Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
32701	Evaluate the Limit	limit as x approaches x from the right of 3/(x^3)-1/x	$lim_{x \to x} \frac{3}{x^{3}} - \frac{1}{x}$
32702	Evaluate the Limit	limit as x approaches 6 of (x-6)/(x^2-15x+54)	$lim_{x \to 6} \frac{x - 6}{x^{2} - 15 x + 54}$
32703	Evaluate the Limit	limit as x approaches (3pi)/2 of (sin(x)^2+4sin(x)+3)/(sin(x)+1)	$lim_{x \to \frac{3 π}{2}} \frac{\sin^{2} (x) + 4 \sin (x) + 3}{\sin (x) + 1}$
32704	Evaluate the Limit	limit as x approaches -1^-1 of (2x-6)/(x+1)	$lim_{x \to - 1^{- 1}} \frac{2 x - 6}{x + 1}$
32705	Evaluate the Limit	limit as x approaches 11/10 of -(22x)/(11-10x)	$lim_{x \to \frac{11}{10}} - \frac{22 x}{11 - 10 x}$
32706	Evaluate the Limit	limit as x approaches 11/2 of (17x)/(11-2x)	$lim_{x \to \frac{11}{2}} \frac{17 x}{11 - 2 x}$
32707	Evaluate the Limit	limit as x approaches 0 of x/(x^2-6x)	$lim_{x \to 0} \frac{x}{x^{2} - 6 x}$
32708	Evaluate the Limit	limit as x approaches 0 of (tan(11x))/(sin(4x))	$lim_{x \to 0} \frac{\tan (11 x)}{\sin (4 x)}$
32709	Evaluate the Limit	limit as x approaches 0 of (tan(2x))/(sin(8x))	$lim_{x \to 0} \frac{\tan (2 x)}{\sin (8 x)}$
32710	Evaluate the Limit	limit as x approaches 0 of (sin(8x))/(-8x)	$lim_{x \to 0} \frac{\sin (8 x)}{- 8 x}$
32711	Evaluate the Limit	limit as x approaches 2/3 of ( log of x-1)/(2x-3x^2)	$lim_{x \to \frac{2}{3}} \frac{\log (x - 1)}{2 x - 3 x^{2}}$
32712	Evaluate the Limit	limit as x approaches 0 of f(x)-gx	$lim_{x \to 0} f (x) - g x$
32713	Evaluate the Limit	limit as x approaches 0 of (x^2-3x-10)/(x-5)	$lim_{x \to 0} \frac{x^{2} - 3 x - 10}{x - 5}$
32714	Evaluate the Limit	limit as x approaches 0 of (e^(9x)-1-9x)/(x^2)	$lim_{x \to 0} \frac{e^{9 x} - 1 - 9 x}{x^{2}}$
32715	Evaluate the Limit	limit as x approaches 0 of (1-cos( square root of x))/x	$lim_{x \to 0} \frac{1 - \cos (\sqrt{x})}{x}$
32716	Evaluate the Limit	limit as x approaches 0 of x^2+10	$lim_{x \to 0} x^{2} + 10$
32717	Evaluate the Limit	limit as x approaches infinity of (e^(2x)+e^(-2x))/(e^(2x)-e^(-2x))	$lim_{x \to \infty} \frac{e^{2 x} + e^{- 2 x}}{e^{2 x} - e^{- 2 x}}$
32718	Evaluate the Limit	limit as x approaches 0 of (sin(x)^3)/(sin(x)-tan(x))	$lim_{x \to 0} \frac{\sin^{3} (x)}{\sin (x) - \tan (x)}$
32719	Find the Derivative - d/dx	(x-x^2)/(2-3x+x^2)	$\frac{x - x^{2}}{2 - 3 x + x^{2}}$
32720	Evaluate the Limit	limit as x approaches 3/2 of 2x^3-3x^2-4x+2	$lim_{x \to \frac{3}{2}} 2 x^{3} - 3 x^{2} - 4 x + 2$
32721	Evaluate the Limit	limit as x approaches 3/2 of square root of (4x^2-9)/(8x^3-27)	$lim_{x \to \frac{3}{2}} \sqrt{\frac{4 x^{2} - 9}{8 x^{3} - 27}}$
32722	Evaluate the Limit	limit as x approaches 3/2 of (4x^2)+6x+9	$lim_{x \to \frac{3}{2}} (4 x^{2}) + 6 x + 9$
32723	Evaluate the Limit	limit as x approaches 0 of x^(sin(x))	$lim_{x \to 0} x^{\sin (x)}$
32724	Evaluate the Limit	limit as x approaches (3pi)/2 of (5cos(x))/(x-((3pi)/2))	$lim_{x \to \frac{3 π}{2}} \frac{5 \cos (x)}{x - (\frac{3 π}{2})}$
32725	Evaluate the Limit	limit as x approaches 0 of (sin(3x))/(tan(2x))	$lim_{x \to 0} \frac{\sin (3 x)}{\tan (2 x)}$
32726	Evaluate the Limit	limit as x approaches 0 of e^(4/x)	$lim_{x \to 0} e^{\frac{4}{x}}$
32727	Evaluate the Limit	limit as x approaches 0 of 0/x	$lim_{x \to 0} \frac{0}{x}$
32728	Evaluate the Limit	limit as t approaches 16 of (16-t)/(4- square root of t)	$lim_{t \to 16} \frac{16 - t}{4 - \sqrt{t}}$
32729	Evaluate the Limit	limit as x approaches 5/3 of (x-7)/(3x+5)	$lim_{x \to \frac{5}{3}} \frac{x - 7}{3 x + 5}$
32730	Evaluate the Limit	limit as x approaches pi/2 of cos(cos(x))	$lim_{x \to \frac{π}{2}} \cos (\cos (x))$
32731	Evaluate the Limit	limit as x approaches (5pi)/16 of cos(8x-cos(8x))	$lim_{x \to \frac{5 π}{16}} \cos (8 x - \cos (8 x))$
32732	Evaluate the Limit	limit as x approaches (5pi)/2 of 9tan(x)	$lim_{x \to \frac{5 π}{2}} 9 \tan (x)$
32733	Evaluate the Limit	limit as x approaches (5pi)/3 of cos(x)	$lim_{x \to \frac{5 π}{3}} \cos (x)$
32734	Evaluate the Limit	limit as h approaches 0 of (f(9+h)-f*9)/h	$lim_{h \to 0} \frac{f (9 + h) - f \cdot 9}{h}$
32735	Evaluate the Limit	limit as x approaches (7pi)/2 of (e)tan(x)	$lim_{x \to \frac{7 π}{2}} (e) \tan (x)$
32736	Evaluate the Limit	limit as x approaches (7pi)/2 of 3xtan(x)	$lim_{x \to \frac{7 π}{2}} 3 x \tan (x)$
32737	Evaluate the Limit	limit as h approaches 0 of ((1+h)^(1/3)-1)/h	$lim_{h \to 0} \frac{{(1 + h)}^{\frac{1}{3}} - 1}{h}$
32738	Evaluate the Limit	limit as h approaches 0 of ((x+h)^4-x^4)/h	$lim_{h \to 0} \frac{{(x + h)}^{4} - x^{4}}{h}$
32739	Evaluate the Limit	limit as h approaches 0 of ( square root of 20h+1-1)/h	$lim_{h \to 0} \frac{\sqrt{20 h + 1} - 1}{h}$
32740	Evaluate the Limit	limit as x approaches -5 of (x^3-5x^2)/(x-5)	$lim_{x \to - 5} \frac{x^{3} - 5 x^{2}}{x - 5}$
32741	Evaluate the Limit	limit as x approaches 48 of ( square root of x+1-7)/(x-48)	$lim_{x \to 48} \frac{\sqrt{x + 1} - 7}{x - 48}$
32742	Evaluate the Limit	limit as x approaches 4 of (x^3+6x^2-28x-48)/(x-4)	$lim_{x \to 4} \frac{x^{3} + 6 x^{2} - 28 x - 48}{x - 4}$
32743	Evaluate the Limit	limit as x approaches -3 of (x^3-3x^2)/(x-3)	$lim_{x \to - 3} \frac{x^{3} - 3 x^{2}}{x - 3}$
32744	Evaluate the Limit	limit as x approaches 3 of (x^3+19x^2-68x+6)/(x^3-9x)	$lim_{x \to 3} \frac{x^{3} + 19 x^{2} - 68 x + 6}{x^{3} - 9 x}$
32745	Evaluate the Limit	limit as n approaches 8 of (2n^2+1)/(n+1)-(2n^2+1)/(n-1)	$lim_{n \to 8} \frac{2 n^{2} + 1}{n + 1} - \frac{2 n^{2} + 1}{n - 1}$
32746	Find the Derivative - d/dx	x^13	$x^{13}$
32747	Evaluate the Limit	limit as x approaches 3 of ( square root of 3x+7-4)/(x^2-9)	$lim_{x \to 3} \frac{\sqrt{3 x + 7} - 4}{x^{2} - 9}$
32748	Evaluate the Limit	limit as x approaches 8 of ((x-4)/(x-1))^(x+3)	$lim_{x \to 8} {(\frac{x - 4}{x - 1})}^{x + 3}$
32749	Evaluate the Limit	limit as x approaches 8 of (3-5x^3)/(1+4x+x^3)	$lim_{x \to 8} \frac{3 - 5 x^{3}}{1 + 4 x + x^{3}}$
32750	Evaluate the Limit	limit as x approaches 8 of (10x^5+3000x+2)/(5x^8+9)	$lim_{x \to 8} \frac{10 x^{5} + 3000 x + 2}{5 x^{8} + 9}$
32751	Evaluate the Limit	limit as x approaches 8 of ( square root of 6x^2-14)/(x+5)	$lim_{x \to 8} \frac{\sqrt{6 x^{2} - 14}}{x + 5}$
32752	Evaluate the Limit	limit as x approaches 8 of (x^6+8000x^3+1000000)/(2x^6+7000x^3)	$lim_{x \to 8} \frac{x^{6} + 8000 x^{3} + 1000000}{2 x^{6} + 7000 x^{3}}$
32753	Evaluate the Limit	limit as x approaches 8 of (12x^2+11x)/(3x^2-7x)	$lim_{x \to 8} \frac{12 x^{2} + 11 x}{3 x^{2} - 7 x}$
32754	Evaluate the Limit	limit as x approaches 8 of (2x^3-2x+5)/(5x^2-2x+1)	$lim_{x \to 8} \frac{2 x^{3} - 2 x + 5}{5 x^{2} - 2 x + 1}$
32755	Evaluate the Limit	limit as x approaches 8 of (24x+14)/(6x-9)	$lim_{x \to 8} \frac{24 x + 14}{6 x - 9}$
32756	Evaluate the Limit	limit as x approaches 8 of (2x-6)/(4-x)	$lim_{x \to 8} \frac{2 x - 6}{4 - x}$
32757	Evaluate the Limit	limit as x approaches 8 of (3x^2+8x-7)/(2x^2-7)	$lim_{x \to 8} \frac{3 x^{2} + 8 x - 7}{2 x^{2} - 7}$
32758	Evaluate the Limit	limit as x approaches 8 of (3x^7+40x^6)/(3000x^9+6)	$lim_{x \to 8} \frac{3 x^{7} + 40 x^{6}}{3000 x^{9} + 6}$
32759	Evaluate the Limit	limit as x approaches 8 of (5-10t^3)/(18t+1)	$lim_{x \to 8} \frac{5 - 10 t^{3}}{18 t + 1}$
32760	Evaluate the Limit	limit as x approaches 8 of (7-6x^5)/(x+3)	$lim_{x \to 8} \frac{7 - 6 x^{5}}{x + 3}$
32761	Evaluate the Limit	limit as x approaches 2 of (x^3+13x^2-31x+2)/(x^3-4x)	$lim_{x \to 2} \frac{x^{3} + 13 x^{2} - 31 x + 2}{x^{3} - 4 x}$
32762	Evaluate the Limit	limit as x approaches 1 of natural log of x/(e^x)	$lim_{x \to 1} \ln (\frac{x}{e^{x}})$
32763	Evaluate the Limit	limit as x approaches 0 of x^( natural log of x)	$lim_{x \to 0} x^{\ln (x)}$
32764	Evaluate the Limit	limit as x approaches 1 of ( square root of x-1)^(sin(pix))	$lim_{x \to 1} {(\sqrt{x - 1})}^{\sin (π x)}$
32765	Evaluate the Limit	limit as x approaches 2 of (x-5)/(x-2)	$lim_{x \to 2} \frac{x - 5}{x - 2}$
32766	Evaluate the Limit	limit as x approaches 8 of square root of 2x+1- square root of 2x	$lim_{x \to 8} \sqrt{2 x + 1} - \sqrt{2 x}$
32767	Evaluate the Limit	limit as x approaches 8 of (2x- square root of 4x^2-x+2 square root of x)/(2 square root of x-x)	$lim_{x \to 8} \frac{2 x - \sqrt{4 x^{2} - x + 2 \sqrt{x}}}{2 \sqrt{x} - x}$
32768	Evaluate the Limit	limit as x approaches 8 of (2x-2)/( square root of x^4+1)	$lim_{x \to 8} \frac{2 x - 2}{\sqrt{x^{4} + 1}}$
32769	Evaluate the Limit	limit as x approaches 8 of (-4x^2+5)/(-3x^2-11)	$lim_{x \to 8} \frac{- 4 x^{2} + 5}{- 3 x^{2} - 11}$
32770	Evaluate the Limit	limit as x approaches square root of 2 of (x^2+3)(x^2-1)	$lim_{x \to \sqrt{2}} (x^{2} + 3) (x^{2} - 1)$
32771	Evaluate the Limit	limit as x approaches square root of 5 of (2 square root of 5)+x	$lim_{x \to \sqrt{5}} (2 \sqrt{5}) + x$
32772	Evaluate the Limit	limit as x approaches x/16 of 3csc(4x)cot(4x)	$lim_{x \to \frac{x}{16}} 3 \csc (4 x) \cot (4 x)$
32773	Evaluate the Limit	limit as x approaches x/2 of tan(x) natural log of sin(x)	$lim_{x \to \frac{x}{2}} \tan (x) \ln (\sin (x))$
32774	Evaluate the Limit	limit as x approaches x^2 of x+3x	$lim_{x \to x^{2}} x + 3 x$
32775	Evaluate the Limit	limit as x approaches -1 of (x^2-1)/(x^2+2x-3)	$lim_{x \to - 1} \frac{x^{2} - 1}{x^{2} + 2 x - 3}$
32776	Evaluate the Limit	limit as x approaches 1 of (1-x^3)/(x-1)	$lim_{x \to 1} \frac{1 - x^{3}}{x - 1}$
32777	Find the Derivative - d/dx	4(5-7x)^5	$4 {(5 - 7 x)}^{5}$
32778	Evaluate the Limit	limit as x approaches infinity of (cos(2x))/(3x)	$lim_{x \to \infty} \frac{\cos (2 x)}{3 x}$
32779	Evaluate the Limit	limit as x approaches infinity of (x- square root of x)/(x+ square root of x)	$lim_{x \to \infty} \frac{x - \sqrt{x}}{x + \sqrt{x}}$
32780	Evaluate the Limit	limit as theta approaches 0 of (sin(3theta))/(tan(2theta))	$lim_{θ \to 0} \frac{\sin (3 θ)}{\tan (2 θ)}$
32781	Evaluate the Limit	limit as x approaches negative infinity of x^3-4x^2+5	$lim_{x \to - \infty} x^{3} - 4 x^{2} + 5$
32782	Evaluate the Limit	limit as x approaches 9 of (x-3)/(x^2-3x)	$lim_{x \to 9} \frac{x - 3}{x^{2} - 3 x}$
32783	Evaluate the Limit	limit as x approaches negative infinity of (2x+1)/( square root of x^2-x)	$lim_{x \to - \infty} \frac{2 x + 1}{\sqrt{x^{2} - x}}$
32784	Evaluate the Limit	limit as x approaches -pi/4 of f(x)	$lim_{x \to - \frac{π}{4}} f (x)$
32785	Evaluate the Limit	limit as x approaches pi/6 of sin(x)+tan(x)	$lim_{x \to \frac{π}{6}} \sin (x) + \tan (x)$
32786	Evaluate the Limit	limit as x approaches pi/6 of (2sin(x)+sin(x)-1)/(2sin(x)-3sin(x)+1)	$lim_{x \to \frac{π}{6}} \frac{2 \sin (x) + \sin (x) - 1}{2 \sin (x) - 3 \sin (x) + 1}$
32787	Evaluate the Limit	limit as x approaches pi/6 of (tan(x)-( square root of 3)/3)/(x-pi/6)	$lim_{x \to \frac{π}{6}} \frac{\tan (x) - \frac{\sqrt{3}}{3}}{x - \frac{π}{6}}$
32788	Evaluate the Limit	limit as x approaches pi/6 of cos(x)	$lim_{x \to \frac{π}{6}} \cos (x)$
32789	Evaluate the Limit	limit as x approaches pi/18 of 5csc(9x)cot(9x)	$lim_{x \to \frac{π}{18}} 5 \csc (9 x) \cot (9 x)$
32790	Evaluate the Limit	limit as x approaches pi/2 of (2x-pi)/(2cos(x))	$lim_{x \to \frac{π}{2}} \frac{2 x - π}{2 \cos (x)}$
32791	Evaluate the Limit	limit as x approaches pi/2 of tan(x)+1/(x-pi/2)	$lim_{x \to \frac{π}{2}} \tan (x) + \frac{1}{x - \frac{π}{2}}$
32792	Evaluate the Limit	limit as x approaches pi/2 of (1-sin(x)^2)/(cos(x))	$lim_{x \to \frac{π}{2}} \frac{1 - \sin^{2} (x)}{\cos (x)}$
32793	Evaluate the Limit	limit as x approaches pi/2 of (1-8cos(x))/(2x)	$lim_{x \to \frac{π}{2}} \frac{1 - 8 \cos (x)}{2 x}$
32794	Evaluate the Limit	limit as x approaches pi/2 of (1-cos(x))/(10x)	$lim_{x \to \frac{π}{2}} \frac{1 - \cos (x)}{10 x}$
32795	Evaluate the Limit	limit as x approaches pi/2 of (cos(x/2)-sin(x/2))/(cos(x))	$lim_{x \to \frac{π}{2}} \frac{\cos (\frac{x}{2}) - \sin (\frac{x}{2})}{\cos (x)}$
32796	Evaluate the Limit	limit as x approaches pi/2 of (1/( square root of sin(x))-1)/(x+pi/2)	$lim_{x \to \frac{π}{2}} \frac{\frac{1}{\sqrt{\sin (x)}} - 1}{x + \frac{π}{2}}$
32797	Evaluate the Limit	limit as x approaches pi/2 of (1+2sec(x))/(1+tan(x))	$lim_{x \to \frac{π}{2}} \frac{1 + 2 \sec (x)}{1 + \tan (x)}$
32798	Evaluate the Limit	limit as x approaches -pi/2 of 4/3x-tan(x)	$lim_{x \to - \frac{π}{2}} \frac{4}{3} x - \tan (x)$
32799	Evaluate the Limit	limit as x approaches pi/2 of 4/3x-tan(x)	$lim_{x \to \frac{π}{2}} \frac{4}{3} x - \tan (x)$
32800	Evaluate the Limit	limit as x approaches pi/2 of (5sec(x)+3)/(tan(x))	$lim_{x \to \frac{π}{2}} \frac{5 \sec (x) + 3}{\tan (x)}$