Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
33401	Evaluate the Limit	limit as x approaches 8 of 4x	$lim_{x \to 8} 4 x$
33402	Evaluate the Limit	limit as x approaches -8 of 4x+ square root of 16x^2+5x-9	$lim_{x \to - 8} 4 x + \sqrt{16 x^{2} + 5 x - 9}$
33403	Evaluate the Limit	limit as x approaches 8 of 4xsin(1/x)	$lim_{x \to 8} 4 x \sin (\frac{1}{x})$
33404	Evaluate the Limit	limit as x approaches 8 of 5-3/x+10/(x^2)	$lim_{x \to 8} 5 - \frac{3}{x} + \frac{10}{x^{2}}$
33405	Evaluate the Limit	limit as x approaches -8 of 5e^(9x)	$lim_{x \to - 8} 5 e^{9 x}$
33406	Evaluate the Limit	limit as x approaches -8 of -5x^11+x^7-2/3x^6-6x^5-9	$lim_{x \to - 8} - 5 x^{11} + x^{7} - \frac{2}{3} x^{6} - 6 x^{5} - 9$
33407	Evaluate the Limit	limit as x approaches 8 of 5x^2	$lim_{x \to 8} 5 x^{2}$
33408	Evaluate the Limit	limit as x approaches 8 of (5x^2)-3x+1	$lim_{x \to 8} (5 x^{2}) - 3 x + 1$
33409	Evaluate the Limit	limit as x approaches -8 of 5x^23	$lim_{x \to - 8} 5 x^{23}$
33410	Evaluate the Limit	limit as x approaches 8 of (sin(6x))/(3x)	$lim_{x \to 8} \frac{\sin (6 x)}{3 x}$
33411	Evaluate the Limit	limit as x approaches 8 of (sin(7x))/(11x)	$lim_{x \to 8} \frac{\sin (7 x)}{11 x}$
33412	Evaluate the Limit	limit as x approaches 8 of (sin(x))/(1-cos(x))	$lim_{x \to 8} \frac{\sin (x)}{1 - \cos (x)}$
33413	Evaluate the Limit	limit as x approaches 8 of (sin(x-8))/(x^2+x-72)	$lim_{x \to 8} \frac{\sin (x - 8)}{x^{2} + x - 72}$
33414	Evaluate the Limit	limit as x approaches 8 of (sin(x-8))/(x^2-64)	$lim_{x \to 8} \frac{\sin (x - 8)}{x^{2} - 64}$
33415	Evaluate the Limit	limit as x approaches 8 of arctan(x^5-x^7)	$lim_{x \to 8} \arctan (x^{5} - x^{7})$
33416	Evaluate the Limit	limit as x approaches 8 of arctan((2x^2+2)/(9-9x))	$lim_{x \to 8} \arctan (\frac{2 x^{2} + 2}{9 - 9 x})$
33417	Evaluate the Limit	limit as x approaches 0 of (sin(3x))/(sin(9x))	$lim_{x \to 0} \frac{\sin (3 x)}{\sin (9 x)}$
33418	Evaluate the Limit	limit as x approaches 8 of (tan(1/x))/(1/x)	$lim_{x \to 8} \frac{\tan (\frac{1}{x})}{\frac{1}{x}}$
33419	Evaluate the Limit	limit as x approaches 8 of (tan(3x))/(3x)	$lim_{x \to 8} \frac{\tan (3 x)}{3 x}$
33420	Evaluate the Limit	limit as x approaches 8 of (tan(x))/(e^x)	$lim_{x \to 8} \frac{\tan (x)}{e^{x}}$
33421	Evaluate the Limit	limit as x approaches 8 of ( log of x)/x	$lim_{x \to 8} \frac{\log (x)}{x}$
33422	Evaluate the Limit	limit as x approaches 8 of log base 13 of 1+13^(-x)	$lim_{x \to 8} \log_{13} (1 + 13^{- x})$
33423	Evaluate the Limit	limit as x approaches 8 of log base 2 of x	$lim_{x \to 8} \log_{2} (x)$
33424	Evaluate the Limit	limit as x approaches 8 of log base 5 of x	$lim_{x \to 8} \log_{5} (x)$
33425	Evaluate the Limit	limit as x approaches 8 of (n-6)/(n-2)	$lim_{x \to 8} \frac{n - 6}{n - 2}$
33426	Evaluate the Limit	limit as x approaches 8 of (sin(x^2))/(sin(x))	$lim_{x \to 8} \frac{\sin (x^{2})}{\sin (x)}$
33427	Evaluate the Limit	limit as x approaches 8 of (sin(13x))/(5x)	$lim_{x \to 8} \frac{\sin (13 x)}{5 x}$
33428	Evaluate the Limit	limit as x approaches 8 of (sin(16x))/(2x)	$lim_{x \to 8} \frac{\sin (16 x)}{2 x}$
33429	Evaluate the Limit	limit as x approaches 8 of (sin(17x))/(2x)	$lim_{x \to 8} \frac{\sin (17 x)}{2 x}$
33430	Evaluate the Limit	limit as x approaches 8 of (sin(2x))/(e^x-3x-1)	$lim_{x \to 8} \frac{\sin (2 x)}{e^{x} - 3 x - 1}$
33431	Evaluate the Limit	limit as x approaches 8 of (sin(2x))/(sin(5x))	$lim_{x \to 8} \frac{\sin (2 x)}{\sin (5 x)}$
33432	Evaluate the Limit	limit as x approaches 8 of arcsec(x/3)	$lim_{x \to 8} arcsec (\frac{x}{3})$
33433	Evaluate the Limit	limit as x approaches 8 of (sin(3x))/(11x)	$lim_{x \to 8} \frac{\sin (3 x)}{11 x}$
33434	Evaluate the Limit	limit as x approaches 8 of (sin(3x))/(5x)	$lim_{x \to 8} \frac{\sin (3 x)}{5 x}$
33435	Evaluate the Limit	limit as x approaches 8 of (sin(4x))/(12x)	$lim_{x \to 8} \frac{\sin (4 x)}{12 x}$
33436	Evaluate the Limit	limit as x approaches 8 of (sin(4x))/x	$lim_{x \to 8} \frac{\sin (4 x)}{x}$
33437	Evaluate the Limit	limit as x approaches 8 of (sin(5x))/(12x)	$lim_{x \to 8} \frac{\sin (5 x)}{12 x}$
33438	Evaluate the Limit	limit as x approaches -8 of square root of x^2+3+x	$lim_{x \to - 8} \sqrt{x^{2} + 3 + x}$
33439	Evaluate the Limit	limit as x approaches 8 of ( square root of x^2+3x)- square root of x^2+x	$lim_{x \to 8} (\sqrt{x^{2} + 3 x}) - \sqrt{x^{2} + x}$
33440	Evaluate the Limit	limit as x approaches 8 of square root of (25x^2)/(6+36x^2)	$lim_{x \to 8} \sqrt{\frac{25 x^{2}}{6 + 36 x^{2}}}$
33441	Evaluate the Limit	limit as x approaches 8 of square root of (2x+1)/(3x-5)	$lim_{x \to 8} \sqrt{\frac{2 x + 1}{3 x - 5}}$
33442	Evaluate the Limit	limit as x approaches (3pi)/2 of sec(x)	$lim_{x \to \frac{3 π}{2}} \sec (x)$
33443	Evaluate the Limit	limit as x approaches 8 of square root of x^2+10x+1-x	$lim_{x \to 8} \sqrt{x^{2} + 10 x + 1 - x}$
33444	Evaluate the Limit	limit as x approaches 8 of ( square root of x^2+12x)-x	$lim_{x \to 8} (\sqrt{x^{2} + 12 x}) - x$
33445	Evaluate the Limit	limit as x approaches 8 of ( square root of x^2+14x-2)-x	$lim_{x \to 8} (\sqrt{x^{2} + 14 x - 2}) - x$
33446	Evaluate the Limit	limit as x approaches 8 of ( square root of x^2+2)-x	$lim_{x \to 8} (\sqrt{x^{2} + 2}) - x$
33447	Evaluate the Limit	limit as x approaches 8 of square root of (5x^2-2)/(x+3)	$lim_{x \to 8} \sqrt{\frac{5 x^{2} - 2}{x + 3}}$
33448	Evaluate the Limit	limit as x approaches 8 of square root of (64x+7)/(25x-11)	$lim_{x \to 8} \sqrt{\frac{64 x + 7}{25 x - 11}}$
33449	Evaluate the Limit	limit as x approaches 8 of square root of (9x^2)/(2+25x^2)	$lim_{x \to 8} \sqrt{\frac{9 x^{2}}{2 + 25 x^{2}}}$
33450	Evaluate the Limit	limit as x approaches 8 of square root of (9x^2+x-3)/((x-7)(x+1))	$lim_{x \to 8} \sqrt{\frac{9 x^{2} + x - 3}{(x - 7) (x + 1)}}$
33451	Evaluate the Limit	limit as x approaches pi/2 of (5cos(x))/(cot(x))	$lim_{x \to \frac{π}{2}} \frac{5 \cos (x)}{\cot (x)}$
33452	Evaluate the Limit	limit as x approaches 8 of (t-t square root of t)/(2t^(3/2)+3t-5)	$lim_{x \to 8} \frac{t - t \sqrt{t}}{2 t^{\frac{3}{2}} + 3 t - 5}$
33453	Evaluate the Limit	limit as x approaches 8 of ( square root of (x+m)(x+n))-x	$lim_{x \to 8} (\sqrt{(x + m) (x + n)}) - x$
33454	Evaluate the Limit	limit as x approaches 8 of square root of (12x^3-5x+7)/(1+4x^2+3x^3)	$lim_{x \to 8} \sqrt{\frac{12 x^{3} - 5 x + 7}{1 + 4 x^{2} + 3 x^{3}}}$
33455	Evaluate the Limit	limit as x approaches 8 of ( square root of \|x\|)- square root of \|x-1\|	$lim_{x \to 8} (\sqrt{\| x \|}) - \sqrt{\| x - 1 \|}$
33456	Evaluate the Limit	limit as x approaches 8 of square root of (1+16x^5)/(x^5+2)	$lim_{x \to 8} \sqrt{\frac{1 + 16 x^{5}}{x^{5} + 2}}$
33457	Evaluate the Limit	limit as t approaches infinity of 40e^(-t)	$lim_{t \to \infty} 40 e^{- t}$
33458	Evaluate the Limit	limit as x approaches 8 of square root of (10x^4+5x^3+1)/(1+2x^4)	$lim_{x \to 8} \sqrt{\frac{10 x^{4} + 5 x^{3} + 1}{1 + 2 x^{4}}}$
33459	Evaluate the Limit	limit as x approaches 8 of square root of (16x^2)/(7+49x^2)	$lim_{x \to 8} \sqrt{\frac{16 x^{2}}{7 + 49 x^{2}}}$
33460	Evaluate the Limit	limit as x approaches -8 of square root of x^6-5x^3-x^3	$lim_{x \to - 8} \sqrt{x^{6} - 5 x^{3}} - x^{3}$
33461	Evaluate the Limit	limit as x approaches 8 of square root of 11+25x^2-5x	$lim_{x \to 8} \sqrt{11 + 25 x^{2}} - 5 x$
33462	Evaluate the Limit	limit as x approaches 8 of square root of 128x+1-8	$lim_{x \to 8} \sqrt{128 x + 1} - 8$
33463	Evaluate the Limit	limit as x approaches 8 of square root of 16x^2+3x-4x	$lim_{x \to 8} \sqrt{16 x^{2} + 3 x} - 4 x$
33464	Evaluate the Limit	limit as x approaches 8 of square root of 3x^2+5x+3- square root of 16x^2-3x+4	$lim_{x \to 8} \sqrt{3 x^{2} + 5 x + 3} - \sqrt{16 x^{2} - 3 x + 4}$
33465	Evaluate the Limit	limit as x approaches 8 of ( square root of 36x^2+x)-6x	$lim_{x \to 8} (\sqrt{36 x^{2} + x}) - 6 x$
33466	Evaluate the Limit	limit as x approaches 8 of square root of x+ square root of x- square root of x-1	$lim_{x \to 8} \sqrt{x + \sqrt{x}} - \sqrt{x - 1}$
33467	Evaluate the Limit	limit as x approaches 8 of square root of x+1- square root of x-1	$lim_{x \to 8} \sqrt{x + 1} - \sqrt{x - 1}$
33468	Evaluate the Limit	limit as x approaches 8 of ( square root of x)e^(-x/2)	$lim_{x \to 8} (\sqrt{x}) e^{- \frac{x}{2}}$
33469	Evaluate the Limit	limit as x approaches 8 of ( square root of x)sin(1/x)	$lim_{x \to 8} (\sqrt{x}) \sin (\frac{1}{x})$
33470	Evaluate the Limit	limit as x approaches 8 of square root of 49x^2+x-7x	$lim_{x \to 8} \sqrt{49 x^{2} + x} - 7 x$
33471	Evaluate the Limit	limit as x approaches 8 of square root of 5x-4	$lim_{x \to 8} \sqrt{5 x - 4}$
33472	Evaluate the Limit	limit as x approaches 8 of square root of 5x-6	$lim_{x \to 8} \sqrt{5 x - 6}$
33473	Find dy/dx	y = square root of natural log of 5x	$y = \sqrt{\ln (5 x)}$
33474	Evaluate the Limit	limit as x approaches 8 of square root of 6x-4	$lim_{x \to 8} \sqrt{6 x - 4}$
33475	Evaluate the Limit	limit as x approaches 8 of square root of 7x-1	$lim_{x \to 8} \sqrt{7 x - 1}$
33476	Evaluate the Limit	limit as x approaches 8 of square root of 81x^2-x-9x	$lim_{x \to 8} \sqrt{81 x^{2} - x} - 9 x$
33477	Evaluate the Limit	limit as x approaches -8 of square root of 4x^2-5x+3x	$lim_{x \to - 8} \sqrt{4 x^{2} - 5 x + 3 x}$
33478	Evaluate the Limit	limit as x approaches 8 of square root of 4x^2-5x+3x	$lim_{x \to 8} \sqrt{4 x^{2} - 5 x + 3 x}$
33479	Evaluate the Limit	limit as x approaches 8 of square root of 4x^3-1087	$lim_{x \to 8} \sqrt{4 x^{3} - 1087}$
33480	Evaluate the Limit	limit as x approaches 8 of square root of 4x^4+12x^3-2x^2	$lim_{x \to 8} \sqrt{4 x^{4} + 12 x^{3}} - 2 x^{2}$
33481	Evaluate the Limit	limit as x approaches -8 of square root of x^2-4	$lim_{x \to - 8} \sqrt{x^{2} - 4}$
33482	Evaluate the Limit	limit as x approaches -8 of (9x^2+4x)/(9-6x^2)	$lim_{x \to - 8} \frac{9 x^{2} + 4 x}{9 - 6 x^{2}}$
33483	Evaluate the Limit	limit as x approaches 8 of (9x^2+7x)/(4x^2+7x-9)	$lim_{x \to 8} \frac{9 x^{2} + 7 x}{4 x^{2} + 7 x - 9}$
33484	Evaluate the Limit	limit as x approaches -8 of (9x^2-8x+7)/(3x^2+1)	$lim_{x \to - 8} \frac{9 x^{2} - 8 x + 7}{3 x^{2} + 1}$
33485	Evaluate the Limit	limit as t approaches 4 of (t^3+25t^2-119t+12)/(t^3-16t)	$lim_{t \to 4} \frac{t^{3} + 25 t^{2} - 119 t + 12}{t^{3} - 16 t}$
33486	Evaluate the Limit	limit as x approaches -8 of (9x^4+x)/(2x^4+5x^2-x+6)	$lim_{x \to - 8} \frac{9 x^{4} + x}{2 x^{4} + 5 x^{2} - x + 6}$
33487	Evaluate the Limit	limit as n approaches infinity of xe^(-x)	$lim_{n \to \infty} x e^{- x}$
33488	Evaluate the Limit	limit as x approaches -8 of 9/(3^x)	$lim_{x \to - 8} \frac{9}{3^{x}}$
33489	Evaluate the Limit	limit as x approaches 8 of 9/(x^4)	$lim_{x \to 8} \frac{9}{x^{4}}$
33490	Evaluate the Limit	limit as x approaches 8 of 9/x-9	$lim_{x \to 8} \frac{9}{x} - 9$
33491	Evaluate the Limit	limit as x approaches 8 of (9-2x)/(12x^2-10)	$lim_{x \to 8} \frac{9 - 2 x}{12 x^{2} - 10}$
33492	Evaluate the Limit	limit as x approaches -8 of (9-8x+sin(2x))/(9x+cos(2x))	$lim_{x \to - 8} \frac{9 - 8 x + \sin (2 x)}{9 x + \cos (2 x)}$
33493	Evaluate the Limit	limit as x approaches 8 of (9x)/(7x-8)	$lim_{x \to 8} \frac{9 x}{7 x - 8}$
33494	Evaluate the Limit	limit as x approaches -8 of (9x+1)/(7x^2+6x-4)	$lim_{x \to - 8} \frac{9 x + 1}{7 x^{2} + 6 x - 4}$
33495	Evaluate the Limit	limit as x approaches -8 of ((9x+5)/(x-6))((14x-14)/(-x-13))	$lim_{x \to - 8} (\frac{9 x + 5}{x - 6}) (\frac{14 x - 14}{- x - 13})$
33496	Evaluate the Limit	limit as x approaches 8 of (9x-7)/(3x+2)	$lim_{x \to 8} \frac{9 x - 7}{3 x + 2}$
33497	Evaluate the Limit	limit as x approaches 8 of (a-bx^4)/(cx^4+x^2)	$lim_{x \to 8} \frac{a - b x^{4}}{c x^{4} + x^{2}}$
33498	Evaluate the Limit	limit as x approaches -8 of ae^(kt)	$lim_{x \to - 8} a e^{k t}$
33499	Evaluate the Limit	limit as x approaches 8 of (arcsin(3x))/( natural log of x+2)	$lim_{x \to 8} \frac{\arcsin (3 x)}{\ln (x + 2)}$
33500	Evaluate the Limit	limit as x approaches 8 of (arctan(x))/(1/x-4)	$lim_{x \to 8} \frac{\arctan (x)}{\frac{1}{x} - 4}$