Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
22801	Evaluate the Limit	limit as t approaches 0 of 5/t-5/(t^2+t)	$lim_{t \to 0} \frac{5}{t} - \frac{5}{t^{2} + t}$
22802	Evaluate the Limit	limit as x approaches 8 of arcsec(x)	$lim_{x \to 8} arcsec (x)$
22803	Evaluate the Limit	limit as x approaches 8 of arctan(x/2)	$lim_{x \to 8} \arctan (\frac{x}{2})$
22804	Evaluate the Limit	limit as x approaches 8 of arctan(x^6-x^8)	$lim_{x \to 8} \arctan (x^{6} - x^{8})$
22805	Evaluate the Limit	limit as x approaches -4 of (x+4)/( square root of 3x+13-1)	$lim_{x \to - 4} \frac{x + 4}{\sqrt{3 x + 13} - 1}$
22806	Evaluate the Limit	limit as x approaches infinity of 4+3/x	$lim_{x \to \infty} 4 + \frac{3}{x}$
22807	Evaluate the Limit	limit as x approaches 8 of (4)arctan(x/3)	$lim_{x \to 8} (4) \arctan (\frac{x}{3})$
22808	Evaluate the Limit	limit as x approaches 4 of (4-x)/( square root of x-2)	$lim_{x \to 4} \frac{4 - x}{\sqrt{x} - 2}$
22809	Evaluate the Limit	limit as x approaches 8 of 3x^5-8x^4+1	$lim_{x \to 8} 3 x^{5} - 8 x^{4} + 1$
22810	Evaluate the Limit	limit as x approaches 8 of 7cos(x)	$lim_{x \to 8} 7 \cos (x)$
22811	Evaluate the Limit	limit as x approaches -8 of -5x^3+23x^2+15x+9	$lim_{x \to - 8} - 5 x^{3} + 23 x^{2} + 15 x + 9$
22812	Evaluate the Limit	limit as x approaches -8 of (x-2)/(x^2+1)	$lim_{x \to - 8} \frac{x - 2}{x^{2} + 1}$
22813	Evaluate the Limit	limit as x approaches infinity of ( square root of t+t^2)/(9t-t^2)	$lim_{x \to \infty} \frac{\sqrt{t} + t^{2}}{9 t - t^{2}}$
22814	Evaluate the Limit	limit as x approaches 8 of x^8e^(-x^7)	$lim_{x \to 8} x^{8} e^{- x^{7}}$
22815	Evaluate the Limit	limit as x approaches 2 of (1/x-1/2)/(x-2)	$lim_{x \to 2} \frac{(\frac{1}{x} - \frac{1}{2})}{x - 2}$
22816	Evaluate the Limit	limit as x approaches 8 of (x+3)/(x^2+7)	$lim_{x \to 8} \frac{x + 3}{x^{2} + 7}$
22817	Evaluate the Limit	limit as x approaches 8 of x^4e^x	$lim_{x \to 8} x^{4} e^{x}$
22818	Evaluate the Limit	limit as x approaches 8 of x^3	$lim_{x \to 8} x^{3}$
22819	Evaluate the Limit	limit as x approaches -8 of x^3	$lim_{x \to - 8} x^{3}$
22820	Evaluate the Limit	limit as x approaches -8 of x^2e^(2x)	$lim_{x \to - 8} x^{2} e^{2 x}$
22821	Evaluate the Limit	limit as x approaches 8 of x^2e^(-2x)	$lim_{x \to 8} x^{2} e^{- 2 x}$
22822	Evaluate the Limit	limit as x approaches 8 of x^17e^(-x)	$lim_{x \to 8} x^{17} e^{- x}$
22823	Evaluate the Limit	limit as x approaches 8 of square root of x-4	$lim_{x \to 8} \sqrt{x - 4}$
22824	Evaluate the Limit	limit as x approaches 8 of fourth root of (7+81x^2)/(x^2+8)	$lim_{x \to 8} \sqrt[4]{\frac{7 + 81 x^{2}}{x^{2} + 8}}$
22825	Evaluate the Limit	limit as x approaches 0 of ((x+3)^2-9)/(2x)	$lim_{x \to 0} \frac{{(x + 3)}^{2} - 9}{2 x}$
22826	Evaluate the Limit	limit as x approaches 0 of (sin(x)(1-cos(x)))/(3x^2)	$lim_{x \to 0} \frac{\sin (x) (1 - \cos (x))}{3 x^{2}}$
22827	Evaluate the Limit	limit as x approaches 1 of ( square root of 5x+4-3)/(x-1)	$lim_{x \to 1} \frac{\sqrt{5 x + 4} - 3}{x - 1}$
22828	Evaluate the Limit	limit as x approaches 0 of (cot(4x))/(cot(3x))	$lim_{x \to 0} \frac{\cot (4 x)}{\cot (3 x)}$
22829	Evaluate the Limit	limit as x approaches 0 of 7/x-7/(\|x\|)	$lim_{x \to 0} \frac{7}{x} - \frac{7}{\| x \|}$
22830	Evaluate the Limit	limit as x approaches 0 of (sin(5x))/(sin(4x))	$lim_{x \to 0} \frac{\sin (5 x)}{\sin (4 x)}$
22831	Evaluate the Limit	limit as x approaches 0 of (1+sin(4x))^(cot(x))	$lim_{x \to 0} {(1 + \sin (4 x))}^{\cot (x)}$
22832	Evaluate the Limit	limit as x approaches pi/4 of (sin(x)-cos(x))/(tan(x)-1)	$lim_{x \to \frac{π}{4}} \frac{\sin (x) - \cos (x)}{\tan (x) - 1}$
22833	Find the Derivative - d/d@VAR	f(x)=1/(x+8)	$f (x) = \frac{1}{x + 8}$
22834	Evaluate the Limit	limit as x approaches 0 of ( log base y of 1+x)/x	$lim_{x \to 0} \frac{\log_{y} (1 + x)}{x}$
22835	Find the Derivative - d/d@VAR	f(x)=(2x-9)^4(x^2+x+1)^5	$f (x) = {(2 x - 9)}^{4} {(x^{2} + x + 1)}^{5}$
22836	Find the Derivative - d/d@VAR	f(t)=(e^(6t)+e^(-6t))/(e^(4t))	$f (t) = \frac{e^{6 t} + e^{- 6 t}}{e^{4 t}}$
22837	Evaluate the Limit	limit as x approaches 0 of (e^(8x)-1)/(2x)	$lim_{x \to 0} \frac{e^{8 x} - 1}{2 x}$
22838	Evaluate the Limit	limit as x approaches 0 of ((9+x)^-1-9^-1)/x	$lim_{x \to 0} \frac{{(9 + x)}^{- 1} - 9^{- 1}}{x}$
22839	Find the Derivative - d/d@VAR	g(x) = square root of 11x	$g (x) = \sqrt{11 x}$
22840	Find the Derivative - d/dt	tan(t)	$\tan (t)$
22841	Evaluate the Limit	limit as x approaches 0 of (1/x)-1/(\|x\|)	$lim_{x \to 0} (\frac{1}{x}) - \frac{1}{\| x \|}$
22842	Evaluate the Limit	limit as x approaches 0 of (sin(2x))/(x^2)	$lim_{x \to 0} \frac{\sin (2 x)}{x^{2}}$
22843	Find the Derivative - d/dx	(4x^3)/(3y^2)	$\frac{4 x^{3}}{3 y^{2}}$
22844	Evaluate the Limit	limit as x approaches 0 of 4/(2+e^(1/x))	$lim_{x \to 0} \frac{4}{2 + e^{\frac{1}{x}}}$
22845	Evaluate the Limit	limit as x approaches 0 of (cos(7x))/x	$lim_{x \to 0} \frac{\cos (7 x)}{x}$
22846	Find the Derivative - d/dx	2^40	$2^{40}$
22847	Evaluate the Limit	limit as x approaches 0 from the left of (6x)/(x^4)	$lim_{x \to 0} \frac{6 x}{x^{4}}$
22848	Find the Derivative - d/dx	4xe^x	$4 x e^{x}$
22849	Evaluate the Limit	limit as x approaches 0 from the left of 3/(sin(x))	$lim_{x \to 0} \frac{3}{\sin (x)}$
22850	Evaluate the Limit	limit as x approaches 0 of (4/x)-4/(sin(x))	$lim_{x \to 0} (\frac{4}{x}) - \frac{4}{\sin (x)}$
22851	Evaluate the Limit	limit as x approaches 0 of (e^(4x)-e^(2x))/(e^x-1)	$lim_{x \to 0} \frac{e^{4 x} - e^{2 x}}{e^{x} - 1}$
22852	Find the Derivative - d/dx	square root of 12x	$\sqrt{12 x}$
22853	Solve for x	3^(2x)-108*3^x+2187=0	$3^{2 x} - 108 \cdot 3^{x} + 2187 = 0$
22854	Evaluate the Limit	limit as r approaches -3 of -3/(r+3)	$lim_{r \to - 3} - \frac{3}{r + 3}$
22855	Evaluate the Limit	limit as x approaches pi/2 of tan(x)^(cos(x))	$lim_{x \to \frac{π}{2}} {\tan (x)}^{\cos (x)}$
22856	Evaluate the Limit	limit as x approaches pi/12 of tan(36(x))	$lim_{x \to \frac{π}{12}} \tan (36 (x))$
22857	Evaluate the Limit	limit as x approaches pi/4 of tan(x)^(tan(2x))	$lim_{x \to \frac{π}{4}} {\tan (x)}^{\tan (2 x)}$
22858	Evaluate the Limit	limit as x approaches pi/4 of tan(x)^(tan(x))	$lim_{x \to \frac{π}{4}} {\tan (x)}^{\tan (x)}$
22859	Evaluate the Limit	limit as n approaches 8 of (1+2+3+n)/(3n+1)-n/6	$lim_{n \to 8} \frac{1 + 2 + 3 + n}{3 n + 1} - \frac{n}{6}$
22860	Evaluate	cos(2)pi	$\cos (2) π$
22861	Evaluate the Limit	limit as x approaches 4 of (12+ square root of x)/( square root of 12+x)	$lim_{x \to 4} \frac{12 + \sqrt{x}}{\sqrt{12 + x}}$
22862	Evaluate the Limit	limit as t approaches 0 of (tan(8t))/(sin(4t))	$lim_{t \to 0} \frac{\tan (8 t)}{\sin (4 t)}$
22863	Evaluate the Limit	limit as x approaches pi/2 from the right of -2/(cos(x))	$lim_{x \to \frac{π}{2}} - \frac{2}{\cos (x)}$
22864	Evaluate the Limit	limit as x approaches pi/2 of sin(x)^2-1	$lim_{x \to \frac{π}{2}} \sin^{2} (x) - 1$
22865	Evaluate the Limit	f(x) = limit as x approaches 0.6 of 2640(400)	$f (x) = lim_{x \to 0.6} 2640 (400)$
22866	Evaluate the Limit	limit as x approaches 0 of (cos(2x-1))/(sin(9x))	$lim_{x \to 0} \frac{\cos (2 x - 1)}{\sin (9 x)}$
22867	Evaluate the Limit	( limit as x approaches 8 of 2x+3)/(5x+7)	$\frac{lim_{x \to 8} 2 x + 3}{5 x + 7}$
22868	Evaluate the Limit	limit as x approaches 8 of (1+sin(x))^(csc(x))	$lim_{x \to 8} {(1 + \sin (x))}^{\csc (x)}$
22869	Evaluate the Limit	( limit as x approaches 7 of cube root of x+1-2)/(x-7)	$\frac{lim_{x \to 7} \sqrt[3]{x + 1} - 2}{x - 7}$
22870	Evaluate the Limit	7 limit as x approaches 5 of g(-2)	$7 lim_{x \to 5} g (- 2)$
22871	Evaluate the Integral	integral of 1/2 with respect to x	$\int \frac{1}{2} d x$
22872	Evaluate the Limit	limit as h approaches 0 of ((x+h)-x)/h	$lim_{h \to 0} \frac{(x + h) - x}{h}$
22873	Evaluate the Limit	limit as h approaches 0 of (sin(5x+5h)-sin(5x))/h	$lim_{h \to 0} \frac{\sin (5 x + 5 h) - \sin (5 x)}{h}$
22874	Evaluate the Limit	limit as h approaches 0 of (tan(2(x+h))-tan(2x))/h	$lim_{h \to 0} \frac{\tan (2 (x + h)) - \tan (2 x)}{h}$
22875	Evaluate the Limit	limit as h approaches 0 of (sin(4h))/(4h)	$lim_{h \to 0} \frac{\sin (4 h)}{4 h}$
22876	Evaluate the Limit	limit as h approaches 0 of ((6+h)^2-36)/h	$lim_{h \to 0} \frac{{(6 + h)}^{2} - 36}{h}$
22877	Evaluate the Limit	limit as h approaches 0 of (5- square root of 4-(3+h)-(5- square root of 4-3))/h	$lim_{h \to 0} \frac{5 - \sqrt{4 - (3 + h)} - (5 - \sqrt{4 - 3})}{h}$
22878	Evaluate the Limit	limit as h approaches 0 of 3h+12	$lim_{h \to 0} 3 h + 12$
22879	Evaluate the Limit	limit as h approaches 0 of ( square root of 5+h- square root of 5)/h	$lim_{h \to 0} \frac{\sqrt{5 + h} - \sqrt{5}}{h}$
22880	Evaluate the Limit	limit as h approaches 0 of ((1+h)^10-1)/h	$lim_{h \to 0} \frac{{(1 + h)}^{10} - 1}{h}$
22881	Evaluate the Limit	limit as n approaches 8 of e^(-n)cos(n)	$lim_{n \to 8} e^{- n} \cos (n)$
22882	Evaluate the Limit	limit as n approaches 8 of (sin(n))/n	$lim_{n \to 8} \frac{\sin (n)}{n}$
22883	Evaluate the Limit	limit as h approaches 0 of 2h+4	$lim_{h \to 0} 2 h + 4$
22884	Evaluate the Limit	limit as h approaches 0 of (f(a+h)-fa)/h	$lim_{h \to 0} \frac{f (a + h) - f a}{h}$
22885	Evaluate the Limit	limit as n approaches 8 of (3n^2+4n+5)/(2n^2-3n+1)	$lim_{n \to 8} \frac{3 n^{2} + 4 n + 5}{2 n^{2} - 3 n + 1}$
22886	Evaluate the Limit	limit as n approaches 8 of (e^n)/(2^n)	$lim_{n \to 8} \frac{e^{n}}{2^{n}}$
22887	Evaluate the Limit	limit as t approaches 25 of (t+5)t^(-1/2)	$lim_{t \to 25} (t + 5) t^{- \frac{1}{2}}$
22888	Evaluate the Integral	integral of square root of 2x+1 with respect to x	$\int \sqrt{2 x + 1} d x$
22889	Evaluate the Limit	( limit as x approaches -6 of x^2+10x+24)/(x+6)	$\frac{lim_{x \to - 6} x^{2} + 10 x + 24}{x + 6}$
22890	Evaluate the Limit	( limit as x approaches 3 of x^2-5x-6)/(x^2-2x-3)	$\frac{lim_{x \to 3} x^{2} - 5 x - 6}{x^{2} - 2 x - 3}$
22891	Evaluate the Limit	( limit as x approaches 4 of 3x^2-17x+20)/(4x^2-25x+36)	$\frac{lim_{x \to 4} 3 x^{2} - 17 x + 20}{4 x^{2} - 25 x + 36}$
22892	Evaluate the Limit	( limit as x approaches 4 of x^2-x-12)/(x-4)	$\frac{lim_{x \to 4} x^{2} - x - 12}{x - 4}$
22893	Evaluate the Integral	integral of sec(theta) with respect to theta	$\int \sec (θ) d θ$
22894	Evaluate the Integral	integral of natural log of x^2+16 with respect to x	$\int \ln (x^{2} + 16) d x$
22895	Evaluate the Limit	( limit as x approaches 4 of 9)/(x^2-8x+16)	$\frac{lim_{x \to 4} 9}{x^{2} - 8 x + 16}$
22896	Evaluate the Integral	integral of cos(6x) with respect to x	$\int \cos (6 x) d x$
22897	Evaluate the Limit	( limit as x approaches -4 of x+8)/(x-4)	$\frac{lim_{x \to - 4} x + 8}{x - 4}$
22898	Evaluate the Limit	( limit as x approaches 49 of square root of x- square root of 7)/(x-49)	$\frac{lim_{x \to 49} \sqrt{x} - \sqrt{7}}{x - 49}$
22899	Graph	f(x)=4x^3-12x	$f (x) = 4 x^{3} - 12 x$
22900	Determine if Continuous	f(x)=4x-5	$f (x) = 4 x - 5$