinity of arcsec(x)	$lim_{x \to \infty} arcsec (x)$
5591	Evaluate the Limit	limit as x approaches -8 of (5x^2-6x-4)/(10-2x-5x^2)	$lim_{x \to - 8} \frac{5 x^{2} - 6 x - 4}{10 - 2 x - 5 x^{2}}$
5592	Evaluate the Limit	limit as x approaches -5 of p	$lim_{x \to - 5} p$
5593	Evaluate the Limit	limit as x approaches 4 of (x^2-5x+4)/(x^2-2x-8)	$lim_{x \to 4} \frac{x^{2} - 5 x + 4}{x^{2} - 2 x - 8}$
5594	Evaluate the Limit	limit as x approaches infinity of natural log of x	$lim_{x \to \infty} \ln (x)$
5595	Evaluate the Limit	limit as x approaches 6 of (\|6-x\|)/(3x-18)	$lim_{x \to 6} \frac{\| 6 - x \|}{3 x - 18}$
5596	Evaluate the Limit	limit as x approaches -6 of 12x+1	$lim_{x \to - 6} 12 x + 1$
5597	Evaluate the Limit	limit as x approaches 0 of (2x)/(x^2+4x)	$lim_{x \to 0} \frac{2 x}{x^{2} + 4 x}$
5598	Evaluate the Limit	limit as x approaches infinity of square root of x^2+2x+1-x	$lim_{x \to \infty} \sqrt{x^{2} + 2 x + 1} - x$
5599	Evaluate the Limit	limit as x approaches infinity of 6cos(x)	$lim_{x \to \infty} 6 \cos (x)$
5600	Evaluate the Limit	limit as x approaches 6 of f(x)	$lim_{x \to 6} f (x)$