Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
58601	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (e^x-1)/(sin(8x))	$lim_{x \to 0} \frac{e^{x} - 1}{\sin (8 x)}$
58602	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of (e^x-e^(-x))/(e^x+e^(-x))	$lim_{x \to \infty} \frac{e^{x} - e^{- x}}{e^{x} + e^{- x}}$
58603	Evaluate Using L'Hospital's Rule	limit as x approaches pi/2 of (1+cos(2theta))/(1-sin(theta))	$lim_{x \to \frac{π}{2}} \frac{1 + \cos (2 θ)}{1 - \sin (θ)}$
58604	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (sin(x^2))/( natural log of cos(x))	$lim_{x \to 0} \frac{\sin (x^{2})}{\ln (\cos (x))}$
58605	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of natural log of 8x- natural log of x+9	$lim_{x \to \infty} \ln (8 x) - \ln (x + 9)$
58606	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of ((5x-4)/(5x+2))^(5x+1)	$lim_{x \to \infty} {(\frac{5 x - 4}{5 x + 2})}^{5 x + 1}$
58607	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (e^x-x)/x	$lim_{x \to 0} \frac{e^{x} - x}{x}$
58608	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of ( natural log of e^(3x)+2)/(2x)	$lim_{x \to \infty} \frac{\ln (e^{3 x} + 2)}{2 x}$
58609	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of (cos(24x))/(24x)	$lim_{x \to \infty} \frac{\cos (24 x)}{24 x}$
58610	Evaluate Using L'Hospital's Rule	limit as c approaches 0 of mg/c(1-e^(-(ct)/m))	$lim_{c \to 0} \frac{mg}{c} (1 - e^{- \frac{c t}{m}})$
58611	Evaluate Using L'Hospital's Rule	limit as x approaches (pi^4)/3 of (3+3sin(x))/(cos(x))	$lim_{x \to \frac{p i^{4}}{3}} \frac{3 + 3 \sin (x)}{\cos (x)}$
58612	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of ( natural log of e^x+3)/(7x)	$lim_{x \to \infty} \frac{\ln (e^{x} + 3)}{7 x}$
58613	Evaluate Using L'Hospital's Rule	limit as x approaches 9 of (x^2-5x-36)/(x-9)	$lim_{x \to 9} \frac{x^{2} - 5 x - 36}{x - 9}$
58614	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of ( natural log of e+x-1)/x	$lim_{x \to 0} \frac{\ln (e + x) - 1}{x}$
58615	Evaluate Using L'Hospital's Rule	limit as theta approaches 0 of (1-cos(theta))/(sin(theta))	$lim_{θ \to 0} \frac{1 - \cos (θ)}{\sin (θ)}$
58616	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (x^2)/(2 natural log of sec(x))	$lim_{x \to 0} \frac{x^{2}}{2 \ln (\sec (x))}$
58617	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (sin(8x))/(tan(3x))	$lim_{x \to 0} \frac{\sin (8 x)}{\tan (3 x)}$
58618	Evaluate Using L'Hospital's Rule	limit as x approaches 1 of (1-x+ natural log of x)/(1+cos(7pix))	$lim_{x \to 1} \frac{1 - x + \ln (x)}{1 + \cos (7 π x)}$
58619	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of natural log of 7x- natural log of x+4	$lim_{x \to \infty} \ln (7 x) - \ln (x + 4)$
58620	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of x/(3^x)	$lim_{x \to \infty} \frac{x}{3^{x}}$
58621	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of 3/(8xcsc(3x))	$lim_{x \to 0} \frac{3}{8 x \csc (3 x)}$
58622	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of xcos(1/x)	$lim_{x \to \infty} x \cos (\frac{1}{x})$
58623	Evaluate Using L'Hospital's Rule	limit as h approaches 0 of (cos((3pi)/2+h)-cos((3pi)/2))/h	$lim_{h \to 0} \frac{\cos (\frac{3 π}{2} + h) - \cos (\frac{3 π}{2})}{h}$
58624	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (cot(x))/( natural log of x)	$lim_{x \to 0} \frac{(\cot (x))}{\ln (x)}$
58625	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of x/(arctan(3x))	$lim_{x \to 0} \frac{x}{\arctan (3 x)}$
58626	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (tan(8x))/(sin(2x))	$lim_{x \to 0} \frac{\tan (8 x)}{\sin (2 x)}$
58627	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of (x-x square root of x)/(2x^(3/2)+3x-5)	$lim_{x \to \infty} \frac{x - x \sqrt{x}}{2 x^{\frac{3}{2}} + 3 x - 5}$
58628	Evaluate Using L'Hospital's Rule	limit as x approaches 4 of ( natural log of x/4)/(x^2-16)	$lim_{x \to 4} \frac{L n (\frac{x}{4})}{x^{2} - 16}$
58629	Evaluate Using L'Hospital's Rule	limit as h approaches 0 of (sin(pi/4+h)-( square root of 2)/2)/h	$lim_{h \to 0} \frac{\sin (\frac{π}{4} + h) - \frac{\sqrt{2}}{2}}{h}$
58630	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of ( natural log of 3x+5)/(2x+5)	$lim_{x \to \infty} \frac{\ln (3 x + 5)}{2 x + 5}$
58631	Evaluate Using L'Hospital's Rule	limit as x approaches 5 of (x^2+3x-40)/(x^2-25)	$lim_{x \to 5} \frac{x^{2} + 3 x - 40}{x^{2} - 25}$
58632	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (e^x-1)/(sin(13x))	$lim_{x \to 0} \frac{e^{x} - 1}{\sin (13 x)}$
58633	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of (1+2x)^(13/(2 natural log of x))	$lim_{x \to \infty} {(1 + 2 x)}^{\frac{13}{2 \ln (x)}}$
58634	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (1-cos(x)^2)/(x^3)	$lim_{x \to 0} \frac{1 - \cos^{2} (x)}{x^{3}}$
58635	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of (e^(3x))/(x^4)	$lim_{x \to \infty} \frac{e^{(3 x)}}{x^{4}}$
58636	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of 2xe^(1/x)-2x	$lim_{x \to \infty} 2 x e^{\frac{1}{x}} - 2 x$
58637	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of (1+6/x)^(x/13)	$lim_{x \to \infty} {(1 + \frac{6}{x})}^{\frac{x}{13}}$
58638	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of (x+x^2)/(3-2x^2)	$lim_{x \to \infty} \frac{x + x^{2}}{3 - 2 x^{2}}$
58639	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (sin(8x))/(tan(5x))	$lim_{x \to 0} \frac{\sin (8 x)}{\tan (5 x)}$
58640	Evaluate Using L'Hospital's Rule	limit as X approaches 7 of (x-7)/(x^2-8x+7)	$lim_{X \to 7} \frac{x - 7}{x^{2} - 8 x + 7}$
58641	Evaluate Using L'Hospital's Rule	limit as t approaches infinity of (t-t square root of t)/(2t^(3/2)+3t-5)	$lim_{t \to \infty} \frac{t - t \sqrt{t}}{2 t^{\frac{3}{2}} + 3 t - 5}$
58642	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of 9xe^(1/x)-9x	$lim_{x \to \infty} 9 x e^{\frac{1}{x}} - 9 x$
58643	Convert Degrees, Minutes, Seconds to Decimal Degrees	47 degrees 48'25''	$47 ° 48' 25''$
58644	Convert Degrees, Minutes, Seconds to Decimal Degrees	22 degrees 41'44''	$22 ° 41' 44''$
58645	Convert Degrees, Minutes, Seconds to Decimal Degrees	-208 degrees 16'20''	$- 208 ° 16' 20''$
58646	Convert Degrees, Minutes, Seconds to Decimal Degrees	54 degrees 44'3''	$54 ° 44' 3''$
58647	Convert Degrees, Minutes, Seconds to Decimal Degrees	116 degrees 35'	$116 ° 35'$
58648	Subtract	4/y-7/3	$\frac{4}{y} - \frac{7}{3}$
58649	Subtract	(7x^4-3x^2-9x)-(-2x^4-3x^2-27x)	$(7 x^{4} - 3 x^{2} - 9 x) - (- 2 x^{4} - 3 x^{2} - 27 x)$
58650	Subtract	2x-x	$2 x - x$
58651	Subtract	(2x+5)/(6x)-(x-6)/(8x)	$\frac{2 x + 5}{6 x} - \frac{x - 6}{8 x}$
58652	Subtract	(1/4+1/7i)-(5/6+7/2i)	$(\frac{1}{4} + \frac{1}{7} i) - (\frac{5}{6} + \frac{7}{2} i)$
58653	Subtract	(5x^2+2x-5)-(4x^2-10)	$(5 x^{2} + 2 x - 5) - (4 x^{2} - 10)$
58654	Subtract	(6x)/(5x^2-16x-45)-x/(x^2-7x+10)	$\frac{6 x}{5 x^{2} - 16 x - 45} - \frac{x}{x^{2} - 7 x + 10}$
58655	Subtract	(7x^2+6)-(2x-5)	$(7 x^{2} + 6) - (2 x - 5)$
58656	Subtract	5/(5x+1)-5/(5x-1)	$\frac{5}{5 x + 1} - \frac{5}{5 x - 1}$
58657	Subtract	x-x	$x - x$
58658	Subtract	2/d-5/6	$\frac{2}{d} - \frac{5}{6}$
58659	Subtract	(7x^2-3x+8)-(3x^2+4x+5)	$(7 x^{2} - 3 x + 8) - (3 x^{2} + 4 x + 5)$
58660	Subtract	(4a^3-3a-8)-(a-5)	$(4 a^{3} - 3 a - 8) - (a - 5)$
58661	Subtract	(f^3-5f+25)-(4f^2-12f+9)	$(f^{3} - 5 f + 25) - (4 f^{2} - 12 f + 9)$
58662	Subtract	(6x-1)/(2x^2)-3/x	$\frac{6 x - 1}{2 x^{2}} - \frac{3}{x}$
58663	Subtract	(6a^3+7a^2)-(5a^3+9a^2+a)	$(6 a^{3} + 7 a^{2}) - (5 a^{3} + 9 a^{2} + a)$
58664	Subtract	(7x)/((9x+8)(7x-6))-5/((7x-6)(7-3x))	$\frac{7 x}{(9 x + 8) (7 x - 6)} - \frac{5}{(7 x - 6) (7 - 3 x)}$
58665	Subtract	1.001-1	$1.001 - 1$
58666	Subtract	(-8y^2-9y)-(-8y^3+9y^2-5y)	$(- 8 y^{2} - 9 y) - (- 8 y^{3} + 9 y^{2} - 5 y)$
58667	Subtract	(71.8x-0.02x^2)-(0.07x^2+4.1x+6800)	$(71.8 x - 0.02 x^{2}) - (0.07 x^{2} + 4.1 x + 6800)$
58668	Subtract	(4r^2-3r+2)-(-r^2-3r)	$(4 r^{2} - 3 r + 2) - (- r^{2} - 3 r)$
58669	Subtract	(5x+3)-(x+2)	$(5 x + 3) - (x + 2)$
58670	Subtract	3x-2x	$3 x - 2 x$
58671	Subtract	(x-3)/(3x^2+10x-8)-(x+1)/(3x^2-17x+10)	$\frac{x - 3}{3 x^{2} + 10 x - 8} - \frac{x + 1}{3 x^{2} - 17 x + 10}$
58672	Subtract	(4x^2)-(3x)	$(4 x^{2}) - (3 x)$
58673	Subtract	(3b-2)/(8b)-(5b-2)/(6b)	$\frac{3 b - 2}{8 b} - \frac{5 b - 2}{6 b}$
58674	Subtract	fourth root of 1+2x-0.1	$\sqrt[4]{1 + 2 x} - 0.1$
58675	Subtract	3/c-4/7	$\frac{3}{c} - \frac{4}{7}$
58676	Subtract	7/(2y^2)-2/(5y^3)	$\frac{7}{2 y^{2}} - \frac{2}{5 y^{3}}$
58677	Subtract	(10a+3b)/(10a^2+3ab-4b^2)-(a+2b)/(25a^2-16b^2)	$\frac{10 a + 3 b}{10 a^{2} + 3 a b - 4 b^{2}} - \frac{a + 2 b}{25 a^{2} - 16 b^{2}}$
58678	Subtract	(8a^2-6ab+4b^2)-(3a^2+5ab-4b^2)	$(8 a^{2} - 6 a b + 4 b^{2}) - (3 a^{2} + 5 a b - 4 b^{2})$
58679	Subtract	(9k-10)/(k+3)-5/(8k^3)	$\frac{9 k - 10}{k + 3} - \frac{5}{8 k^{3}}$
58680	Subtract	(-1/2x^2+700x)-(5800+200x)	$(- \frac{1}{2} x^{2} + 700 x) - (5800 + 200 x)$
58681	Subtract	square root of x- square root of x	$\sqrt{x} - \sqrt{x}$
58682	Subtract	(t^4-t^2+t)-(12-9t^2-7t)	$(t^{4} - t^{2} + t) - (12 - 9 t^{2} - 7 t)$
58683	Subtract	5/(6x)-7/(8x)	$\frac{5}{6 x} - \frac{7}{8 x}$
58684	Subtract	3 square root of x-6 square root of x	$3 \sqrt{x} - 6 \sqrt{x}$
58685	Subtract	-3x-3x	$- 3 x - 3 x$
58686	Subtract	3x-(0.05x^2+0.3x+2)	$3 x - (0.05 x^{2} + 0.3 x + 2)$
58687	Subtract	(20 natural log of 4x+1)-(x/4)	$(20 \ln (4 x + 1)) - (\frac{x}{4})$
58688	Subtract	(4c)/(c-5)-20/(c-5)	$\frac{4 c}{c - 5} - \frac{20}{c - 5}$
58689	Subtract	(5a+3)/(6a)-(2a+1)/(8a)	$\frac{5 a + 3}{6 a} - \frac{2 a + 1}{8 a}$
58690	Find Trig Functions Using Triangle Sides	cot(theta)=12/5 , sin(theta)<0	$\cot (θ) = \frac{12}{5}$ , $\sin (θ) < 0$
58691	Write as a Function of c	(c(x))/x=165+8.9x	$\frac{c (x)}{x} = 165 + 8.9 x$
58692	Write as a Function of y	x=3y-y^2	$x = 3 y - y^{2}$
58693	Write as a Function of y	y=11 square root of x	$y = 11 \sqrt{x}$
58694	Write as a Function of y	x^2-y^2=7	$x^{2} - y^{2} = 7$
58695	Write as a Function of y	y=-0.025x^2+5x	$y = - 0.025 x^{2} + 5 x$
58696	Write as a Function of x	4x+3y+5=0	$4 x + 3 y + 5 = 0$
58697	Write as a Function of x	y=-0.025x^2+5x	$y = - 0.025 x^{2} + 5 x$
58698	Write as a Function of x	x=3y-y^2	$x = 3 y - y^{2}$
58699	Write as a Function of x	x^2+(y-2)^2=4	$x^{2} + {(y - 2)}^{2} = 4$
58700	Write as a Function of x	(c(x))/x=165+8.9x	$\frac{c (x)}{x} = 165 + 8.9 x$