Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
34001	Evaluate the Limit	limit as x approaches 8 of (-10x^2-2x+7)/( square root of x^16-3x-1)	$lim_{x \to 8} \frac{- 10 x^{2} - 2 x + 7}{\sqrt{x^{16} - 3 x - 1}}$
34002	Evaluate the Limit	limit as x approaches 8 of (P(x))/(Q(x))	$lim_{x \to 8} \frac{P (x)}{Q (x)}$
34003	Evaluate the Limit	limit as x approaches 8 of (sin(5x))/(3x)	$lim_{x \to 8} \frac{\sin (5 x)}{3 x}$
34004	Evaluate the Limit	limit as x approaches 8 of (3-x^2)/(2x^3-x^2+9)	$lim_{x \to 8} \frac{3 - x^{2}}{2 x^{3} - x^{2} + 9}$
34005	Evaluate the Limit	limit as x approaches 8 of (3x^2+20x)/(2x^4*(3x^3)-29)	$lim_{x \to 8} \frac{3 x^{2} + 20 x}{2 x^{4} \cdot (3 x^{3}) - 29}$
34006	Evaluate the Limit	limit as x approaches 8 of cos(6/x)^x	$lim_{x \to 8} {\cos (\frac{6}{x})}^{x}$
34007	Evaluate the Limit	limit as x approaches 8 of ( natural log of 2x)/( natural log of 3x)	$lim_{x \to 8} \frac{\ln (2 x)}{\ln (3 x)}$
34008	Evaluate the Limit	limit as x approaches 8 of (x-8)/( square root of x+1-3)	$lim_{x \to 8} \frac{x - 8}{\sqrt{x + 1} - 3}$
34009	Evaluate the Limit	limit as x approaches 8 of (x-8)/(\|x-8\|)	$lim_{x \to 8} \frac{x - 8}{\| x - 8 \|}$
34010	Evaluate the Limit	limit as x approaches 8 of (x-8)/(x^2-16x+64)	$lim_{x \to 8} \frac{x - 8}{x^{2} - 16 x + 64}$
34011	Evaluate the Limit	limit as x approaches 8 of (x-8)/(x^2-8x)	$lim_{x \to 8} \frac{x - 8}{x^{2} - 8 x}$
34012	Evaluate the Limit	limit as x approaches 8 of (xcos(xpi))/(2x-1)	$lim_{x \to 8} \frac{x \cos (x π)}{2 x - 1}$
34013	Evaluate the Limit	limit as x approaches 8 of (x-x square root of x)/(2x^(3/2)+3x-5)	$lim_{x \to 8} \frac{x - x \sqrt{x}}{2 x^{\frac{3}{2}} + 3 x - 5}$
34014	Evaluate the Limit	limit as x approaches 8 of ((x/(x+1))-(8/9))/(x-8)	$lim_{x \to 8} \frac{(\frac{x}{x + 1}) - (\frac{8}{9})}{x - 8}$
34015	Evaluate the Limit	limit as x approaches 8 of ((5x^4-4x+3)^3)/((5x^3-3x^2-2)^4)	$lim_{x \to 8} \frac{{(5 x^{4} - 4 x + 3)}^{3}}{{(5 x^{3} - 3 x^{2} - 2)}^{4}}$
34016	Evaluate the Limit	limit as x approaches 8 of ((7.99)^2-64)/((7.99)-8)	$lim_{x \to 8} \frac{{(7.99)}^{2} - 64}{(7.99) - 8}$
34017	Evaluate the Limit	limit as x approaches 8 of (-e^(-x^8)-1)/8	$lim_{x \to 8} \frac{- e^{- x^{8}} - 1}{8}$
34018	Evaluate the Limit	limit as x approaches 8 of (e^(11x)-1-11x)/(x^2)	$lim_{x \to 8} \frac{e^{11 x} - 1 - 11 x}{x^{2}}$
34019	Evaluate the Limit	limit as x approaches -8 of (e^2-x^4)/(31x-2x^3)	$lim_{x \to - 8} \frac{e^{2} - x^{4}}{31 x - 2 x^{3}}$
34020	Evaluate the Limit	limit as x approaches 8 of ((100)^2+2)/((100)^2-1)	$lim_{x \to 8} \frac{{(100)}^{2} + 2}{{(100)}^{2} - 1}$
34021	Evaluate the Limit	limit as x approaches negative infinity of ( square root of 3x^4+x)/(x^2-8)	$lim_{x \to - \infty} \frac{\sqrt{3 x^{4} + x}}{x^{2} - 8}$
34022	Evaluate the Limit	limit as x approaches 8 of -(e^-5x)/10	$lim_{x \to 8} - \frac{e^{- 5} x}{10}$
34023	Evaluate the Limit	limit as x approaches infinity of (1-(2/x))^x	$lim_{x \to \infty} {(1 - (\frac{2}{x}))}^{x}$
34024	Evaluate the Limit	limit as x approaches 8 of (e^x)/((x-8)^3)	$lim_{x \to 8} \frac{e^{x}}{{(x - 8)}^{3}}$
34025	Evaluate the Limit	limit as x approaches 8 of (300x^3-25)/(2x^3-100x)	$lim_{x \to 8} \frac{300 x^{3} - 25}{2 x^{3} - 100 x}$
34026	Evaluate the Limit	limit as x approaches -8 of (3x^2+10x-1)/(2x^2-5x)	$lim_{x \to - 8} \frac{3 x^{2} + 10 x - 1}{2 x^{2} - 5 x}$
34027	Evaluate the Limit	limit as x approaches 8 of (3x^2-2x-1)/(x^4-16)	$lim_{x \to 8} \frac{3 x^{2} - 2 x - 1}{x^{4} - 16}$
34028	Evaluate the Limit	limit as x approaches 8 of (3x^4-5x^3+12x^2-72)/(7x^4+3)	$lim_{x \to 8} \frac{3 x^{4} - 5 x^{3} + 12 x^{2} - 72}{7 x^{4} + 3}$
34029	Evaluate the Limit	limit as x approaches 8 of (48^x)/(x!)	$lim_{x \to 8} \frac{48^{x}}{x!}$
34030	Evaluate the Limit	limit as x approaches 8 of (4x^2)/(x^2+4x+55)	$lim_{x \to 8} \frac{4 x^{2}}{x^{2} + 4 x + 55}$
34031	Evaluate the Limit	limit as x approaches 8 of (5x^2)/(x+6)	$lim_{x \to 8} \frac{5 x^{2}}{x + 6}$
34032	Evaluate the Limit	limit as x approaches 8 of (64/x-8)/(8-x)	$lim_{x \to 8} \frac{\frac{64}{x} - 8}{8 - x}$
34033	Evaluate the Limit	limit as x approaches 8 of (6e^x)/(1+e^(-x))	$lim_{x \to 8} \frac{6 e^{x}}{1 + e^{- x}}$
34034	Evaluate the Limit	limit as x approaches 8 of (6x^3-8)/(x^2)	$lim_{x \to 8} \frac{6 x^{3} - 8}{x^{2}}$
34035	Evaluate the Limit	limit as x approaches -8 of (7x^5-6x^3+11x)/(4x^3-2x+1)	$lim_{x \to - 8} \frac{7 x^{5} - 6 x^{3} + 11 x}{4 x^{3} - 2 x + 1}$
34036	Evaluate the Limit	limit as x approaches 8 of (7^x)/(3^x)	$lim_{x \to 8} \frac{7^{x}}{3^{x}}$
34037	Evaluate the Limit	limit as x approaches 0 of x/( square root of 1-cos(x))	$lim_{x \to 0} \frac{x}{\sqrt{1 - \cos (x)}}$
34038	Evaluate the Limit	limit as x approaches 8 of (ax^4)/(dx^3)+(bx^2)/(ex^2)+c/(fx)+1/g	$lim_{x \to 8} \frac{a x^{4}}{d x^{3}} + \frac{b x^{2}}{e x^{2}} + \frac{c}{f x} + \frac{1}{g}$
34039	Evaluate the Limit	limit as x approaches 8 of (ax^4+bx^2+c)/(dx^5+ex^3+fx)	$lim_{x \to 8} \frac{a x^{4} + b x^{2} + c}{d x^{5} + e x^{3} + f x}$
34040	Evaluate the Limit	limit as x approaches 8 of (b^3-7b^2+12b)/(4-b^3)	$lim_{x \to 8} \frac{b^{3} - 7 b^{2} + 12 b}{4 - b^{3}}$
34041	Evaluate the Limit	limit as x approaches 8 of ( square root of x^2+1-1)/( square root of x^2+2-4)	$lim_{x \to 8} \frac{\sqrt{x^{2} + 1 - 1}}{\sqrt{x^{2} + 2 - 4}}$
34042	Evaluate the Limit	limit as x approaches 8 of ( square root of x^2+25)/(x+5)	$lim_{x \to 8} \frac{\sqrt{x^{2} + 25}}{x + 5}$
34043	Evaluate the Limit	limit as x approaches 8 of ( square root of x^2+4x)/(4x+1)	$lim_{x \to 8} \frac{\sqrt{x^{2} + 4 x}}{4 x + 1}$
34044	Evaluate the Limit	limit as x approaches -8 of ( square root of x^2+6x)/(6x+5)	$lim_{x \to - 8} \frac{\sqrt{x^{2} + 6 x}}{6 x + 5}$
34045	Evaluate the Limit	limit as x approaches 8 of ( natural log of (x+2)^2)/( natural log of x^4)	$lim_{x \to 8} \frac{\ln ({(x + 2)}^{2})}{\ln (x^{4})}$
34046	Evaluate the Limit	limit as x approaches 1 of (1+cos(ax))/(x^2-2x+1)	$lim_{x \to 1} \frac{1 + \cos (a x)}{x^{2} - 2 x + 1}$
34047	Evaluate the Limit	limit as x approaches 8 of (px^5)/(x^5-5x^4)	$lim_{x \to 8} \frac{p x^{5}}{x^{5} - 5 x^{4}}$
34048	Evaluate the Limit	limit as x approaches 8 of (px^5)/(x^5-5x^5)	$lim_{x \to 8} \frac{p x^{5}}{x^{5} - 5 x^{5}}$
34049	Evaluate the Limit	limit as x approaches 8 of (arcsin(3+2x))/(arcsin(5+2x))	$lim_{x \to 8} \frac{\arcsin (3 + 2 x)}{\arcsin (5 + 2 x)}$
34050	Evaluate the Limit	limit as x approaches 8 of (sin(x)^2)/(x^2)	$lim_{x \to 8} \frac{\sin^{2} (x)}{x^{2}}$
34051	Evaluate the Limit	limit as x approaches 8 of ( square root of x^2-2x-24)/(22-4x)	$lim_{x \to 8} \frac{\sqrt{x^{2} - 2 x - 24}}{22 - 4 x}$
34052	Evaluate the Limit	limit as x approaches 8 of ( square root of x^2-6)/(9x-5)	$lim_{x \to 8} \frac{\sqrt{x^{2} - 6}}{9 x - 5}$
34053	Evaluate the Limit	limit as x approaches 0 of 2x-1	$lim_{x \to 0} 2 x - 1$
34054	Evaluate the Limit	limit as x approaches 8 of ( square root of x^2-9)/(2x+6)	$lim_{x \to 8} \frac{\sqrt{x^{2} - 9}}{2 x + 6}$
34055	Evaluate the Limit	limit as x approaches 1 of ( square root of 10-x-3)/( square root of 2-x-1)	$lim_{x \to 1} \frac{\sqrt{10 - x} - 3}{\sqrt{2 - x} - 1}$
34056	Evaluate the Limit	limit as x approaches -2 of (2x^2+3x-2)/(x^2-2x-8)	$lim_{x \to - 2} \frac{2 x^{2} + 3 x - 2}{x^{2} - 2 x - 8}$
34057	Evaluate the Limit	limit as x approaches 8 of ( square root of x^10-1)/(x^6-1)	$lim_{x \to 8} \frac{\sqrt{x^{10} - 1}}{x^{6} - 1}$
34058	Evaluate the Limit	limit as x approaches 8 of ( square root of 25x^2+7)/(4x+7)	$lim_{x \to 8} \frac{\sqrt{25 x^{2} + 7}}{4 x + 7}$
34059	Evaluate the Limit	limit as x approaches 9 of (x^2-81)/( square root of x-3)	$lim_{x \to 9} \frac{x^{2} - 81}{\sqrt{x} - 3}$
34060	Evaluate the Limit	limit as x approaches 8 of ( square root of x^4-3x^3-5)/(1x^2+5)	$lim_{x \to 8} \frac{\sqrt{x^{4} - 3 x^{3} - 5}}{1 x^{2} + 5}$
34061	Evaluate the Limit	limit as x approaches 8 of ( square root of x^6+1)/(x^4-1)	$lim_{x \to 8} \frac{\sqrt{x^{6} + 1}}{x^{4} - 1}$
34062	Evaluate the Limit	limit as x approaches 8 of ( square root of x^8-1)/(x^6-1)	$lim_{x \to 8} \frac{\sqrt{x^{8} - 1}}{x^{6} - 1}$
34063	Evaluate the Limit	limit as x approaches 8 of ( square root of 1+1/(x^2))/1	$lim_{x \to 8} \frac{\sqrt{1 + \frac{1}{x^{2}}}}{1}$
34064	Evaluate the Limit	limit as x approaches -8 of ( square root of 10x^2-4)/(x+18)	$lim_{x \to - 8} \frac{\sqrt{10 x^{2} - 4}}{x + 18}$
34065	Evaluate the Limit	limit as x approaches 8 of ( square root of 100t^2-1000)/(t-10)	$lim_{x \to 8} \frac{\sqrt{100 t^{2} - 1000}}{t - 10}$
34066	Evaluate the Limit	limit as x approaches 8 of ( square root of 11+39x^2)/(2x+3)	$lim_{x \to 8} \frac{\sqrt{11 + 39 x^{2}}}{2 x + 3}$
34067	Evaluate the Limit	limit as x approaches 8 of ( square root of 16x^2+4)/(4x+1)	$lim_{x \to 8} \frac{\sqrt{16 x^{2} + 4}}{4 x + 1}$
34068	Evaluate the Limit	limit as x approaches 8 of ( square root of 16x-x^2-4)/x	$lim_{x \to 8} \frac{\sqrt{16 x - x^{2} - 4}}{x}$
34069	Evaluate the Limit	limit as x approaches -8 of ( square root of 2x^2+1)/(3x-5)	$lim_{x \to - 8} \frac{\sqrt{2 x^{2} + 1}}{3 x - 5}$
34070	Evaluate the Limit	limit as x approaches 8 of ( square root of 2x^2-4)/(x+20)	$lim_{x \to 8} \frac{\sqrt{2 x^{2} - 4}}{x + 20}$
34071	Evaluate the Limit	limit as x approaches 8 of ( square root of 25x^2-4)/( square root of 9x^2+2x+5)	$lim_{x \to 8} \frac{\sqrt{25 x^{2} - 4}}{\sqrt{9 x^{2} + 2 x + 5}}$
34072	Evaluate the Limit	limit as x approaches 8 of ( square root of 25x+2)/( square root of x+2)	$lim_{x \to 8} \frac{\sqrt{25 x + 2}}{\sqrt{x + 2}}$
34073	Evaluate the Limit	limit as x approaches 8 of ( square root of 27x^4+3x-5)/(3x^2-10)	$lim_{x \to 8} \frac{\sqrt{27 x^{4} + 3 x - 5}}{3 x^{2} - 10}$
34074	Evaluate the Limit	limit as x approaches -8 of ( square root of 3x^2+6x-5)/(x+2)	$lim_{x \to - 8} \frac{\sqrt{3 x^{2} + 6 x - 5}}{x + 2}$
34075	Evaluate the Limit	limit as x approaches 8 of ( square root of 3x^2-1)/(2x)	$lim_{x \to 8} \frac{\sqrt{3 x^{2} - 1}}{2 x}$
34076	Evaluate the Limit	limit as x approaches 8 of ( square root of 3x^2-5)/(x+11)	$lim_{x \to 8} \frac{\sqrt{3 x^{2} - 5}}{x + 11}$
34077	Evaluate the Limit	limit as x approaches 8 of ( square root of 3x^2-7)/(x+6)	$lim_{x \to 8} \frac{\sqrt{3 x^{2} - 7}}{x + 6}$
34078	Evaluate the Limit	limit as x approaches 8 of ( square root of 3+8x^2)/(8+8x)	$lim_{x \to 8} \frac{\sqrt{3 + 8 x^{2}}}{8 + 8 x}$
34079	Evaluate the Limit	limit as x approaches 8 of ( square root of 36x^2+7)/(7x+4)	$lim_{x \to 8} \frac{\sqrt{36 x^{2} + 7}}{7 x + 4}$
34080	Evaluate the Limit	limit as x approaches 8 of ( square root of 3x+2)/(6x-8)	$lim_{x \to 8} \frac{\sqrt{3 x + 2}}{6 x - 8}$
34081	Evaluate the Limit	limit as x approaches 8 of ( square root of 4x^2+1)/(3x-1)	$lim_{x \to 8} \frac{\sqrt{4 x^{2} + 1}}{3 x - 1}$
34082	Evaluate the Limit	limit as x approaches 8 of ( square root of 4x^2+1)/(5x+2)	$lim_{x \to 8} \frac{\sqrt{4 x^{2} + 1}}{5 x + 2}$
34083	Evaluate the Limit	limit as x approaches -8 of ( square root of 4x^2+3x-2)/(6x-5)	$lim_{x \to - 8} \frac{\sqrt{4 x^{2} + 3 x - 2}}{6 x - 5}$
34084	Evaluate the Limit	limit as x approaches 8 of ( square root of 4x^2-10)/(x-5)	$lim_{x \to 8} \frac{\sqrt{4 x^{2} - 10}}{x - 5}$
34085	Evaluate the Limit	limit as x approaches 8 of ( square root of 4x^2-3x+1)/(x+7)	$lim_{x \to 8} \frac{\sqrt{4 x^{2} - 3 x + 1}}{x + 7}$
34086	Evaluate the Limit	limit as x approaches -8 of ( square root of 4x^6)/(x^3)	$lim_{x \to - 8} \frac{\sqrt{4 x^{6}}}{x^{3}}$
34087	Evaluate the Limit	limit as x approaches 8 of ( square root of x^2-x-20)/(8-4x)	$lim_{x \to 8} \frac{\sqrt{x^{2} - x - 20}}{8 - 4 x}$
34088	Evaluate the Limit	limit as x approaches 8 of ( square root of x^4-x^3-9)/(7x^2-3)	$lim_{x \to 8} \frac{\sqrt{x^{4} - x^{3} - 9}}{7 x^{2} - 3}$
34089	Evaluate the Limit	limit as x approaches 8 of ( square root of x^4+1)/(3x^2)	$lim_{x \to 8} \frac{\sqrt{x^{4} + 1}}{3 x^{2}}$
34090	Evaluate the Limit	limit as x approaches 6 of 3	$lim_{x \to 6} 3$
34091	Evaluate the Limit	limit as x approaches 8 of (4x^3)/(2x^3 square root of 9x^6+15x^4)	$lim_{x \to 8} \frac{4 x^{3}}{2 x^{3} \sqrt{9 x^{6} + 15 x^{4}}}$
34092	Evaluate the Limit	limit as x approaches 8 of (4x^3+1)/(x-x^3)	$lim_{x \to 8} \frac{4 x^{3} + 1}{x - x^{3}}$
34093	Evaluate the Limit	limit as x approaches 8 of (4x^3-2x)/(2-3x+5x^4)	$lim_{x \to 8} \frac{4 x^{3} - 2 x}{2 - 3 x + 5 x^{4}}$
34094	Evaluate the Limit	limit as x approaches 8 of (4+3x)/(5-6x)	$lim_{x \to 8} \frac{4 + 3 x}{5 - 6 x}$
34095	Evaluate the Limit	limit as x approaches 8 of ((4-x)(x^2+x))/( square root of x^8)	$lim_{x \to 8} \frac{(4 - x) (x^{2} + x)}{\sqrt{x^{8}}}$
34096	Evaluate the Limit	limit as x approaches 8 of (4x)/(2x-2)	$lim_{x \to 8} \frac{4 x}{2 x - 2}$
34097	Evaluate the Limit	limit as x approaches 8 of (4x+1)/(12x^2-7)	$lim_{x \to 8} \frac{4 x + 1}{12 x^{2} - 7}$
34098	Evaluate the Limit	limit as x approaches 8 of (4x+1)/(7x^2-1)	$lim_{x \to 8} \frac{4 x + 1}{7 x^{2} - 1}$
34099	Evaluate the Limit	limit as x approaches -8 of (4x-1)/(2 square root of x^2-1)	$lim_{x \to - 8} \frac{4 x - 1}{2 \sqrt{x^{2} - 1}}$
34100	Evaluate the Limit	limit as x approaches 8 of (4x-7)/( square root of 4x^2+8)	$lim_{x \to 8} \frac{4 x - 7}{\sqrt{4 x^{2} + 8}}$