Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
22901	Evaluate the Limit	( limit as x approaches 12 of 13-x)/((x-12)^2)	$\frac{lim_{x \to 12} 13 - x}{{(x - 12)}^{2}}$
22902	Find the Inflection Points	6x^4+32x^3	$6 x^{4} + 32 x^{3}$
22903	Evaluate the Limit	( limit as x approaches 2 of x^2-4)/(x^2+3x-10)	$\frac{lim_{x \to 2} x^{2} - 4}{x^{2} + 3 x - 10}$
22904	Evaluate the Limit	( limit as x approaches 2 of square root of x- square root of 2)/( square root of x^2-4)	$\frac{lim_{x \to 2} \sqrt{x} - \sqrt{2}}{\sqrt{x^{2} - 4}}$
22905	Evaluate the Limit	( limit as x approaches 0 of sin(8x))/(tan(5x))	$\frac{lim_{x \to 0} \sin (8 x)}{\tan (5 x)}$
22906	Evaluate the Limit	( limit as x approaches 1 of n^x-1)/(m^x-1)	$\frac{lim_{x \to 1} n^{x} - 1}{m^{x} - 1}$
22907	Evaluate the Limit	( limit as x approaches 1 of u^4-1)/(u^3-1)	$\frac{lim_{x \to 1} u^{4} - 1}{u^{3} - 1}$
22908	Evaluate the Limit	( limit as x approaches 1 of cube root of x+1- cube root of 2)/(x-1)	$\frac{lim_{x \to 1} \sqrt[3]{x + 1} - \sqrt[3]{2}}{x - 1}$
22909	Evaluate the Limit	( limit as x approaches -1 of x^3-4x^2+x+6)/(x+1)	$\frac{lim_{x \to - 1} x^{3} - 4 x^{2} + x + 6}{x + 1}$
22910	Find the Critical Points	f(x)=x^4-4x^3+7	$f (x) = x^{4} - 4 x^{3} + 7$
22911	Evaluate the Limit	( limit as x approaches 0 of sin(3x))/(2x)	$\frac{lim_{x \to 0} \sin (3 x)}{2 x}$
22912	Find the Critical Points	2x+3x^(2/3)	$2 x + 3 x^{\frac{2}{3}}$
22913	Find the Difference Quotient	f(x)=-x^2-4x-3	$f (x) = - x^{2} - 4 x - 3$
22914	Find the Antiderivative	(6x+5)^2	${(6 x + 5)}^{2}$
22915	Evaluate the Limit	( limit as x approaches 0 of sin(bx)-4sin(ax))/(bx-ax)	$\frac{lim_{x \to 0} \sin (b x) - 4 \sin (a x)}{b x - a x}$
22916	Evaluate the Limit	( limit as x approaches 0 of natural log of x+e^x)/(e^(sin(x))-cos(x))	$\frac{lim_{x \to 0} \ln (x + e^{x})}{e^{\sin (x)} - \cos (x)}$
22917	Evaluate the Limit	limit as t approaches 0 of ( square root of t^2+9-3)/(t^2)	$lim_{t \to 0} \frac{\sqrt{t^{2} + 9} - 3}{t^{2}}$
22918	Evaluate the Limit	limit as x approaches 0 of ( square root of x^2+64-8)/x	$lim_{x \to 0} \frac{\sqrt{x^{2} + 64} - 8}{x}$
22919	Evaluate the Limit	( limit as x approaches 0 of sin(pi/6+x)-1/2)/x	$\frac{lim_{x \to 0} \sin (\frac{π}{6} + x) - \frac{1}{2}}{x}$
22920	Evaluate the Limit	( limit as x approaches 0 of tan(8x))/(tan(5x))	$\frac{lim_{x \to 0} \tan (8 x)}{\tan (5 x)}$
22921	Evaluate the Limit	( limit as x approaches 0 of square root of x^2+1-x)/x	$\frac{lim_{x \to 0} \sqrt{x^{2} + 1} - x}{x}$
22922	Evaluate the Limit	( limit as x approaches 0 of x^2-3x)/x	$\frac{lim_{x \to 0} x^{2} - 3 x}{x}$
22923	Evaluate the Limit	limit as x approaches -0.2 of square root of (x+5)/(x+1)	$lim_{x \to - 0.2} \sqrt{\frac{x + 5}{x + 1}}$
22924	Evaluate the Limit	limit as x approaches 0 of (tan(4x))/x	$lim_{x \to 0} \frac{\tan (4 x)}{x}$
22925	Evaluate the Limit	( limit as x approaches 0 of 1)/(x^2)*((sin(x))/(sin(h(x)))-1)	$\frac{lim_{x \to 0} 1}{x^{2}} \cdot (\frac{\sin (x)}{\sinh (x)} - 1)$
22926	Evaluate the Limit	( limit as x approaches 0 of 1-cos(x)^2)/x	$\frac{lim_{x \to 0} 1 - \cos^{2} (x)}{x}$
22927	Evaluate the Limit	limit as x approaches 0 of (tan(17x))/(sin(5x))	$lim_{x \to 0} \frac{\tan (17 x)}{\sin (5 x)}$
22928	Evaluate the Limit	limit as x approaches 0 of (sin(4x))/(sin(5x))	$lim_{x \to 0} \frac{\sin (4 x)}{\sin (5 x)}$
22929	Evaluate the Limit	( limit as x approaches 0 of 9-9cos(x))/(x^2)	$\frac{lim_{x \to 0} 9 - 9 \cos (x)}{x^{2}}$
22930	Evaluate the Limit	limit as x approaches 55 of ( square root of x+9-8)/(x-55)	$lim_{x \to 55} \frac{\sqrt{x + 9} - 8}{x - 55}$
22931	Evaluate the Limit	( limit as x approaches 0 of 5x^4+27x^2)/(3x^2-6x^2)	$\frac{lim_{x \to 0} 5 x^{4} + 27 x^{2}}{3 x^{2} - 6 x^{2}}$
22932	Evaluate the Limit	( limit as t approaches 0 of t^2)/(1-cos(t)^2)	$\frac{lim_{t \to 0} t^{2}}{1 - \cos^{2} (t)}$
22933	Evaluate the Limit	( limit as n approaches 8 of x^2+xe^(xn)+1)/(e^(nx)+1)	$\frac{lim_{n \to 8} x^{2} + x e^{x n} + 1}{e^{n x} + 1}$
22934	Evaluate the Limit	( limit as r approaches 0 of 3^r-1)/r	$\frac{lim_{r \to 0} 3^{r} - 1}{r}$
22935	Evaluate the Limit	( limit as h approaches 0 of 2^h-1)/h	$\frac{lim_{h \to 0} 2^{h} - 1}{h}$
22936	Evaluate the Limit	( limit as h approaches 2 of ( square root of 9+h)-3)/h	$\frac{lim_{h \to 2} (\sqrt{9 + h}) - 3}{h}$
22937	Evaluate the Limit	( limit as n approaches 8 of (lgn)^901)/(n^900)	$\frac{lim_{n \to 8} {(l g n)}^{901}}{n^{900}}$
22938	Evaluate the Limit	( limit as t approaches 1 of square root of t-1)/(t-1)	$\frac{lim_{t \to 1} \sqrt{t} - 1}{t - 1}$
22939	Evaluate the Limit	( limit as x approaches -1/8 of 4x^2+x+1/16)/((8x+1)^2)	$\frac{lim_{x \to - \frac{1}{8}} 4 x^{2} + x + \frac{1}{16}}{{(8 x + 1)}^{2}}$
22940	Evaluate the Limit	( limit as x approaches pi/3 of sin(x-pi/3))/(1-cos(2x))	$\frac{lim_{x \to \frac{π}{3}} \sin (x - \frac{π}{3})}{1 - \cos (2 x)}$
22941	Evaluate the Limit	( limit as x approaches -b of (x+b)^7+(x+b)^10)/(4(x+b))	$\frac{lim_{x \to - b} {(x + b)}^{7} + {(x + b)}^{10}}{4 (x + b)}$
22942	Evaluate the Limit	limit as x approaches pi of cos(4x)	$lim_{x \to π} \cos (4 x)$
22943	Evaluate the Limit	limit as x approaches pi of 9x^2tan(pix)	$lim_{x \to π} 9 x^{2} \tan (π x)$
22944	Evaluate the Limit	limit as x approaches pi of cos(x+sin(x))	$lim_{x \to π} \cos (x + \sin (x))$
22945	Evaluate the Limit	limit as x approaches pi of x/(cos(x))	$lim_{x \to π} \frac{x}{\cos (x)}$
22946	Evaluate the Limit	limit as x approaches pi of 3sin(x)	$lim_{x \to π} 3 \sin (x)$
22947	Evaluate the Limit	limit as x approaches 0 of (sin(3x))/(5x^3-4x)	$lim_{x \to 0} \frac{\sin (3 x)}{5 x^{3} - 4 x}$
22948	Evaluate the Limit	limit as x approaches 2 of (x^5-32)/(x-2)	$lim_{x \to 2} \frac{(x^{5} - 32)}{x - 2}$
22949	Evaluate the Limit	limit as x approaches 12 of (x-12)/(x^2-144)	$lim_{x \to 12} \frac{x - 12}{x^{2} - 144}$
22950	Evaluate the Limit	limit as t approaches 2 of (3t^2-7t+2)/(2-t)	$lim_{t \to 2} \frac{3 t^{2} - 7 t + 2}{2 - t}$
22951	Evaluate the Limit	limit as x approaches -3 of (x^2-2x-15)/(x+3)	$lim_{x \to - 3} \frac{x^{2} - 2 x - 15}{x + 3}$
22952	Evaluate the Limit	limit as x approaches pi of (cos(x))/(x-pi)	$lim_{x \to π} \frac{\cos (x)}{x - π}$
22953	Evaluate the Limit	limit as y approaches 1 of (y-4 square root of y+3)/(y^2)	$lim_{y \to 1} \frac{y - 4 \sqrt{y + 3}}{y^{2}}$
22954	Evaluate the Limit	limit as y approaches 2 of y^2-1/y	$lim_{y \to 2} y^{2} - \frac{1}{y}$
22955	Evaluate the Limit	limit as y approaches 2 of (y+2)/(y^2+5y+6)	$lim_{y \to 2} \frac{y + 2}{y^{2} + 5 y + 6}$
22956	Evaluate the Limit	limit as x approaches 0 of (1-cos(x))/(x^2)	$lim_{x \to 0} \frac{(1 - \cos (x))}{x^{2}}$
22957	Evaluate the Limit	( limit as h approaches 0 of (h+10)^2-100)/h	$\frac{lim_{h \to 0} {(h + 10)}^{2} - 100}{h}$
22958	Evaluate the Limit	( limit as x approaches 0 of (12)^x-13^x)/x	$\frac{lim_{x \to 0} {(12)}^{x} - 13^{x}}{x}$
22959	Evaluate the Limit	limit as z approaches -1 of (3x^2+x+1)/(x^3+1)	$lim_{z \to - 1} \frac{3 x^{2} + x + 1}{x^{3} + 1}$
22960	Evaluate the Limit	(( limit as x approaches 4 of x)/(x+1)-4/5)/(x-4)	$\frac{\frac{lim_{x \to 4} x}{x + 1} - \frac{4}{5}}{x - 4}$
22961	Evaluate the Limit	limit as y approaches 0 of (y^2)/(1-cos(y))	$lim_{y \to 0} \frac{y^{2}}{1 - \cos (y)}$
22962	Evaluate the Limit	limit as y approaches 0 of 1/y	$lim_{y \to 0} \frac{1}{y}$
22963	Evaluate the Limit	limit as y approaches -3 of square root of (y^(2-9))/(2y^2+7y+3)	$lim_{y \to - 3} \sqrt{\frac{y^{2 - 9}}{2 y^{2} + 7 y + 3}}$
22964	Evaluate the Limit	limit as y approaches 81 of (81-y)/(9- square root of y)	$lim_{y \to 81} \frac{81 - y}{9 - \sqrt{y}}$
22965	Evaluate the Limit	limit as x approaches 1 of x/(x-1)	$lim_{x \to 1} \frac{x}{x - 1}$
22966	Find the Derivative - d/dx	y=1/(x^9)	$y = \frac{1}{x^{9}}$
22967	Find the Integral	2 square root of x	$2 \sqrt{x}$
22968	Evaluate the Limit	limit as x approaches 269 of (x-269)/( square root of x+20-17)	$lim_{x \to 269} \frac{x - 269}{\sqrt{x + 20} - 17}$
22969	Evaluate the Limit	limit as x approaches 3 of f(3)	$lim_{x \to 3} f (3)$
22970	Evaluate the Limit	limit as x approaches 0 from the right of 1/x-1/(\|x\|)	$lim_{x \to 0} \frac{1}{x} - \frac{1}{\| x \|}$
22971	Evaluate the Limit	limit as x approaches 0 from the right of f'(x)	$lim_{x \to 0} f' (x)$
22972	Find the Derivative - d/d@VAR	f(x)=e^(3x) natural log of 2x^2-2	$f (x) = e^{3 x} \ln (2 x^{2} - 2)$
22973	Find the x and y Intercepts	f(x)=(3x^3-x^2-48x+16)/(x^2+5x+4)	$f (x) = \frac{3 x^{3} - x^{2} - 48 x + 16}{x^{2} + 5 x + 4}$
22974	Find dy/dx	xsin(y)+ysin(x)=6	$x \sin (y) + y \sin (x) = 6$
22975	Evaluate the Limit	limit as x approaches 0 of x^2sin(x)	$lim_{x \to 0} x^{2} \sin (x)$
22976	Find dy/dx	x^4+y^4=1	$x^{4} + y^{4} = 1$
22977	Find dy/dx	x^4+3x^3y^2=x-y^4	$x^{4} + 3 x^{3} y^{2} = x - y^{4}$
22978	Find dy/dx	y=(5x^2-9x+11)/(2x+4)	$y = \frac{5 x^{2} - 9 x + 11}{2 x + 4}$
22979	Evaluate the Limit	limit as x approaches 0 of ( square root of x)sin(1/x)	$lim_{x \to 0} (\sqrt{x}) \sin (\frac{1}{x})$
22980	Find dy/dx	y=(x-1)^2+1	$y = {(x - 1)}^{2} + 1$
22981	Find the Derivative - d/d@VAR	f(x)=(e^(2x))/(x^10)	$f (x) = \frac{e^{2 x}}{x^{10}}$
22982	Find the Derivative - d/dx	natural log of 3x+5	$\ln (3 x + 5)$
22983	Find the Derivative - d/d@VAR	f(x)=4x^2+3x	$f (x) = 4 x^{2} + 3 x$
22984	Find the Derivative - d/d@VAR	f(x)=4x^4 natural log of x	$f (x) = 4 x^{4} \ln (x)$
22985	Evaluate the Limit	limit as x approaches 0 of csc(x)-1/x	$lim_{x \to 0} \csc (x) - \frac{1}{x}$
22986	Evaluate the Limit	limit as x approaches 0 of (6x^2)(cot(x))(csc(2x))	$lim_{x \to 0} (6 x^{2}) (\cot (x)) (\csc (2 x))$
22987	Evaluate the Limit	limit as x approaches 1 of x-1/(\|x-1\|)	$lim_{x \to 1} x - \frac{1}{\| x - 1 \|}$
22988	Simplify	(x^(1/3)-1/(4x^(1/3)))^2	${(x^{\frac{1}{3}} - \frac{1}{4 x^{\frac{1}{3}}})}^{2}$
22989	Simplify	cos(infinity)	$\cos (\infty)$
22990	Evaluate the Limit	limit as x approaches 1 of (1/(1-x))-3/(1-x^3)	$lim_{x \to 1} (\frac{1}{1 - x}) - \frac{3}{1 - x^{3}}$
22991	Evaluate the Limit	limit as x approaches -3 of x^2-16+ cube root of x^2-36	$lim_{x \to - 3} x^{2} - 16 + \sqrt[3]{x^{2} - 36}$
22992	Evaluate the Limit	limit as x approaches 3 of x+7	$lim_{x \to 3} x + 7$
22993	Evaluate the Limit	limit as x approaches 2.9 of (2x-1)/(x-3)	$lim_{x \to 2.9} \frac{2 x - 1}{x - 3}$
22994	Find the 2nd Derivative	f(x)=x square root of 9-x	$f (x) = x \sqrt{9 - x}$
22995	Find the 2nd Derivative	cot(theta)	$\cot (θ)$
22996	Evaluate the Limit	limit as x approaches 2 from the right of (x^7-128)/(2x-4)	$lim_{x \to 2} \frac{x^{7} - 128}{2 x - 4}$
22997	Evaluate the Limit	limit as x approaches 2 from the right of (5-2x)/(x-2)	$lim_{x \to 2} \frac{5 - 2 x}{x - 2}$
22998	Evaluate the Limit	limit as x approaches 25 of (x^2-625)/(x-25)	$lim_{x \to 25} \frac{x^{2} - 625}{x - 25}$
22999	Evaluate the Limit	limit as x approaches 2 of x^3+2x^2-8x+5	$lim_{x \to 2} x^{3} + 2 x^{2} - 8 x + 5$
23000	Evaluate the Integral	integral of tan(3x) with respect to x	$\int \tan (3 x) d x$