Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
31601	Evaluate the Limit	( limit as x approaches -2 of x-5)/(7x^2-8x+5)	$\frac{lim_{x \to - 2} x - 5}{7 x^{2} - 8 x + 5}$
31602	Evaluate the Limit	( limit as x approaches 20 of x^2-4x-21)/(x^2-16x+63)	$\frac{lim_{x \to 20} x^{2} - 4 x - 21}{x^{2} - 16 x + 63}$
31603	Find the Derivative - d/dx	natural log of 12x	$\ln (12 x)$
31604	Evaluate the Limit	( limit as x approaches 225 of square root of x-15)/(x-225)	$\frac{lim_{x \to 225} \sqrt{x} - 15}{x - 225}$
31605	Evaluate the Limit	( limit as x approaches 25 of square root of x-5)/(25-x)	$\frac{lim_{x \to 25} \sqrt{x} - 5}{25 - x}$
31606	Evaluate the Limit	( limit as x approaches 25 of 25-x)/( square root of x-5)	$\frac{lim_{x \to 25} 25 - x}{\sqrt{x} - 5}$
31607	Evaluate the Limit	( limit as x approaches 25 of 2x)/( square root of 625-x^2)	$\frac{lim_{x \to 25} 2 x}{\sqrt{625 - x^{2}}}$
31608	Evaluate the Limit	( limit as x approaches 25 of 5- square root of x)/(x-25)	$\frac{lim_{x \to 25} 5 - \sqrt{x}}{x - 25}$
31609	Evaluate the Limit	( limit as x approaches 256 of square root of x-16)/(x-256)	$\frac{lim_{x \to 256} \sqrt{x} - 16}{x - 256}$
31610	Evaluate the Limit	( limit as x approaches 3 of 1/x-1/3)/(x-3)	$\frac{lim_{x \to 3} \frac{1}{x} - \frac{1}{3}}{x - 3}$
31611	Evaluate the Limit	( limit as x approaches -3 of 4/x+4/3)/(x-3)	$\frac{lim_{x \to - 3} \frac{4}{x} + \frac{4}{3}}{x - 3}$
31612	Evaluate the Limit	( limit as x approaches -3 of square root of x^2+7-4)/(5- square root of x^2+16)	$\frac{lim_{x \to - 3} \sqrt{x^{2} + 7} - 4}{5 - \sqrt{x^{2} + 16}}$
31613	Evaluate the Limit	( limit as x approaches 3 of cube root of x^2-1-2)/(2- square root of x^2-5)	$\frac{lim_{x \to 3} \sqrt[3]{x^{2} - 1} - 2}{2 - \sqrt{x^{2} - 5}}$
31614	Evaluate the Limit	( limit as x approaches 3 of (x^2+2x-15)sin(9-3x))/(tan(2x-6)^2)	$\frac{lim_{x \to 3} (x^{2} + 2 x - 15) \sin (9 - 3 x)}{\tan^{2} (2 x - 6)}$
31615	Evaluate the Limit	( limit as x approaches 3 of x^2+7)/(2x-3)	$\frac{lim_{x \to 3} x^{2} + 7}{2 x - 3}$
31616	Evaluate the Limit	( limit as x approaches 3 of x^2-2x-3)/(x^2+4x-21)	$\frac{lim_{x \to 3} x^{2} - 2 x - 3}{x^{2} + 4 x - 21}$
31617	Evaluate the Limit	( limit as x approaches 3 of x^2-9)/(\|x-3\|)	$\frac{lim_{x \to 3} x^{2} - 9}{\| x - 3 \|}$
31618	Evaluate the Limit	( limit as x approaches 3 of x^3-2x^2-9)/(x^2-2x-3)	$\frac{lim_{x \to 3} x^{3} - 2 x^{2} - 9}{x^{2} - 2 x - 3}$
31619	Evaluate the Limit	( limit as x approaches 2 of 3x-6)/(x^2-4)	$\frac{lim_{x \to 2} 3 x - 6}{x^{2} - 4}$
31620	Evaluate the Limit	( limit as x approaches -2 of x+2)/2	$\frac{lim_{x \to - 2} x + 2}{2}$
31621	Evaluate the Limit	( limit as x approaches 2 of x+5)/(x-2)	$\frac{lim_{x \to 2} x + 5}{x - 2}$
31622	Evaluate the Limit	( limit as x approaches 2 of 64x^2-441)/(8x+21)	$\frac{lim_{x \to 2} 64 x^{2} - 441}{8 x + 21}$
31623	Evaluate the Limit	limit as x approaches 2 of (e)^(3/(2-x))	$lim_{x \to 2} {(e)}^{\frac{3}{2 - x}}$
31624	Evaluate the Limit	( limit as x approaches 2 of ( natural log of x)- natural log of 2)/(x-2)	$\frac{lim_{x \to 2} (\ln (x)) - \ln (2)}{x - 2}$
31625	Evaluate the Limit	( limit as x approaches 2 of sin(pix))/(2-x)	$\frac{lim_{x \to 2} \sin (π x)}{2 - x}$
31626	Evaluate the Limit	( limit as x approaches 2 of tan(x-2))/(x^2-4)	$\frac{lim_{x \to 2} \tan (x - 2)}{x^{2} - 4}$
31627	Evaluate the Limit	( limit as x approaches -2 of x(2x^2-8))/(x^2-4x-12)	$\frac{lim_{x \to - 2} x (2 x^{2} - 8)}{x^{2} - 4 x - 12}$
31628	Evaluate the Limit	( limit as x approaches 2 of x(2x^2-8))/(x^2-4x-12)	$\frac{lim_{x \to 2} x (2 x^{2} - 8)}{x^{2} - 4 x - 12}$
31629	Evaluate the Limit	( limit as x approaches 2 of x+2)/(x^2-2x+4)	$\frac{lim_{x \to 2} x + 2}{x^{2} - 2 x + 4}$
31630	Evaluate the Limit	( limit as x approaches -2 of 4x^(2+6x-4))/(2x^2-8)	$\frac{lim_{x \to - 2} 4 x^{2 + 6 x - 4}}{2 x^{2} - 8}$
31631	Evaluate the Limit	( limit as x approaches 2 of 4x-8)/(x^2-4)	$\frac{lim_{x \to 2} 4 x - 8}{x^{2} - 4}$
31632	Evaluate the Limit	( limit as x approaches -2 of 5x^2-3x^2-68)/(2x^5-3x^2+2x+80)	$\frac{lim_{x \to - 2} 5 x^{2} - 3 x^{2} - 68}{2 x^{5} - 3 x^{2} + 2 x + 80}$
31633	Evaluate the Limit	( limit as x approaches 2 of 2x-4)/(x-2)	$\frac{lim_{x \to 2} 2 x - 4}{x - 2}$
31634	Evaluate the Limit	( limit as x approaches 2 of 3(3x-6))/(x^3-8)	$\frac{lim_{x \to 2} 3 (3 x - 6)}{x^{3} - 8}$
31635	Evaluate the Limit	( limit as x approaches 2 of 3- square root of x+7)/(x-2)	$\frac{lim_{x \to 2} 3 - \sqrt{x + 7}}{x - 2}$
31636	Evaluate the Limit	( limit as x approaches 2 of (3x^2-4x)+2)/(x^3-5)	$\frac{lim_{x \to 2} (3 x^{2} - 4 x) + 2}{x^{3} - 5}$
31637	Evaluate the Limit	( limit as x approaches 2 of 3x^2-x-10)/(x^2-4)	$\frac{lim_{x \to 2} 3 x^{2} - x - 10}{x^{2} - 4}$
31638	Evaluate the Limit	( limit as x approaches 2 of x^2-4)/(x^3-8)*f(x)	$\frac{lim_{x \to 2} x^{2} - 4}{x^{3} - 8} \cdot f (x)$
31639	Evaluate the Limit	( limit as x approaches 2 of x^2-4)/(2x^2-x-6)	$\frac{lim_{x \to 2} x^{2} - 4}{2 x^{2} - x - 6}$
31640	Evaluate the Limit	( limit as x approaches 2 of x^3-2x^2-4x+8)/(x^4-8x^2-x+16)	$\frac{lim_{x \to 2} x^{3} - 2 x^{2} - 4 x + 8}{x^{4} - 8 x^{2} - x + 16}$
31641	Evaluate the Limit	( limit as x approaches 2 of \|x^2-4\|)/(x-2)	$\frac{lim_{x \to 2} \| x^{2} - 4 \|}{x - 2}$
31642	Evaluate the Limit	( limit as x approaches 2 of (1/x)-1/2)/(x^3-8)	$\frac{lim_{x \to 2} (\frac{1}{x}) - \frac{1}{2}}{x^{3} - 8}$
31643	Evaluate the Limit	( limit as x approaches 2 of 1/(x+3)-1/5)/(x^2-4)	$\frac{lim_{x \to 2} \frac{1}{x + 3} - \frac{1}{5}}{x^{2} - 4}$
31644	Evaluate the Limit	( limit as x approaches 2 of square root of x^2+12-4)/(x-2)	$\frac{lim_{x \to 2} \sqrt{x^{2} + 12} - 4}{x - 2}$
31645	Evaluate the Limit	( limit as x approaches 2 of square root of x^2-4x+4)/(x-2)	$\frac{lim_{x \to 2} \sqrt{x^{2} - 4 x + 4}}{x - 2}$
31646	Evaluate the Limit	( limit as x approaches 2 of square root of 2x^3+4)/( square root of x^2+1)	$\frac{lim_{x \to 2} \sqrt{2 x^{3} + 4}}{\sqrt{x^{2} + 1}}$
31647	Evaluate the Limit	( limit as x approaches 2 from the left of square root of 2-x)/(x^2+5x)	$\frac{lim_{x \to 2} \sqrt{2 - x}}{x^{2} + 5 x}$
31648	Find the Derivative - d/dx	y=( natural log of x)/(x^9)	$y = \frac{\ln (x)}{x^{9}}$
31649	Find the Derivative - d/dx	y=e^(9 square root of x)	$y = e^{9 \sqrt{x}}$
31650	Evaluate the Limit	( limit as x approaches 2 of x^3-3x-2)/(x-2)	$\frac{lim_{x \to 2} x^{3} - 3 x - 2}{x - 2}$
31651	Find the Derivative - d/dx	y=(8x+7)(x^2-3x)	$y = (8 x + 7) (x^{2} - 3 x)$
31652	Evaluate the Limit	( limit as x approaches 2 of 2x^2-8)/(x-2)	$\frac{lim_{x \to 2} 2 x^{2} - 8}{x - 2}$
31653	Evaluate the Limit	( limit as x approaches 2 of 3x^2-4x-4)/(2x^2-8)	$\frac{lim_{x \to 2} 3 x^{2} - 4 x - 4}{2 x^{2} - 8}$
31654	Find the Derivative - d/d@VAR	f(x)=3(x+2)^(4/3)	$f (x) = 3 {(x + 2)}^{\frac{4}{3}}$
31655	Find ds/dt	s=6t^3-3t^6	$s = 6 t^{3} - 3 t^{6}$
31656	Find dy/dx	4x^2-3y^2=2	$4 x^{2} - 3 y^{2} = 2$
31657	Evaluate the Limit	limit as x approaches -17 of (x+10)^(2/3)	$lim_{x \to - 17} {(x + 10)}^{\frac{2}{3}}$
31658	Evaluate the Limit	( limit as x approaches 2 of x^2+3x-10)/(x^2-4x+4)	$\frac{lim_{x \to 2} x^{2} + 3 x - 10}{x^{2} - 4 x + 4}$
31659	Evaluate the Limit	( limit as x approaches -2 of x^2-2x-8)/(x^2-4)	$\frac{lim_{x \to - 2} x^{2} - 2 x - 8}{x^{2} - 4}$
31660	Evaluate the Limit	( limit as x approaches -2 of x^2-3x-10)/(x+2)	$\frac{lim_{x \to - 2} x^{2} - 3 x - 10}{x + 2}$
31661	Find dy/dx	1/x+1/y=6	$\frac{1}{x} + \frac{1}{y} = 6$
31662	Find dy/dx	y=sin(7x^2)^3	$y = \sin^{3} (7 x^{2})$
31663	Evaluate the Limit	( limit as x approaches 1 of -2x)/((x-1)^2)	$\frac{lim_{x \to 1} - 2 x}{{(x - 1)}^{2}}$
31664	Find dy/dx	y = fifth root of 6x	$y = \sqrt[5]{6 x}$
31665	Evaluate the Limit	( limit as x approaches 1 of 2x)/(x^2-1)	$\frac{lim_{x \to 1} 2 x}{x^{2} - 1}$
31666	Find dy/dx	y=3x^2-6x	$y = 3 x^{2} - 6 x$
31667	Evaluate the Limit	limit as x approaches -1 of (3(2x-1))^2	$lim_{x \to - 1} {(3 (2 x - 1))}^{2}$
31668	Evaluate the Limit	( limit as x approaches 1 of 4x^2-7)/(g(x)+2)	$\frac{lim_{x \to 1} 4 x^{2} - 7}{g (x) + 2}$
31669	Evaluate the Limit	( limit as x approaches 1 of 5x^2+3x-7)/(2x+5)	$\frac{lim_{x \to 1} 5 x^{2} + 3 x - 7}{2 x + 5}$
31670	Evaluate the Limit	( limit as x approaches 1 of arctan(x))/(arcsin(x)+1)	$\frac{lim_{x \to 1} \arctan (x)}{\arcsin (x) + 1}$
31671	Evaluate the Limit	limit as x approaches 1 from the left of (e)^(3/(1-x))	$lim_{x \to 1} {(e)}^{\frac{3}{1 - x}}$
31672	Evaluate the Limit	limit as x approaches 1 of (e)^(x^3-x)	$lim_{x \to 1} {(e)}^{x^{3} - x}$
31673	Evaluate the Limit	limit as x approaches 1 of (e)^(4x^4-4x)	$lim_{x \to 1} {(e)}^{4 x^{4} - 4 x}$
31674	Evaluate the Limit	( limit as x approaches 1 of natural log of 1+x)/x	$\frac{lim_{x \to 1} \ln (1 + x)}{x}$
31675	Evaluate the Limit	( limit as x approaches 1 of natural log of x)/( natural log of 2x-1)	$\frac{lim_{x \to 1} \ln (x)}{\ln (2 x - 1)}$
31676	Evaluate the Limit	( limit as x approaches 1 of natural log of x)/(sin(pix))	$\frac{lim_{x \to 1} \ln (x)}{\sin (π x)}$
31677	Evaluate the Limit	( limit as x approaches 1 of sin(x^2-1))/(x-1)	$\frac{lim_{x \to 1} \sin (x^{2} - 1)}{x - 1}$
31678	Evaluate the Limit	( limit as x approaches 1 of sin(3x))/x	$\frac{lim_{x \to 1} \sin (3 x)}{x}$
31679	Evaluate the Limit	( limit as x approaches -1 of sin(x))/x	$\frac{lim_{x \to - 1} \sin (x)}{x}$
31680	Evaluate the Limit	( limit as x approaches 1 of sin(x-1))/(x^2+1-1)	$\frac{lim_{x \to 1} \sin (x - 1)}{x^{2} + 1 - 1}$
31681	Evaluate the Limit	( limit as x approaches 1 of sin(x-1))/(x-1)	$\frac{lim_{x \to 1} \sin (x - 1)}{x - 1}$
31682	Evaluate the Limit	( limit as x approaches -1 of tan((x+1)/4))/x	$\frac{lim_{x \to - 1} \tan (\frac{x + 1}{4})}{x}$
31683	Evaluate the Limit	( limit as x approaches 1 of x*\|x-1\|)/(x-1)	$\frac{lim_{x \to 1} x \cdot \| x - 1 \|}{x - 1}$
31684	Evaluate the Limit	( limit as x approaches 1 of x)/( natural log of x)	$\frac{lim_{x \to 1} x}{\ln (x)}$
31685	Evaluate the Limit	( limit as x approaches 1 of x- square root of x)/(x^(1/3)-1)	$\frac{lim_{x \to 1} x - \sqrt{x}}{x^{\frac{1}{3}} - 1}$
31686	Evaluate the Limit	( limit as x approaches 1 of x+xcos(x))/(sin(x)cos(x))	$\frac{lim_{x \to 1} x + x \cos (x)}{\sin (x) \cos (x)}$
31687	Evaluate the Limit	( limit as x approaches 1 of x-1)/( square root of x+7-2)	$\frac{lim_{x \to 1} x - 1}{\sqrt{x + 7} - 2}$
31688	Evaluate the Limit	( limit as x approaches 13 of 101x)/(4x+9)	$\frac{lim_{x \to 13} 101 x}{4 x + 9}$
31689	Evaluate the Limit	( limit as x approaches -13 of x+13)/(x^2-169)	$\frac{lim_{x \to - 13} x + 13}{x^{2} - 169}$
31690	Evaluate the Limit	( limit as x approaches 13 of x-13)/(x^2-13x)	$\frac{lim_{x \to 13} x - 13}{x^{2} - 13 x}$
31691	Evaluate the Limit	( limit as x approaches 14 of x^2-4x-21)/(x^2-9x+14)	$\frac{lim_{x \to 14} x^{2} - 4 x - 21}{x^{2} - 9 x + 14}$
31692	Evaluate the Limit	( limit as x approaches 15 of x+15)/(x-15)	$\frac{lim_{x \to 15} x + 15}{x - 15}$
31693	Evaluate the Limit	( limit as x approaches 16 of vx-16)/(x-16)	$\frac{lim_{x \to 16} v x - 16}{x - 16}$
31694	Evaluate the Limit	( limit as x approaches 100 of square root of x-10)/(x-100)	$\frac{lim_{x \to 100} \sqrt{x - 10}}{x - 100}$
31695	Evaluate the Limit	( limit as x approaches 11 of \|11-x\|)/(11-x)	$\frac{lim_{x \to 11} \| 11 - x \|}{11 - x}$
31696	Evaluate the Limit	( limit as x approaches -11 from the left of \|x+11\|)/(x+11)	$\frac{lim_{x \to - 11} \| x + 11 \|}{x + 11}$
31697	Evaluate the Limit	( limit as x approaches 11 of square root of x^2-2x-63)/(34-4x)	$\frac{lim_{x \to 11} \sqrt{x^{2} - 2 x - 63}}{34 - 4 x}$
31698	Evaluate the Limit	( limit as x approaches 11 of x-11)/(x^2-121)	$\frac{lim_{x \to 11} x - 11}{x^{2} - 121}$
31699	Evaluate the Limit	( limit as x approaches 1 from the left of x-1)/( square root of x-1)	$\frac{lim_{x \to 1} x - 1}{\sqrt{x} - 1}$
31700	Evaluate the Limit	( limit as x approaches 1 of x^4-1)/(x^6)	$\frac{lim_{x \to 1} x^{4} - 1}{x^{6}}$