Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
20601	Evaluate the Limit	limit as x approaches 2 of (x^2-4x+11)/(x^3-8x^2+19)	$lim_{x \to 2} \frac{x^{2} - 4 x + 11}{x^{3} - 8 x^{2} + 19}$
20602	Evaluate the Limit	limit as x approaches 2 of (x^2-4x+4)/(sin(pix)^2)	$lim_{x \to 2} \frac{x^{2} - 4 x + 4}{\sin^{2} (π x)}$
20603	Evaluate the Limit	limit as x approaches -7 of (x^2-49)/(2x^2+15x+7)	$lim_{x \to - 7} \frac{x^{2} - 49}{2 x^{2} + 15 x + 7}$
20604	Evaluate the Limit	limit as x approaches 2 of (x^2-x)^5	$lim_{x \to 2} {(x^{2} - x)}^{5}$
20605	Evaluate the Limit	limit as x approaches 4 of (x^2-5x+4)/(x-4)	$lim_{x \to 4} \frac{x^{2} - 5 x + 4}{x - 4}$
20606	Evaluate the Limit	limit as x approaches 9 of (x^2-6x-27)/(x-9)	$lim_{x \to 9} \frac{x^{2} - 6 x - 27}{x - 9}$
20607	Evaluate the Limit	limit as x approaches 2 of (3x-8)^3*(3x)/(5x-4)	$lim_{x \to 2} {(3 x - 8)}^{3} \cdot \frac{3 x}{5 x - 4}$
20608	Evaluate the Limit	limit as x approaches -2 of (w^3-w)/(2w^2+3w)	$lim_{x \to - 2} \frac{w^{3} - w}{2 w^{2} + 3 w}$
20609	Evaluate the Limit	limit as x approaches -2 of (x^2-4)/(x^2+3x+2)	$lim_{x \to - 2} \frac{x^{2} - 4}{x^{2} + 3 x + 2}$
20610	Evaluate the Limit	limit as x approaches 2 of (x^2-5x+6)/(x^2+3x-10)	$lim_{x \to 2} \frac{x^{2} - 5 x + 6}{x^{2} + 3 x - 10}$
20611	Evaluate the Limit	limit as x approaches 2 of (x^2-2x)/(x^2-4)	$lim_{x \to 2} \frac{x^{2} - 2 x}{x^{2} - 4}$
20612	Evaluate the Limit	limit as y approaches 4 of (y^2-16)/( square root of y-2)	$lim_{y \to 4} \frac{y^{2} - 16}{\sqrt{y} - 2}$
20613	Evaluate the Limit	limit as x approaches 2 of (x^2-2x-8)/(x^2-5x+6)	$lim_{x \to 2} \frac{x^{2} - 2 x - 8}{x^{2} - 5 x + 6}$
20614	Evaluate the Limit	limit as x approaches -2 of ( cube root of 4x-x^3)/(3x^2*(13x)+14)	$lim_{x \to - 2} \frac{\sqrt[3]{4 x - x^{3}}}{3 x^{2} \cdot (13 x) + 14}$
20615	Evaluate the Limit	limit as x approaches 2 of (x+1)/(3x-6)	$lim_{x \to 2} \frac{x + 1}{3 x - 6}$
20616	Evaluate the Limit	limit as x approaches 6 of (x^2-2x-24)/(x-6)	$lim_{x \to 6} \frac{x^{2} - 2 x - 24}{x - 6}$
20617	Evaluate the Limit	limit as x approaches 2 of 1/x	$lim_{x \to 2} \frac{1}{x}$
20618	Evaluate the Limit	limit as x approaches infinity of (2x^2+1)/((2-x)(2+x))	$lim_{x \to \infty} \frac{2 x^{2} + 1}{(2 - x) (2 + x)}$
20619	Evaluate the Limit	limit as x approaches 2 of (x^2-8x+12)/(x^2-4)	$lim_{x \to 2} \frac{x^{2} - 8 x + 12}{x^{2} - 4}$
20620	Evaluate the Limit	limit as x approaches 2 of (x^3-x^2-x-2)/(2x^3-5y^2+5y-6)	$lim_{x \to 2} \frac{x^{3} - x^{2} - x - 2}{2 x^{3} - 5 y^{2} + 5 y - 6}$
20621	Evaluate the Limit	limit as x approaches 2 of \|x-2\|	$lim_{x \to 2} \| x - 2 \|$
20622	Evaluate the Limit	limit as x approaches 2 of 3x-7	$lim_{x \to 2} 3 x - 7$
20623	Evaluate the Limit	limit as x approaches -2 of (2-\|x\|)/(2+x)	$lim_{x \to - 2} \frac{(2 - \| x \|)}{2 + x}$
20624	Evaluate the Limit	limit as x approaches 2 of sec((pix)/3)	$lim_{x \to 2} \sec (\frac{π x}{3})$
20625	Evaluate the Limit	limit as x approaches 2 of tan((pix)/4)	$lim_{x \to 2} \tan (\frac{π x}{4})$
20626	Evaluate the Limit	limit as x approaches 2 of arctan((x^2-4)/(3x^2-6x))	$lim_{x \to 2} \arctan (\frac{x^{2} - 4}{3 x^{2} - 6 x})$
20627	Evaluate the Limit	limit as x approaches 2 of arctan((4x^2-16)/(7x^2-14x))	$lim_{x \to 2} \arctan (\frac{4 x^{2} - 16}{7 x^{2} - 14 x})$
20628	Find the 2nd Derivative	y=(3x-2)/(2x+1)	$y = \frac{3 x - 2}{2 x + 1}$
20629	Evaluate the Limit	limit as x approaches -2 of f(-2)	$lim_{x \to - 2} f (- 2)$
20630	Evaluate the Limit	limit as x approaches -2 of (F(x^2-4))/(\|x+2\|)	$lim_{x \to - 2} \frac{F (x^{2} - 4)}{\| x + 2 \|}$
20631	Evaluate the Limit	limit as x approaches 2 of R(x)	$lim_{x \to 2} R (x)$
20632	Evaluate the Limit	limit as x approaches -2 of h(x)	$lim_{x \to - 2} h (x)$
20633	Evaluate the Limit	limit as x approaches 2 of natural log of x^2-4	$lim_{x \to 2} \ln (x^{2} - 4)$
20634	Evaluate the Limit	limit as x approaches 2 of x-3	$lim_{x \to 2} x - 3$
20635	Evaluate the Limit	limit as x approaches 2 of x+1	$lim_{x \to 2} x + 1$
20636	Evaluate the Limit	limit as x approaches 2 of x+5	$lim_{x \to 2} x + 5$
20637	Evaluate the Limit	limit as x approaches -2 of (4x^2+ax+a+12)/(x^2+x-2)	$lim_{x \to - 2} \frac{4 x^{2} + a x + a + 12}{x^{2} + x - 2}$
20638	Evaluate the Limit	limit as x approaches infinity of (x-1)/(x^(2/3)-1)	$lim_{x \to \infty} \frac{x - 1}{x^{\frac{2}{3}} - 1}$
20639	Evaluate the Limit	limit as x approaches 3 of (x^2-4)(x^3+5x+1)	$lim_{x \to 3} (x^{2} - 4) (x^{3} + 5 x + 1)$
20640	Evaluate the Limit	limit as x approaches infinity of e^(-8x)cos(x)	$lim_{x \to \infty} e^{- 8 x} \cos (x)$
20641	Evaluate the Limit	limit as x approaches 3 of ( square root of x+1)/(x-4)	$lim_{x \to 3} \frac{\sqrt{x + 1}}{x - 4}$
20642	Evaluate the Limit	limit as x approaches 2pi of csc(x)	$lim_{x \to 2 π} \csc (x)$
20643	Evaluate the Limit	limit as x approaches -3 of (x^2-9)/(x^2+2x-3)	$lim_{x \to - 3} \frac{x^{2} - 9}{x^{2} + 2 x - 3}$
20644	Evaluate the Limit	limit as x approaches 1 of (x^2+4x-5)/(x^2-1)	$lim_{x \to 1} \frac{x^{2} + 4 x - 5}{x^{2} - 1}$
20645	Evaluate the Limit	limit as x approaches 1 of (x^2+x-2)/(x-1)	$lim_{x \to 1} \frac{x^{2} + x - 2}{x - 1}$
20646	Evaluate the Limit	limit as x approaches 3 of (2x-1)/(x-3)	$lim_{x \to 3} \frac{2 x - 1}{x - 3}$
20647	Evaluate the Limit	limit as x approaches 2 of x^2+8x-2	$lim_{x \to 2} x^{2} + 8 x - 2$
20648	Evaluate the Limit	limit as x approaches -7 of (x^3+343)/(x+7)	$lim_{x \to - 7} \frac{x^{3} + 343}{x + 7}$
20649	Evaluate the Limit	limit as x approaches 15 of (x-15)/(x^2-225)	$lim_{x \to 15} \frac{x - 15}{x^{2} - 225}$
20650	Evaluate the Limit	limit as x approaches 0 of (tan(6x))/(sin(2x))	$lim_{x \to 0} \frac{\tan (6 x)}{\sin (2 x)}$
20651	Evaluate the Limit	limit as x approaches 9 of (x^2-5x-36)/(x-9)	$lim_{x \to 9} \frac{x^{2} - 5 x - 36}{x - 9}$
20652	Evaluate the Limit	limit as x approaches infinity of (4-x^2)/(x^2-1)	$lim_{x \to \infty} \frac{4 - x^{2}}{x^{2} - 1}$
20653	Evaluate the Limit	limit as x approaches 2 of cube root of 10x+7	$lim_{x \to 2} \sqrt[3]{10 x + 7}$
20654	Evaluate the Limit	limit as x approaches 2 of cube root of 12x+3	$lim_{x \to 2} \sqrt[3]{12 x + 3}$
20655	Evaluate the Limit	limit as x approaches -2 of cube root of 4x^2-25	$lim_{x \to - 2} \sqrt[3]{4 x^{2} - 25}$
20656	Evaluate the Limit	limit as x approaches 2 of square root of (x^2+3x+4)/(x^3+1)	$lim_{x \to 2} \sqrt{\frac{x^{2} + 3 x + 4}{x^{3} + 1}}$
20657	Evaluate the Limit	limit as x approaches -2 of square root of x^4+3x+6	$lim_{x \to - 2} \sqrt{x^{4} + 3 x + 6}$
20658	Evaluate the Limit	limit as x approaches 2 of (3x^2-x-10)/(x^2-x-2)	$lim_{x \to 2} \frac{3 x^{2} - x - 10}{x^{2} - x - 2}$
20659	Evaluate the Limit	limit as x approaches 2 of (3x^2-7x+2)/(2x^2+x-10)	$lim_{x \to 2} \frac{3 x^{2} - 7 x + 2}{2 x^{2} + x - 10}$
20660	Evaluate the Limit	limit as x approaches 2 of (2x^2-8)/(x+2)	$lim_{x \to 2} \frac{2 x^{2} - 8}{x + 2}$
20661	Evaluate the Limit	limit as x approaches 2 of (4- square root of 18-x)/(x-2)	$lim_{x \to 2} \frac{4 - \sqrt{18 - x}}{x - 2}$
20662	Evaluate the Limit	limit as x approaches 0 of ((7+x)^3-343)/x	$lim_{x \to 0} \frac{{(7 + x)}^{3} - 343}{x}$
20663	Evaluate the Limit	limit as x approaches 2 of (2-x)/(\|2-x\|)	$lim_{x \to 2} \frac{2 - x}{\| 2 - x \|}$
20664	Evaluate the Limit	limit as x approaches 2 of 5/(x-2)	$lim_{x \to 2} \frac{5}{x - 2}$
20665	Evaluate the Limit	limit as x approaches -2 of 6/(x^2-4)	$lim_{x \to - 2} \frac{6}{x^{2} - 4}$
20666	Evaluate the Limit	limit as x approaches 2 of (7x-14)/(6x^2-24)	$lim_{x \to 2} \frac{7 x - 14}{6 x^{2} - 24}$
20667	Evaluate the Limit	limit as x approaches 2 of (90+60x)/(x+5)	$lim_{x \to 2} \frac{90 + 60 x}{x + 5}$
20668	Evaluate the Limit	limit as x approaches -2 of x^3-6x+1	$lim_{x \to - 2} x^{3} - 6 x + 1$
20669	Evaluate the Limit	limit as x approaches 2 of x^3-8	$lim_{x \to 2} x^{3} - 8$
20670	Evaluate the Limit	limit as x approaches 2 of square root of 6x-5	$lim_{x \to 2} \sqrt{6 x - 5}$
20671	Evaluate the Integral	integral of ( square root of x^2-9)/x with respect to x	$\int \frac{\sqrt{x^{2} - 9}}{x} d x$
20672	Evaluate the Limit	limit as x approaches 0 of ( square root of 16+x-4)/x	$lim_{x \to 0} \frac{\sqrt{16 + x} - 4}{x}$
20673	Evaluate the Limit	limit as x approaches 0 of (7^(2x)-1)/(7^x-1)	$lim_{x \to 0} \frac{7^{2 x} - 1}{7^{x} - 1}$
20674	Evaluate the Limit	limit as x approaches 0 of 5/(x square root of 1+x)-5/x	$lim_{x \to 0} \frac{5}{x \sqrt{1 + x}} - \frac{5}{x}$
20675	Evaluate the Limit	limit as t approaches -4 of (t^2-16)/(2t^2+9t+4)	$lim_{t \to - 4} \frac{t^{2} - 16}{2 t^{2} + 9 t + 4}$
20676	Evaluate the Limit	limit as x approaches 2 of x^2-1	$lim_{x \to 2} x^{2} - 1$
20677	Evaluate the Limit	limit as t approaches -7 of (t^2-49)/(2t^2+15t+7)	$lim_{t \to - 7} \frac{t^{2} - 49}{2 t^{2} + 15 t + 7}$
20678	Evaluate the Limit	limit as x approaches 2 of 2x-1	$lim_{x \to 2} 2 x - 1$
20679	Evaluate the Limit	limit as x approaches 2 of 3x^2-4x-1	$lim_{x \to 2} 3 x^{2} - 4 x - 1$
20680	Evaluate the Limit	limit as x approaches 2 of 3x^2-11x+10	$lim_{x \to 2} 3 x^{2} - 11 x + 10$
20681	Evaluate the Limit	limit as x approaches 2 of 3 natural log of x-1	$lim_{x \to 2} 3 \ln (x - 1)$
20682	Evaluate the Limit	limit as x approaches 2 of -2x^2+3x-1	$lim_{x \to 2} - 2 x^{2} + 3 x - 1$
20683	Evaluate the Limit	limit as x approaches -2 of 0	$lim_{x \to - 2} 0$
20684	Evaluate the Limit	limit as x approaches -2 of 10	$lim_{x \to - 2} 10$
20685	Evaluate the Limit	limit as x approaches 2 of 10x	$lim_{x \to 2} 10 x$
20686	Evaluate the Limit	limit as x approaches 2 of square root of x^2-4	$lim_{x \to 2} \sqrt{x^{2} - 4}$
20687	Evaluate the Limit	limit as x approaches infinity of (-3x^3+4x^2)/(4x+6x^3)	$lim_{x \to \infty} \frac{- 3 x^{3} + 4 x^{2}}{4 x + 6 x^{3}}$
20688	Evaluate the Limit	limit as x approaches infinity of (e^(3x)-e^(-3x))/(e^(3x)+e^(-3x))	$lim_{x \to \infty} \frac{e^{3 x} - e^{- 3 x}}{e^{3 x} + e^{- 3 x}}$
20689	Evaluate the Limit	limit as x approaches 0 of (6x-9)/(x^3-12x+3)	$lim_{x \to 0} \frac{6 x - 9}{x^{3} - 12 x + 3}$
20690	Evaluate the Limit	limit as x approaches 1 of 1/(x-1)-3/(x^3-1)	$lim_{x \to 1} \frac{1}{x - 1} - \frac{3}{x^{3} - 1}$
20691	Evaluate the Limit	limit as x approaches 1 of (x^2-4x)^3	$lim_{x \to 1} {(x^{2} - 4 x)}^{3}$
20692	Evaluate the Limit	limit as x approaches 1 of (2-x)^(tan((pix)/2))	$lim_{x \to 1} {(2 - x)}^{\tan (\frac{π x}{2})}$
20693	Evaluate the Limit	limit as x approaches 1 of (3x^3-4x^2-5x+2)/(x^2-x-2)	$lim_{x \to 1} \frac{3 x^{3} - 4 x^{2} - 5 x + 2}{x^{2} - x - 2}$
20694	Evaluate the Limit	limit as x approaches -1 of (-1.001^3-(-1.001))/(-1.001+1)	$lim_{x \to - 1} \frac{- {1.001}^{3} - (- 1.001)}{- 1.001 + 1}$
20695	Evaluate the Limit	limit as x approaches 1 of ((10x-5)^2-25)/(5x-5)	$lim_{x \to 1} \frac{{(10 x - 5)}^{2} - 25}{5 x - 5}$
20696	Evaluate the Limit	limit as x approaches 1 of ((2x-1)^2-1)/(2x-2)	$lim_{x \to 1} \frac{{(2 x - 1)}^{2} - 1}{2 x - 2}$
20697	Evaluate the Limit	limit as x approaches 1 of (\|x-1\|)/(1-x)	$lim_{x \to 1} \frac{\| x - 1 \|}{1 - x}$
20698	Evaluate the Limit	limit as x approaches 1 of (x-2)^(tan((2x)/pi))	$lim_{x \to 1} {(x - 2)}^{\tan (\frac{2 x}{π})}$
20699	Evaluate the Limit	limit as x approaches 1 of ((8x-4)^2-16)/(4x-4)	$lim_{x \to 1} \frac{{(8 x - 4)}^{2} - 16}{4 x - 4}$
20700	Evaluate the Limit	limit as x approaches 1 of (x^2+4x-5)/(\|x^2-4\|)	$lim_{x \to 1} \frac{x^{2} + 4 x - 5}{\| x^{2} - 4 \|}$