Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
22701	Evaluate the Limit	limit as x approaches 16 of (x-16)/(x^2-256)	$lim_{x \to 16} \frac{x - 16}{x^{2} - 256}$
22702	Evaluate the Limit	limit as x approaches -6 of (36-x^2)/(6x^2+x^3)	$lim_{x \to - 6} \frac{36 - x^{2}}{6 x^{2} + x^{3}}$
22703	Evaluate the Limit	limit as x approaches 8 of (4x^4-3x^2)/(8x^4+5x^2+4x)	$lim_{x \to 8} \frac{4 x^{4} - 3 x^{2}}{8 x^{4} + 5 x^{2} + 4 x}$
22704	Evaluate the Limit	limit as x approaches 0 of (sin(3x))/(sin(5x))	$lim_{x \to 0} \frac{\sin (3 x)}{\sin (5 x)}$
22705	Evaluate the Limit	limit as x approaches 7 of f(x)	$lim_{x \to 7} f (x)$
22706	Evaluate the Limit	limit as x approaches 8 of (4x)/(20x+1)	$lim_{x \to 8} \frac{4 x}{20 x + 1}$
22707	Evaluate the Limit	limit as x approaches 8 of (6x-5)/(7x)	$lim_{x \to 8} \frac{6 x - 5}{7 x}$
22708	Evaluate the Limit	limit as x approaches 8 of (3x-2x^2+4x^3)/(7-2x-x^3)	$lim_{x \to 8} \frac{3 x - 2 x^{2} + 4 x^{3}}{7 - 2 x - x^{3}}$
22709	Evaluate the Limit	limit as x approaches 8 of (3x^2-6x^4)/(9x^2-3x-6)	$lim_{x \to 8} \frac{3 x^{2} - 6 x^{4}}{9 x^{2} - 3 x - 6}$
22710	Evaluate the Limit	limit as x approaches 8 of (2x^2)/(e^(6x))	$lim_{x \to 8} \frac{2 x^{2}}{e^{6 x}}$
22711	Evaluate the Limit	limit as x approaches -8 of (2x^2+3x+1)/(x^4-x^2)	$lim_{x \to - 8} \frac{2 x^{2} + 3 x + 1}{x^{4} - x^{2}}$
22712	Evaluate the Limit	limit as x approaches -8 of (1-3x^3)/(2x^3-6x+2)	$lim_{x \to - 8} \frac{1 - 3 x^{3}}{2 x^{3} - 6 x + 2}$
22713	Evaluate the Limit	limit as theta approaches 0 of (sin(theta))/theta	$lim_{θ \to 0} \frac{\sin (θ)}{θ}$
22714	Evaluate the Limit	limit as x approaches 8 of (2x^2-1)/(x^3+x^2+1)	$lim_{x \to 8} \frac{2 x^{2} - 1}{x^{3} + x^{2} + 1}$
22715	Evaluate the Limit	limit as x approaches 8 of 1/(x^3)	$lim_{x \to 8} \frac{1}{x^{3}}$
22716	Evaluate the Limit	limit as x approaches 8 of (x^6)/(6^x)	$lim_{x \to 8} \frac{x^{6}}{6^{x}}$
22717	Evaluate the Limit	limit as x approaches 2 of ( square root of x^2+32-6)/(x-2)	$lim_{x \to 2} \frac{\sqrt{x^{2} + 32} - 6}{x - 2}$
22718	Evaluate the Limit	limit as x approaches 8 of 1/(sin(1/x))	$lim_{x \to 8} \frac{1}{\sin (\frac{1}{x})}$
22719	Evaluate the Limit	limit as x approaches 49 of (7- square root of x)/(49x-x^2)	$lim_{x \to 49} \frac{(7 - \sqrt{x})}{49 x - x^{2}}$
22720	Evaluate the Limit	limit as x approaches 8 of (x^(1/3)-2)/(x-8)	$lim_{x \to 8} \frac{x^{\frac{1}{3}} - 2}{x - 8}$
22721	Evaluate the Limit	limit as x approaches 8 of ( square root of 9x^2+16)/(2+ square root of x^3+1)	$lim_{x \to 8} \frac{\sqrt{9 x^{2} + 16}}{2 + \sqrt{x^{3} + 1}}$
22722	Evaluate the Limit	limit as x approaches 8 of (x^2-x-56)/(x-8)	$lim_{x \to 8} \frac{x^{2} - x - 56}{x - 8}$
22723	Evaluate the Limit	limit as x approaches 8 of (x^3)/(e^(3x))	$lim_{x \to 8} \frac{x^{3}}{e^{3 x}}$
22724	Evaluate the Limit	limit as x approaches 11 of (x-11)/(x^2-121)	$lim_{x \to 11} \frac{x - 11}{x^{2} - 121}$
22725	Evaluate the Limit	limit as x approaches 8 of (x^2+3x-2)/(-3x^2+6)	$lim_{x \to 8} \frac{x^{2} + 3 x - 2}{- 3 x^{2} + 6}$
22726	Find the Derivative - d/dx	895+10 square root of x	$895 + 10 \sqrt{x}$
22727	Evaluate the Limit	limit as x approaches 8 of (x/(x+1))^x	$lim_{x \to 8} {(\frac{x}{x + 1})}^{x}$
22728	Evaluate the Limit	limit as x approaches 8 of (2x^2-3x-6)/( square root of x^4-1)	$lim_{x \to 8} \frac{2 x^{2} - 3 x - 6}{\sqrt{x^{4} - 1}}$
22729	Evaluate the Limit	limit as x approaches -8 of ((x^2+x-1)/(8x^2-3))^(1/3)	$lim_{x \to - 8} {(\frac{x^{2} + x - 1}{8 x^{2} - 3})}^{\frac{1}{3}}$
22730	Evaluate the Limit	limit as x approaches -8 of x+ square root of x^2+4x	$lim_{x \to - 8} x + \sqrt{x^{2} + 4 x}$
22731	Evaluate the Limit	limit as x approaches -8 of ( square root of x^2-9)/(2x-6)	$lim_{x \to - 8} \frac{\sqrt{x^{2} - 9}}{2 x - 6}$
22732	Evaluate the Limit	limit as x approaches 8 of ( square root of 4x^4+3)/(5x^2+2)	$lim_{x \to 8} \frac{\sqrt{4 x^{4} + 3}}{5 x^{2} + 2}$
22733	Evaluate the Limit	limit as x approaches -8 of ( square root of x^10-1)/(x^8-1)	$lim_{x \to - 8} \frac{\sqrt{x^{10} - 1}}{x^{8} - 1}$
22734	Evaluate the Limit	limit as x approaches -8 of ( square root of 3x^4+x)/(x^2-8)	$lim_{x \to - 8} \frac{\sqrt{3 x^{4} + x}}{x^{2} - 8}$
22735	Evaluate the Limit	limit as x approaches 8 of ( square root of x^4-3x^3-1)/(1x^2+2)	$lim_{x \to 8} \frac{\sqrt{x^{4} - 3 x^{3} - 1}}{1 x^{2} + 2}$
22736	Evaluate the Limit	limit as x approaches -1 of (x^2+6x+5)/(x^2-5x-6)	$lim_{x \to - 1} \frac{x^{2} + 6 x + 5}{x^{2} - 5 x - 6}$
22737	Evaluate the Limit	limit as x approaches 3 of (1/x-1/3)/(x-3)	$lim_{x \to 3} \frac{(\frac{1}{x} - \frac{1}{3})}{x - 3}$
22738	Evaluate the Limit	limit as x approaches 8 of ( natural log of (x)^2)/x	$lim_{x \to 8} \frac{\ln ({(x)}^{2})}{x}$
22739	Evaluate the Limit	limit as x approaches 8 of cos(1/x)^x	$lim_{x \to 8} {\cos (\frac{1}{x})}^{x}$
22740	Evaluate the Limit	limit as x approaches 8 of ( natural log of x)^(1/x)	$lim_{x \to 8} {(\ln (x))}^{\frac{1}{x}}$
22741	Evaluate the Limit	limit as x approaches 5 of (12x-60)/(x^2-6x+5)	$lim_{x \to 5} \frac{12 x - 60}{x^{2} - 6 x + 5}$
22742	Evaluate the Limit	limit as x approaches -9 of (x^2+15x+54)/(x+9)	$lim_{x \to - 9} \frac{x^{2} + 15 x + 54}{x + 9}$
22743	Find the Derivative - d/dx	9xe^(-kx)	$9 x e^{- k x}$
22744	Evaluate the Limit	limit as x approaches -9 of (x^4+9x^3-8x^2+10x+6)/(x+9)	$lim_{x \to - 9} \frac{x^{4} + 9 x^{3} - 8 x^{2} + 10 x + 6}{x + 9}$
22745	Evaluate the Limit	limit as x approaches 9 of 1/(x-9)	$lim_{x \to 9} \frac{1}{x - 9}$
22746	Evaluate the Limit	limit as x approaches 9 of square root of 49	$lim_{x \to 9} \sqrt{49}$
22747	Evaluate the Limit	limit as x approaches 9 of square root of x^2-81	$lim_{x \to 9} \sqrt{x^{2} - 81}$
22748	Evaluate the Limit	limit as x approaches 9 of (x-9)/(x^2-18x+81)	$lim_{x \to 9} \frac{x - 9}{x^{2} - 18 x + 81}$
22749	Evaluate the Limit	limit as x approaches 9 of (55+ square root of x)/( square root of 55+x)	$lim_{x \to 9} \frac{55 + \sqrt{x}}{\sqrt{55 + x}}$
22750	Evaluate the Limit	limit as x approaches -9 of (9-\|x\|)/(9+x)	$lim_{x \to - 9} \frac{(9 - \| x \|)}{9 + x}$
22751	Evaluate the Limit	limit as x approaches b of ((x-b)^50-x+b)/(x-b)	$lim_{x \to b} \frac{{(x - b)}^{50} - x + b}{x - b}$
22752	Evaluate the Limit	limit as x approaches 2 of (x^4+3x^3-10x^2)/(x^2-2x)	$lim_{x \to 2} \frac{x^{4} + 3 x^{3} - 10 x^{2}}{x^{2} - 2 x}$
22753	Evaluate the Limit	limit as theta approaches 0 of (1-cos(theta))/(2sin(theta)^2)	$lim_{θ \to 0} \frac{1 - \cos (θ)}{2 \sin^{2} (θ)}$
22754	Evaluate the Limit	limit as x approaches negative infinity of arctan(x)	$lim_{x \to - \infty} \arctan (x)$
22755	Evaluate the Limit	limit as x approaches infinity of (2x^2-9)/(7x^2+5x-6)	$lim_{x \to \infty} \frac{2 x^{2} - 9}{7 x^{2} + 5 x - 6}$
22756	Evaluate the Limit	limit as x approaches 0 of e^xcos(x)	$lim_{x \to 0} e^{x} \cos (x)$
22757	Find dy/dx	x^2+y^3-x+5y=3	$x^{2} + y^{3} - x + 5 y = 3$
22758	Find dy/dx	y^2(y^2-4)=x^2(x^2-5)	$y^{2} (y^{2} - 4) = x^{2} (x^{2} - 5)$
22759	Find dy/dx	6xy+1=0	$6 x y + 1 = 0$
22760	Find the Local Maxima and Minima	x^4-2x^2+4	$x^{4} - 2 x^{2} + 4$
22761	Evaluate the Limit	limit as x approaches 8 of log of x	$lim_{x \to 8} \log (x)$
22762	Evaluate the Limit	limit as x approaches -8 of arctan(e^x)	$lim_{x \to - 8} \arctan (e^{x})$
22763	Evaluate the Limit	limit as x approaches 8 of arctan(1+ square root of x)	$lim_{x \to 8} \arctan (1 + \sqrt{x})$
22764	Evaluate the Limit	limit as x approaches pi/2 of (cos(x))/(cot(x))	$lim_{x \to \frac{π}{2}} \frac{\cos (x)}{\cot (x)}$
22765	Evaluate the Limit	limit as x approaches 8 of arctan( natural log of x)	$lim_{x \to 8} \arctan (\ln (x))$
22766	Find the Local Maxima and Minima	xe^x	$x e^{x}$
22767	Evaluate the Limit	limit as x approaches 1 of e^(x^3-x)	$lim_{x \to 1} e^{x^{3} - x}$
22768	Evaluate the Limit	( limit as x approaches 8 of (x)(x-4))/(3x^2-8x-16)+4	$\frac{lim_{x \to 8} (x) (x - 4)}{3 x^{2} - 8 x - 16} + 4$
22769	Evaluate the Limit	limit as t approaches 0 of (sin(7t))/(6t)	$lim_{t \to 0} \frac{\sin (7 t)}{6 t}$
22770	Evaluate the Limit	limit as x approaches 8 of (x)sin(1/x)	$lim_{x \to 8} (x) \sin (\frac{1}{x})$
22771	Evaluate the Limit	limit as x approaches 8 of xcos(1/x)	$lim_{x \to 8} x \cos (\frac{1}{x})$
22772	Evaluate the Limit	limit as x approaches 0 of (x-5)/(x^2-5x)	$lim_{x \to 0} \frac{x - 5}{x^{2} - 5 x}$
22773	Evaluate the Limit	limit as x approaches 8 of xtan(pi/x)	$lim_{x \to 8} x \tan (\frac{π}{x})$
22774	Evaluate the Limit	limit as x approaches infinity of 1/(x^2)	$lim_{x \to \infty} \frac{1}{x^{2}}$
22775	Evaluate the Limit	limit as x approaches infinity of ( square root of 2x^2+1)/(3x-5)	$lim_{x \to \infty} \frac{\sqrt{2 x^{2} + 1}}{3 x - 5}$
22776	Evaluate the Limit	limit as x approaches 1 of (x^2+2x-3)/(x^2-5x+4)	$lim_{x \to 1} \frac{x^{2} + 2 x - 3}{x^{2} - 5 x + 4}$
22777	Evaluate the Limit	limit as x approaches 8 of x natural log of 1+2/x	$lim_{x \to 8} x \ln (1 + \frac{2}{x})$
22778	Evaluate the Limit	limit as x approaches 5 of (x^2-5x)/(x^2-25)	$lim_{x \to 5} \frac{x^{2} - 5 x}{x^{2} - 25}$
22779	Evaluate the Limit	limit as x approaches 0 of square root of x+1	$lim_{x \to 0} \sqrt{x + 1}$
22780	Evaluate the Limit	limit as x approaches 0 of 3/(x square root of 1+x)-3/x	$lim_{x \to 0} \frac{3}{x \sqrt{1 + x}} - \frac{3}{x}$
22781	Evaluate the Limit	limit as x approaches -9 of (18-y)^(2/3)	$lim_{x \to - 9} {(18 - y)}^{\frac{2}{3}}$
22782	Evaluate the Limit	limit as theta approaches 0 of (1/(2+sin(theta))-1/2)/(sin(theta))	$lim_{θ \to 0} \frac{\frac{1}{2 + \sin (θ)} - \frac{1}{2}}{\sin (θ)}$
22783	Evaluate the Limit	limit as x approaches 9 of 2x^2+5x-4	$lim_{x \to 9} 2 x^{2} + 5 x - 4$
22784	Evaluate the Limit	limit as x approaches 8 of (-8x)/( square root of 36x^2+8)	$lim_{x \to 8} \frac{- 8 x}{\sqrt{36 x^{2} + 8}}$
22785	Evaluate the Limit	limit as x approaches 0 of (x^2-x+sin(x))/(2x)	$lim_{x \to 0} \frac{x^{2} - x + \sin (x)}{2 x}$
22786	Evaluate the Limit	limit as t approaches 0 of (sin(9t))/(8t)	$lim_{t \to 0} \frac{\sin (9 t)}{8 t}$
22787	Evaluate the Limit	limit as x approaches 0 of ( square root of x^2+16-4)/(x^2)	$lim_{x \to 0} \frac{\sqrt{x^{2} + 16} - 4}{x^{2}}$
22788	Evaluate the Limit	limit as x approaches 8 of ( natural log of 5x)/( square root of 5x)	$lim_{x \to 8} \frac{\ln (5 x)}{\sqrt{5 x}}$
22789	Evaluate the Limit	limit as x approaches negative infinity of (7-3x^3)/(2x^3+1)	$lim_{x \to - \infty} \frac{7 - 3 x^{3}}{2 x^{3} + 1}$
22790	Evaluate the Limit	limit as x approaches 8 of (50x^2-1)/(e^(x/2)+3)	$lim_{x \to 8} \frac{50 x^{2} - 1}{e^{\frac{x}{2}} + 3}$
22791	Evaluate the Limit	limit as x approaches 8 of (7x^3)/(x^3-3x^2+6x)	$lim_{x \to 8} \frac{7 x^{3}}{x^{3} - 3 x^{2} + 6 x}$
22792	Evaluate the Limit	limit as x approaches 8 of square root of 4x^2+9- square root of 4x^2-5	$lim_{x \to 8} \sqrt{4 x^{2} + 9} - \sqrt{4 x^{2} - 5}$
22793	Evaluate the Limit	limit as x approaches 1 of ( square root of x^2+3-2)/(x-1)	$lim_{x \to 1} \frac{\sqrt{x^{2} + 3} - 2}{x - 1}$
22794	Evaluate the Limit	limit as x approaches 1 of ( square root of x^2+15-4)/(x-1)	$lim_{x \to 1} \frac{\sqrt{x^{2} + 15} - 4}{x - 1}$
22795	Evaluate the Limit	limit as x approaches 8 of ( square root of x^2+3x)-x	$lim_{x \to 8} (\sqrt{x^{2} + 3 x}) - x$
22796	Evaluate the Limit	limit as x approaches 8 of square root of (49x^2)/(2+4x^2)	$lim_{x \to 8} \sqrt{\frac{49 x^{2}}{2 + 4 x^{2}}}$
22797	Evaluate the Limit	limit as x approaches 8 of square root of (2x^2-1)/(x+8x^2)	$lim_{x \to 8} \sqrt{\frac{2 x^{2} - 1}{x + 8 x^{2}}}$
22798	Evaluate the Limit	limit as x approaches 1 of (x^2-1)/(x-1)	$lim_{x \to 1} \frac{(x^{2} - 1)}{x - 1}$
22799	Evaluate the Limit	limit as x approaches 8 of arcsec(x/3.75)	$lim_{x \to 8} arcsec (\frac{x}{3.75})$
22800	Evaluate the Limit	limit as x approaches 8 of (sin(3/x))/(tan(6/x))	$lim_{x \to 8} \frac{\sin (\frac{3}{x})}{\tan (\frac{6}{x})}$