Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
36001	Evaluate the Limit	limit as x approaches -3.001 of x/( square root of x^2-9)	$lim_{x \to - 3.001} \frac{x}{\sqrt{x^{2} - 9}}$
36002	Evaluate the Limit	limit as x approaches -3.01 of 2x^2-3x+1	$lim_{x \to - 3.01} 2 x^{2} - 3 x + 1$
36003	Evaluate the Limit	limit as x approaches -3.010 of (x^3-9x)/(x+3)	$lim_{x \to - 3.01} \frac{x^{3} - 9 x}{x + 3}$
36004	Evaluate the Limit	limit as x approaches -3.1 of ( square root of 1-x-2)/(x+3)	$lim_{x \to - 3.1} \frac{\sqrt{1 - x} - 2}{x + 3}$
36005	Evaluate the Limit	limit as x approaches 3.1 of (x-3)/(3- square root of 12-x)	$lim_{x \to 3.1} \frac{x - 3}{3 - \sqrt{12 - x}}$
36006	Evaluate the Limit	limit as x approaches -3.1 of f(x)	$lim_{x \to - 3.1} f (x)$
36007	Evaluate the Limit	limit as x approaches 3.9995 of (x^3-64)/(x^2-16)	$lim_{x \to 3.9995} \frac{x^{3} - 64}{x^{2} - 16}$
36008	Evaluate the Limit	limit as x approaches 3.9999 of x^2+ square root of 7-x	$lim_{x \to 3.9999} x^{2} + \sqrt{7 - x}$
36009	Evaluate the Limit	limit as x approaches negative infinity of x^2+2x^5	$lim_{x \to - \infty} x^{2} + 2 x^{5}$
36010	Evaluate the Limit	limit as x approaches negative infinity of x^4+2x^7	$lim_{x \to - \infty} x^{4} + 2 x^{7}$
36011	Evaluate the Limit	limit as x approaches infinity of square root of x^4-9x^2-x^2	$lim_{x \to \infty} \sqrt{x^{4} - 9 x^{2}} - x^{2}$
36012	Evaluate the Limit	limit as x approaches 6 of (x^3-6x^2)/(x-6)	$lim_{x \to 6} \frac{x^{3} - 6 x^{2}}{x - 6}$
36013	Evaluate the Limit	limit as x approaches 7 of (6x^2-37x-35)/(x-7)	$lim_{x \to 7} \frac{6 x^{2} - 37 x - 35}{x - 7}$
36014	Find the Derivative - d/dx	y=(sec(x)^2)(tan(x)^2)	$y = (\sec^{2} (x)) (\tan^{2} (x))$
36015	Evaluate the Limit	limit as x approaches 5 of ( natural log of x- natural log of 6)/(x-6)	$lim_{x \to 5} \frac{\ln (x) - \ln (6)}{x - 6}$
36016	Evaluate the Limit	limit as x approaches 179 of (x-179)/( square root of x+17-14)	$lim_{x \to 179} \frac{x - 179}{\sqrt{x + 17} - 14}$
36017	Evaluate the Limit	limit as x approaches 16 of (x^2-256)/(16-x)	$lim_{x \to 16} \frac{x^{2} - 256}{16 - x}$
36018	Evaluate the Limit	limit as x approaches 12 of (x^2-144)/(12-x)	$lim_{x \to 12} \frac{x^{2} - 144}{12 - x}$
36019	Evaluate the Limit	limit as x approaches 1000 of 18pi^2	$lim_{x \to 1000} 18 π^{2}$
36020	Evaluate the Limit	limit as x approaches (3pi)/4 of 2cos(x)	$lim_{x \to \frac{3 π}{4}} 2 \cos (x)$
36021	Evaluate the Limit	limit as x approaches (3pi)/4 of sec(x-pi/1)	$lim_{x \to \frac{3 π}{4}} \sec (x - \frac{π}{1})$
36022	Evaluate the Limit	limit as x approaches (3x)/2 of (sin(x))/(3x)	$lim_{x \to \frac{3 x}{2}} \frac{\sin (x)}{3 x}$
36023	Evaluate the Limit	limit as x approaches 1 of arcsin(x)	$lim_{x \to 1} \arcsin (x)$
36024	Evaluate the Limit	limit as h approaches 0 of ((9+h)^-1-9^-1)/h	$lim_{h \to 0} \frac{{(9 + h)}^{- 1} - 9^{- 1}}{h}$
36025	Evaluate the Limit	limit as x approaches 64 of (64-x)/(8- square root of x)	$lim_{x \to 64} \frac{64 - x}{8 - \sqrt{x}}$
36026	Evaluate the Limit	limit as x approaches pi of csc(x)	$lim_{x \to π} \csc (x)$
36027	Evaluate the Limit	limit as x approaches 4 of (x-4)/(x^2+6x+8)	$lim_{x \to 4} \frac{x - 4}{x^{2} + 6 x + 8}$
36028	Evaluate the Limit	limit as x approaches 4 of (x^2-y^2)/(x-4)	$lim_{x \to 4} \frac{x^{2} - y^{2}}{x - 4}$
36029	Evaluate the Limit	limit as x approaches -4 of (2x)/(x+4)+8/(x+4)	$lim_{x \to - 4} \frac{2 x}{x + 4} + \frac{8}{x + 4}$
36030	Evaluate the Limit	limit as x approaches -4 of (x-4)^4sin(1/(4-x))+4	$lim_{x \to - 4} {(x - 4)}^{4} \sin (\frac{1}{4 - x}) + 4$
36031	Evaluate the Limit	limit as x approaches 39 of (x-39)/( square root of x+10-7)	$lim_{x \to 39} \frac{x - 39}{\sqrt{x + 10} - 7}$
36032	Evaluate the Limit	limit as x approaches 2 of f(3-x)	$lim_{x \to 2} f (3 - x)$
36033	Evaluate the Limit	limit as x approaches 36 of 1/( square root of x+6)	$lim_{x \to 36} \frac{1}{\sqrt{x} + 6}$
36034	Evaluate the Limit	limit as x approaches 36 of 8/( square root of x-6)-96/(x-36)	$lim_{x \to 36} \frac{8}{\sqrt{x} - 6} - \frac{96}{x - 36}$
36035	Evaluate the Limit	limit as x approaches 36 of (36-x)/(6- square root of x)	$lim_{x \to 36} \frac{36 - x}{6 - \sqrt{x}}$
36036	Evaluate the Limit	limit as x approaches 36 of ( square root of 0.0833-6)/(0.0833-36)	$lim_{x \to 36} \frac{\sqrt{0.0833} - 6}{0.0833 - 36}$
36037	Evaluate the Limit	limit as x approaches 36 of ( square root of x)/(x-1)	$lim_{x \to 36} \frac{\sqrt{x}}{x - 1}$
36038	Evaluate the Limit	limit as x approaches 3.99 of 8x+4	$lim_{x \to 3.99} 8 x + 4$
36039	Evaluate the Limit	limit as x approaches 0 of (sin(4x))/(sin(8x))	$lim_{x \to 0} \frac{\sin (4 x)}{\sin (8 x)}$
36040	Evaluate the Limit	limit as s approaches 1 of (s^3-s)/(s^2-1)	$lim_{s \to 1} \frac{s^{3} - s}{s^{2} - 1}$
36041	Evaluate the Limit	limit as x approaches 0 of (sin(x))/(tan(x))	$lim_{x \to 0} \frac{\sin (x)}{\tan (x)}$
36042	Evaluate the Limit	limit as x approaches 5 of (x^2-11x+30)/(x-5)	$lim_{x \to 5} \frac{x^{2} - 11 x + 30}{x - 5}$
36043	Evaluate the Limit	limit as x approaches 9 of (3- square root of x)/(9-x)	$lim_{x \to 9} \frac{3 - \sqrt{x}}{9 - x}$
36044	Evaluate the Limit	limit as x approaches 30 of ( square root of x)-6	$lim_{x \to 30} (\sqrt{x}) - 6$
36045	Evaluate the Limit	limit as x approaches -30 of x	$lim_{x \to - 30} x$
36046	Evaluate the Limit	limit as x approaches 303 of (x-303)/( square root of x+21-18)	$lim_{x \to 303} \frac{x - 303}{\sqrt{x + 21 - 18}}$
36047	Evaluate the Limit	limit as x approaches 31 of ( square root of x+5-6)/(x-31)	$lim_{x \to 31} \frac{\sqrt{x + 5} - 6}{x - 31}$
36048	Evaluate the Limit	limit as x approaches -35 of 34+x	$lim_{x \to - 35} 34 + x$
36049	Evaluate the Limit	limit as x approaches 35 of 8.7x	$lim_{x \to 35} 8.7 x$
36050	Find the Derivative - d/dx	y=5xe^(2x)	$y = 5 x e^{2 x}$
36051	Evaluate the Limit	limit as x approaches 36 of (36-t)/(6- square root of t)	$lim_{x \to 36} \frac{36 - t}{6 - \sqrt{t}}$
36052	Find the Derivative - d/dx	y=( square root of x)/(2+x)	$y = \frac{\sqrt{x}}{2 + x}$
36053	Evaluate the Limit	limit as x approaches 36 of (6- square root of x)/(36-x)	$lim_{x \to 36} \frac{6 - \sqrt{x}}{36 - x}$
36054	Evaluate the Limit	limit as x approaches 36 of (9 square root of x-54)/(x-36)	$lim_{x \to 36} \frac{9 \sqrt{x} - 54}{x - 36}$
36055	Evaluate the Limit	limit as x approaches 36 of ( square root of x- square root of 36)/(x-36)	$lim_{x \to 36} \frac{\sqrt{x} - \sqrt{36}}{x - 36}$
36056	Evaluate the Limit	limit as x approaches 36 of ( square root of x-6)/(36-x)	$lim_{x \to 36} \frac{\sqrt{x} - 6}{36 - x}$
36057	Evaluate the Limit	limit as x approaches 4 of ( square root of 2x+1-3)/( square root of x-2 square root of 2)	$lim_{x \to 4} \frac{\sqrt{2 x + 1 - 3}}{\sqrt{x - 2 \sqrt{2}}}$
36058	Evaluate the Limit	limit as x approaches 4 of ( square root of 6x+1-5)/(x-4)	$lim_{x \to 4} \frac{\sqrt{6 x + 1} - 5}{x - 4}$
36059	Evaluate the Limit	limit as x approaches 4 of ( square root of x-2)/(3x-12)	$lim_{x \to 4} \frac{\sqrt{x} - 2}{3 x - 12}$
36060	Evaluate the Limit	limit as x approaches -3 of (8x+24)/(\|x+3\|)	$lim_{x \to - 3} \frac{8 x + 24}{\| x + 3 \|}$
36061	Evaluate the Limit	limit as x approaches 4 of (\|x-4\|)/(\|x\|-4)	$lim_{x \to 4} \frac{\| x - 4 \|}{\| x \| - 4}$
36062	Evaluate the Limit	limit as x approaches infinity of (x+2)/( square root of 81x^2+1)	$lim_{x \to \infty} \frac{x + 2}{\sqrt{81 x^{2} + 1}}$
36063	Evaluate the Limit	limit as x approaches 4 of (1/x-1/4)/(x-4)	$lim_{x \to 4} \frac{\frac{1}{x} - \frac{1}{4}}{x - 4}$
36064	Evaluate the Limit	limit as x approaches 4 of (x^2+3x-6)/(x+2)	$lim_{x \to 4} \frac{x^{2} + 3 x - 6}{x + 2}$
36065	Evaluate the Limit	limit as x approaches 4 of (x^2+5x-36)/(x^2-16)	$lim_{x \to 4} \frac{x^{2} + 5 x - 36}{x^{2} - 16}$
36066	Evaluate the Limit	limit as x approaches 5 of (3x-15)/( square root of x- square root of 5)	$lim_{x \to 5} \frac{3 x - 15}{\sqrt{x} - \sqrt{5}}$
36067	Evaluate the Limit	limit as x approaches 4 of (x^2-16)/(x^2-7x+12)	$lim_{x \to 4} \frac{x^{2} - 16}{x^{2} - 7 x + 12}$
36068	Evaluate the Limit	limit as x approaches 4 of (x^2-16)/(x^2-9x+20)	$lim_{x \to 4} \frac{x^{2} - 16}{x^{2} - 9 x + 20}$
36069	Evaluate the Limit	limit as x approaches 4 of (x^2-16)/(2- square root of 6)	$lim_{x \to 4} \frac{x^{2} - 16}{2 - \sqrt{6}}$
36070	Evaluate the Limit	limit as x approaches 4 of (x^2-16)/(2- square root of x)	$lim_{x \to 4} \frac{x^{2} - 16}{2 - \sqrt{x}}$
36071	Evaluate the Limit	limit as x approaches -4 of ( square root of x^2-9-5)/(x+4)	$lim_{x \to - 4} \frac{\sqrt{x^{2} - 9} - 5}{x + 4}$
36072	Evaluate the Limit	limit as x approaches 4 of (x^4-256)/(x^3-64)	$lim_{x \to 4} \frac{x^{4} - 256}{x^{3} - 64}$
36073	Evaluate the Limit	limit as x approaches 4 of (x^4-81)/(x^3-27)	$lim_{x \to 4} \frac{x^{4} - 81}{x^{3} - 27}$
36074	Evaluate the Limit	limit as x approaches 3 of (x^2-3x)/(x-3)	$lim_{x \to 3} \frac{x^{2} - 3 x}{x - 3}$
36075	Evaluate the Limit	limit as x approaches 4 of \|x-1\|	$lim_{x \to 4} \| x - 1 \|$
36076	Evaluate the Limit	limit as x approaches 4 of x square root of 20-x^2	$lim_{x \to 4} x \sqrt{20 - x^{2}}$
36077	Evaluate the Limit	limit as x approaches -4 of (x^2-16)/(x-4)	$lim_{x \to - 4} \frac{x^{2} - 16}{x - 4}$
36078	Evaluate the Limit	limit as x approaches 4 of (x^2-2x-8)/(x^2-16)	$lim_{x \to 4} \frac{x^{2} - 2 x - 8}{x^{2} - 16}$
36079	Evaluate the Limit	limit as x approaches 1 of (x^3-1)/(x^2-1)	$lim_{x \to 1} \frac{(x^{3} - 1)}{(x^{2} - 1)}$
36080	Evaluate the Limit	limit as x approaches 4 of (-5x^2+20x)/(x^3-3x^2-4x)	$lim_{x \to 4} \frac{- 5 x^{2} + 20 x}{x^{3} - 3 x^{2} - 4 x}$
36081	Evaluate the Limit	limit as x approaches -4 of 1/2x-1	$lim_{x \to - 4} \frac{1}{2} x - 1$
36082	Evaluate the Limit	limit as x approaches -4 of 1/2x-4	$lim_{x \to - 4} \frac{1}{2} x - 4$
36083	Evaluate the Limit	limit as x approaches -4 of 1/2x-8	$lim_{x \to - 4} \frac{1}{2} x - 8$
36084	Evaluate the Limit	limit as x approaches -4 of 1/4x^4-6x	$lim_{x \to - 4} \frac{1}{4} x^{4} - 6 x$
36085	Evaluate the Limit	limit as x approaches -4 of (16-x^2)/(4x^2+x^3)	$lim_{x \to - 4} \frac{16 - x^{2}}{4 x^{2} + x^{3}}$
36086	Evaluate the Limit	limit as x approaches 9 of (x^2-9x)/(x^2-x-72)	$lim_{x \to 9} \frac{x^{2} - 9 x}{x^{2} - x - 72}$
36087	Evaluate the Limit	limit as x approaches -4 of (2x^2-32)/(x+4)	$lim_{x \to - 4} \frac{2 x^{2} - 32}{x + 4}$
36088	Evaluate the Limit	limit as x approaches 0 of (sin(3x)(1-cos(2x)))/(x^2)	$lim_{x \to 0} \frac{\sin (3 x) (1 - \cos (2 x))}{x^{2}}$
36089	Evaluate the Limit	limit as x approaches 4 of (3.99-4)/(3.99-4)	$lim_{x \to 4} \frac{3.99 - 4}{3.99 - 4}$
36090	Evaluate the Limit	limit as x approaches 4 of (3.999-4)/(3.999-4)	$lim_{x \to 4} \frac{3.999 - 4}{3.999 - 4}$
36091	Evaluate the Limit	limit as x approaches -4 of (3- square root of x^2-7)/(x+4)	$lim_{x \to - 4} \frac{3 - \sqrt{x^{2} - 7}}{x + 4}$
36092	Evaluate the Limit	limit as x approaches 4 of 3/4x+5	$lim_{x \to 4} \frac{3}{4} x + 5$
36093	Evaluate the Limit	limit as x approaches 0 of (cot(x))/(csc(x))	$lim_{x \to 0} \frac{\cot (x)}{\csc (x)}$
36094	Evaluate the Limit	limit as x approaches 4 of (4x^2-64)/(x^2-8x+16)	$lim_{x \to 4} \frac{4 x^{2} - 64}{x^{2} - 8 x + 16}$
36095	Evaluate the Limit	limit as x approaches 4 of 4/(x-4)-1/( square root of x-2)	$lim_{x \to 4} \frac{4}{x - 4} - \frac{1}{\sqrt{x} - 2}$
36096	Evaluate the Limit	limit as x approaches 4 of (4x-x^2)/( square root of x-2)	$lim_{x \to 4} \frac{4 x - x^{2}}{\sqrt{x} - 2}$
36097	Evaluate the Limit	limit as x approaches 8 of ( square root of x-4-2)/(x-8)	$lim_{x \to 8} \frac{\sqrt{x - 4} - 2}{x - 8}$
36098	Evaluate the Limit	limit as x approaches 4 of (5x^2-80)/(x^2-8x+16)	$lim_{x \to 4} \frac{5 x^{2} - 80}{x^{2} - 8 x + 16}$
36099	Evaluate the Limit	limit as x approaches 4 of 5/(x/(x-4))-(5/4)/(x-4)	$lim_{x \to 4} \frac{5}{\frac{x}{x - 4}} - \frac{\frac{5}{4}}{x - 4}$
36100	Evaluate the Limit	limit as x approaches infinity of (3x^2+27)/(x^3-27)	$lim_{x \to \infty} \frac{3 x^{2} + 27}{x^{3} - 27}$