Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
30801	Evaluate the Limit	limit as y approaches -9 of (18-y)^(7/3)	$lim_{y \to - 9} {(18 - y)}^{\frac{7}{3}}$
30802	Evaluate the Limit	limit as y approaches 9 of (9-y)/(3- square root of y)	$lim_{y \to 9} \frac{9 - y}{3 - \sqrt{y}}$
30803	Evaluate the Limit	limit as y approaches pi of (1+cos(y))/(y-pi)	$lim_{y \to π} \frac{1 + \cos (y)}{y - π}$
30804	Evaluate the Limit	limit as x approaches 1 of ( square root of x-1)/( square root of 2x+3- square root of 5)	$lim_{x \to 1} \frac{\sqrt{x} - 1}{\sqrt{2 x + 3} - \sqrt{5}}$
30805	Evaluate the Limit	limit as h approaches 0 of ( square root of 18h+1-1)/h	$lim_{h \to 0} \frac{\sqrt{18 h + 1} - 1}{h}$
30806	Evaluate the Limit	limit as h approaches 0 of (f(6+h)-f*6)/h	$lim_{h \to 0} \frac{f (6 + h) - f \cdot 6}{h}$
30807	Evaluate the Limit	limit as z approaches 2/3 of 3z(2z-1)	$lim_{z \to \frac{2}{3}} 3 z (2 z - 1)$
30808	Evaluate the Limit	limit as z approaches 0 of z((e^(z^2)-1)/(z^2))	$lim_{z \to 0} z (\frac{e^{z^{2}} - 1}{z^{2}})$
30809	Evaluate the Limit	limit as z approaches 8 of ze^(-sz)	$lim_{z \to 8} z e^{- s z}$
30810	Evaluate the Limit	limit as z approaches 0 of ((1+z)^3-1)/z	$lim_{z \to 0} \frac{{(1 + z)}^{3} - 1}{z}$
30811	Evaluate the Limit	limit as z approaches 0 of (z^2-3z+1)/(2z^2+5)	$lim_{z \to 0} \frac{z^{2} - 3 z + 1}{2 z^{2} + 5}$
30812	Evaluate the Limit	limit as z approaches 0 of (1-(cos(z)^2))/(z^2)	$lim_{z \to 0} \frac{1 - (\cos^{2} (z))}{z^{2}}$
30813	Evaluate the Limit	limit as z approaches 0 of (e^z-1)/z	$lim_{z \to 0} \frac{e^{z} - 1}{z}$
30814	Evaluate the Limit	limit as z approaches 0 of ((x+z)^3-x^3)/z	$lim_{z \to 0} \frac{{(x + z)}^{3} - x^{3}}{z}$
30815	Evaluate the Limit	limit as z approaches 0 of (\|z\|)/z	$lim_{z \to 0} \frac{\| z \|}{z}$
30816	Evaluate the Limit	limit as z approaches 0 of (z^2-5z-4)/(z^2+1)	$lim_{z \to 0} \frac{z^{2} - 5 z - 4}{z^{2} + 1}$
30817	Evaluate the Limit	limit as z approaches 0 of (z^3)/(sin(2z)^3)	$lim_{z \to 0} \frac{z^{3}}{\sin^{3} (2 z)}$
30818	Evaluate the Limit	limit as z approaches 0 of (2e^(1/z))/(e^(1/z)+1)	$lim_{z \to 0} \frac{2 e^{\frac{1}{z}}}{e^{\frac{1}{z}} + 1}$
30819	Evaluate the Limit	limit as z approaches 0 of (sin(4z))/(sin(3z))	$lim_{z \to 0} \frac{\sin (4 z)}{\sin (3 z)}$
30820	Evaluate the Limit	limit as y approaches 3 of x/(x-3)	$lim_{y \to 3} \frac{x}{x - 3}$
30821	Evaluate the Limit	limit as y approaches 4 of (y^2-4^2)/(y-4)	$lim_{y \to 4} \frac{y^{2} - 4^{2}}{y - 4}$
30822	Evaluate the Limit	limit as y approaches 4 of (4-y)/( square root of y-2)	$lim_{y \to 4} \frac{4 - y}{\sqrt{y} - 2}$
30823	Evaluate the Limit	limit as y approaches -4 of (4-y)^(5/3)	$lim_{y \to - 4} {(4 - y)}^{\frac{5}{3}}$
30824	Evaluate the Limit	limit as y approaches 4 of (7y^2-7)/(8y^2(y-1)^3)	$lim_{y \to 4} \frac{7 y^{2} - 7}{8 y^{2} {(y - 1)}^{3}}$
30825	Evaluate the Limit	limit as y approaches 4 of (2y^3-11y^2+10y+8)/(3y^3-17y^2+16y+16)	$lim_{y \to 4} \frac{2 y^{3} - 11 y^{2} + 10 y + 8}{3 y^{3} - 17 y^{2} + 16 y + 16}$
30826	Evaluate the Limit	limit as y approaches 5 of (1/y-(1/5))/(y-5)	$lim_{y \to 5} \frac{\frac{1}{y} - (\frac{1}{5})}{y - 5}$
30827	Evaluate the Limit	limit as y approaches 5 of (22-y)^(4/3)	$lim_{y \to 5} {(22 - y)}^{\frac{4}{3}}$
30828	Evaluate the Limit	limit as y approaches -5 of (3-y)^(7/3)	$lim_{y \to - 5} {(3 - y)}^{\frac{7}{3}}$
30829	Evaluate the Limit	limit as y approaches 6 of (4y+12)/(y+6)	$lim_{y \to 6} \frac{4 y + 12}{y + 6}$
30830	Evaluate the Limit	limit as y approaches 64 of (3 square root of y+ square root of y)^2	$lim_{y \to 64} {(3 \sqrt{y} + \sqrt{y})}^{2}$
30831	Evaluate the Limit	limit as y approaches 64 of (64-y)/(8- square root of y)	$lim_{y \to 64} \frac{64 - y}{8 - \sqrt{y}}$
30832	Evaluate the Limit	limit as y approaches 64 of (64-y)/(8-y)	$lim_{y \to 64} \frac{64 - y}{8 - y}$
30833	Evaluate the Limit	limit as y approaches 7 of (1/y-1/7)/(y-7)	$lim_{y \to 7} \frac{\frac{1}{y} - \frac{1}{7}}{y - 7}$
30834	Evaluate the Limit	limit as y approaches 7 of (y^2-4y-21)/(3y^2-17y-28)	$lim_{y \to 7} \frac{y^{2} - 4 y - 21}{3 y^{2} - 17 y - 28}$
30835	Evaluate the Limit	limit as y approaches 8 of (4y^2-3y^3)/(2y^3+3y^2)	$lim_{y \to 8} \frac{4 y^{2} - 3 y^{3}}{2 y^{3} + 3 y^{2}}$
30836	Evaluate the Limit	limit as y approaches 8 of (1/y-1/8)/(y-8)	$lim_{y \to 8} \frac{\frac{1}{y} - \frac{1}{8}}{y - 8}$
30837	Evaluate the Limit	limit as y approaches 8 of (7-8y^2)/(6y^2+7y)	$lim_{y \to 8} \frac{7 - 8 y^{2}}{6 y^{2} + 7 y}$
30838	Evaluate the Limit	limit as y approaches -8 of (4y^3+1)/(8y^2+y-7)	$lim_{y \to - 8} \frac{4 y^{3} + 1}{8 y^{2} + y - 7}$
30839	Evaluate the Limit	limit as y approaches 8 of ( square root of y^2+2)/(5y-6)	$lim_{y \to 8} \frac{\sqrt{y^{2}} + 2}{5 y - 6}$
30840	Evaluate the Limit	limit as y approaches 0 of sin((20y)/(9y))	$lim_{y \to 0} \sin (\frac{20 y}{9 y})$
30841	Evaluate the Limit	limit as y approaches 0 of tan((2y)/(3y))	$lim_{y \to 0} \tan (\frac{2 y}{3 y})$
30842	Evaluate the Limit	limit as y approaches 0 of (z(x+y))-zx	$lim_{y \to 0} (z (x + y)) - z x$
30843	Evaluate the Limit	limit as h approaches 0 of 8/( square root of 8h+4+4)	$lim_{h \to 0} \frac{8}{\sqrt{8 h + 4} + 4}$
30844	Evaluate the Limit	limit as y approaches 1 of ((y)^(1/3)-1)/y-1	$lim_{y \to 1} \frac{{(y)}^{\frac{1}{3}} - 1}{y} - 1$
30845	Evaluate the Limit	limit as y approaches -1 of (y^2-y+1)/(3y-2)	$lim_{y \to - 1} \frac{y^{2} - y + 1}{3 y - 2}$
30846	Evaluate the Limit	limit as y approaches -1 of y^3-2y^2+3y-4	$lim_{y \to - 1} y^{3} - 2 y^{2} + 3 y - 4$
30847	Evaluate the Limit	limit as y approaches 1 of y^3-2y^2+3y-4	$lim_{y \to 1} y^{3} - 2 y^{2} + 3 y - 4$
30848	Evaluate the Limit	limit as y approaches -1 of y^3-2y+3y-4	$lim_{y \to - 1} y^{3} - 2 y + 3 y - 4$
30849	Evaluate the Limit	limit as y approaches 1 of (y-1)/( square root of y+3-2)	$lim_{y \to 1} \frac{y - 1}{\sqrt{y + 3} - 2}$
30850	Evaluate the Limit	limit as y approaches 1 of (y-4 square root of y+3)/(y^2-1)	$lim_{y \to 1} \frac{y - 4 \sqrt{y + 3}}{y^{2} - 1}$
30851	Evaluate the Limit	limit as y approaches -1 of ((4y^3+8y)/(y+4))^(1/3)	$lim_{y \to - 1} {(\frac{4 y^{3} + 8 y}{y + 4})}^{\frac{1}{3}}$
30852	Evaluate the Limit	limit as y approaches 1 of (y^2-2y+1)/(y^2-4y+3)	$lim_{y \to 1} \frac{y^{2} - 2 y + 1}{y^{2} - 4 y + 3}$
30853	Evaluate the Limit	limit as y approaches 1 of ((y-1)(y^2+2y-3))/(y^2-2y+1)	$lim_{y \to 1} \frac{(y - 1) (y^{2} + 2 y - 3)}{y^{2} - 2 y + 1}$
30854	Evaluate the Limit	limit as y approaches 1 of (y^3-y)/(y^2-1)	$lim_{y \to 1} \frac{y^{3} - y}{y^{2} - 1}$
30855	Evaluate the Limit	limit as y approaches 1 of (x+3y)/( square root of x^2+2y^2)	$lim_{y \to 1} \frac{x + 3 y}{\sqrt{x^{2} + 2 y^{2}}}$
30856	Evaluate the Limit	limit as y approaches 0 of (\|y\|)/y	$lim_{y \to 0} \frac{\| y \|}{y}$
30857	Evaluate the Limit	limit as y approaches 1 of sec(ysec(y)^2-tan(y-1)^2)	$lim_{y \to 1} \sec (y \sec^{2} (y) - \tan^{2} (y - 1))$
30858	Evaluate the Limit	limit as y approaches -10 of (17-y)^(5/3)	$lim_{y \to - 10} {(17 - y)}^{\frac{5}{3}}$
30859	Evaluate the Limit	limit as y approaches -2 of (y^4-16)/(y+2)	$lim_{y \to - 2} \frac{y^{4} - 16}{y + 2}$
30860	Evaluate the Limit	limit as y approaches 2 of (2y^2+2y-12)/(3y^2-5y-2)	$lim_{y \to 2} \frac{2 y^{2} + 2 y - 12}{3 y^{2} - 5 y - 2}$
30861	Evaluate the Limit	limit as y approaches 2 of (4y^3+8y)/y	$lim_{y \to 2} \frac{4 y^{3} + 8 y}{y}$
30862	Evaluate the Limit	limit as y approaches 0 of (sin(6y))/(17y)	$lim_{y \to 0} \frac{\sin (6 y)}{17 y}$
30863	Evaluate the Limit	limit as y approaches 0 of (sin(x)(1-cos(x)))/(x^2)	$lim_{y \to 0} \frac{\sin (x) (1 - \cos (x))}{x^{2}}$
30864	Evaluate the Limit	limit as y approaches 0 of (tan(6x))/x	$lim_{y \to 0} \frac{\tan (6 x)}{x}$
30865	Evaluate the Limit	limit as y approaches 0 of square root of 3x+5	$lim_{y \to 0} \sqrt{3 x + 5}$
30866	Evaluate the Limit	limit as y approaches 0 of (y*5^y)/(5^y-1)	$lim_{y \to 0} \frac{y \cdot 5^{y}}{5^{y} - 1}$
30867	Evaluate the Limit	limit as y approaches 0 of y/(x^2)	$lim_{y \to 0} \frac{y}{x^{2}}$
30868	Evaluate the Limit	limit as y approaches 0 of 3tan(x+y)-(tan(3x))/y	$lim_{y \to 0} 3 \tan (x + y) - \frac{\tan (3 x)}{y}$
30869	Evaluate the Limit	limit as y approaches 0 of 5y^(2(cot(-5y))(csc(-8y)))	$lim_{y \to 0} 5 y^{2 (\cot (- 5 y)) (\csc (- 8 y))}$
30870	Evaluate the Limit	limit as y approaches 0 of 1/y*sin(y/3)	$lim_{y \to 0} \frac{1}{y} \cdot \sin (\frac{y}{3})$
30871	Evaluate the Limit	limit as y approaches 0 of (1-cos(y))/(y^2)	$lim_{y \to 0} \frac{1 - \cos (y)}{y^{2}}$
30872	Evaluate the Limit	limit as y approaches 0 of (2xy-6y^2)/y	$lim_{y \to 0} \frac{2 x y - 6 y^{2}}{y}$
30873	Evaluate the Limit	limit as y approaches 0 of (3 square root of h+x-3 square root of x)/h	$lim_{y \to 0} \frac{3 \sqrt{h + x} - 3 \sqrt{x}}{h}$
30874	Evaluate the Limit	limit as y approaches 0 of (7(x+y)^2-7x^2)/y	$lim_{y \to 0} \frac{7 {(x + y)}^{2} - 7 x^{2}}{y}$
30875	Evaluate the Limit	limit as y approaches 0 of (sin(y^2+6y))/y	$lim_{y \to 0} \frac{\sin (y^{2} + 6 y)}{y}$
30876	Evaluate the Limit	limit as y approaches 0 of (sin(10y))/(7y)	$lim_{y \to 0} \frac{\sin (10 y)}{7 y}$
30877	Evaluate the Limit	limit as y approaches 0 of (sin(15y))/(2y)	$lim_{y \to 0} \frac{\sin (15 y)}{2 y}$
30878	Evaluate the Limit	limit as y approaches 0 of (sin(16y))/(17y)	$lim_{y \to 0} \frac{\sin (16 y)}{17 y}$
30879	Evaluate the Limit	limit as y approaches 0 of ( square root of 6+y- square root of 6)/y	$lim_{y \to 0} \frac{\sqrt{6 + y} - \sqrt{6}}{y}$
30880	Evaluate the Limit	limit as y approaches 0 of (x^2+y)/(x+2y)	$lim_{y \to 0} \frac{x^{2} + y}{x + 2 y}$
30881	Evaluate the Limit	limit as x approaches pi of tan(5x)	$lim_{x \to π} \tan (5 x)$
30882	Evaluate the Limit	limit as x approaches pi of sin(x+3sin(x))	$lim_{x \to π} \sin (x + 3 \sin (x))$
30883	Evaluate the Limit	limit as x approaches -pi of tan(x)	$lim_{x \to - π} \tan (x)$
30884	Evaluate the Limit	limit as x approaches pi of (x(cos(pi-x)))/2	$lim_{x \to π} \frac{x (\cos (π - x))}{2}$
30885	Evaluate the Limit	( limit as x approaches 8 of (x)^11)/( natural log of x)	$\frac{lim_{x \to 8} {(x)}^{11}}{\ln (x)}$
30886	Evaluate the Limit	( limit as x approaches 5 of (e)^x-e^5)/(x-5)	$\frac{lim_{x \to 5} {(e)}^{x} - e^{5}}{x - 5}$
30887	Evaluate the Limit	(( limit as x approaches -6 of 1)/6+1/x)/(6+x)	$\frac{\frac{lim_{x \to - 6} 1}{6} + \frac{1}{x}}{6 + x}$
30888	Evaluate the Limit	( limit as x approaches 7 of (x)^2-49)/(x-7)	$\frac{lim_{x \to 7} {(x)}^{2} - 49}{x - 7}$
30889	Evaluate the Limit	limit as z approaches 10 of 1/(z-10)	$lim_{z \to 10} \frac{1}{z - 10}$
30890	Evaluate the Limit	limit as z approaches 15 of square root of y+3	$lim_{z \to 15} \sqrt{y + 3}$
30891	Evaluate the Limit	limit as z approaches -2 of z^3+8	$lim_{z \to - 2} z^{3} + 8$
30892	Evaluate the Limit	limit as z approaches 2 of (z^3-27)/(x-2)	$lim_{z \to 2} \frac{z^{3} - 27}{x - 2}$
30893	Evaluate the Limit	( limit as x approaches 0 of (cos(4x))^2)/(x^2)
30894	Evaluate the Limit	( limit as x approaches 0 of sin(x))/(x^(1/(x^2)))	$\frac{lim_{x \to 0} \sin (x)}{x^{\frac{1}{x^{2}}}}$
30895	Find the Derivative - d/dx	1/(9x^(8/9))	$\frac{1}{9 x^{\frac{8}{9}}}$
30896	Evaluate the Limit	( limit as x approaches 1 of 1+3x^3)/((1+4x^2+3x^4)^3)	$\frac{lim_{x \to 1} 1 + 3 x^{3}}{{(1 + 4 x^{2} + 3 x^{4})}^{3}}$
30897	Evaluate the Limit	( limit as x approaches 2 of (x^3-4x)^2+3x+2)/(x-2)	$\frac{lim_{x \to 2} {(x^{3} - 4 x)}^{2} + 3 x + 2}{x - 2}$
30898	Evaluate the Limit	( limit as x approaches 2 of (x)^3-8)/(x^2-4)	$\frac{lim_{x \to 2} {(x)}^{3} - 8}{x^{2} - 4}$
30899	Evaluate the Limit	( limit as h approaches 0 of (e^(2+h)-e)^2)/h	$\frac{lim_{h \to 0} {(e^{2 + h} - e)}^{2}}{h}$
30900	Evaluate the Limit	( limit as h approaches 0 of (e^(x+h)-e)^x)/h = limit as h approaches 0 of (e^(x+h)-e^x)/h	$\frac{lim_{h \to 0} {(e^{x + h} - e)}^{x}}{h} = lim_{h \to 0} \frac{e^{x + h} - e^{x}}{h}$