Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
6101	Evaluate the Limit	( limit as x approaches 0 of e^x+e^(-x)-2)/(x^2)	$\frac{lim_{x \to 0} e^{x} + e^{- x} - 2}{x^{2}}$
6102	Evaluate the Limit	limit as x approaches negative infinity of (x^2)/(x^2+1)	$lim_{x \to - \infty} \frac{x^{2}}{x^{2} + 1}$
6103	Evaluate the Limit	( limit as x approaches 0 of 1-cos(x)+sin(x))/(1-cos(x)-sin(x))	$\frac{lim_{x \to 0} 1 - \cos (x) + \sin (x)}{1 - \cos (x) - \sin (x)}$
6104	Evaluate the Limit	( limit as x approaches 0 of 6x^5-8x^3)/(9x^3-6x^5)	$\frac{lim_{x \to 0} 6 x^{5} - 8 x^{3}}{9 x^{3} - 6 x^{5}}$
6105	Evaluate the Limit	( limit as x approaches 0 of sin(2x))/(5x)	$\frac{lim_{x \to 0} \sin (2 x)}{5 x}$
6106	Evaluate the Limit	( limit as x approaches 0 of 6x-9)/(x^3-12x+3)	$\frac{lim_{x \to 0} 6 x - 9}{x^{3} - 12 x + 3}$
6107	Evaluate the Limit	( limit as x approaches 1 of (4x-2)^2-4)/(2x-2)	$\frac{lim_{x \to 1} {(4 x - 2)}^{2} - 4}{2 x - 2}$
6108	Evaluate the Limit	( limit as x approaches 0.1 of 10x-1)/(\|10x^3-x^2\|)	$\frac{lim_{x \to 0.1} 10 x - 1}{\| 10 x^{3} - x^{2} \|}$
6109	Evaluate the Limit	( limit as x approaches 0 of x+xcos(x))/(sin(x)cos(x))	$\frac{lim_{x \to 0} x + x \cos (x)}{\sin (x) \cos (x)}$
6110	Evaluate the Limit	( limit as x approaches 0 of x-sin(x))/(x-tan(x))	$\frac{lim_{x \to 0} x - \sin (x)}{x - \tan (x)}$
6111	Evaluate the Limit	( limit as x approaches 0 of sin(4x))/(5x)	$\frac{lim_{x \to 0} \sin (4 x)}{5 x}$
6112	Evaluate the Limit	( limit as x approaches 0 of sin(x))/( cube root of x)	$\frac{lim_{x \to 0} \sin (x)}{\sqrt[3]{x}}$
6113	Evaluate the Limit	( limit as x approaches 0 of sin(5x))/(sin(7x))	$\frac{lim_{x \to 0} \sin (5 x)}{\sin (7 x)}$
6114	Evaluate the Limit	( limit as x approaches 0 of sin(7x))/x	$\frac{lim_{x \to 0} \sin (7 x)}{x}$
6115	Evaluate the Limit	( limit as x approaches 0 of sin(8x))/x	$\frac{lim_{x \to 0} \sin (8 x)}{x}$
6116	Evaluate the Limit	( limit as x approaches 0 of sin(8x))/(tan(x))	$\frac{lim_{x \to 0} \sin (8 x)}{\tan (x)}$
6117	Evaluate the Limit	( limit as x approaches 0 of tan(x))/(3x)	$\frac{lim_{x \to 0} \tan (x)}{3 x}$
6118	Evaluate the Limit	( limit as x approaches 0 of tan(3x))/(tan(5x))	$\frac{lim_{x \to 0} \tan (3 x)}{\tan (5 x)}$
6119	Find the Derivative - d/dx	y = natural log of square root of x+6	$y = \ln (\sqrt{x + 6})$
6120	Find the Tangent Line at the Point	y = natural log of x^2-8 , (3,0)	$y = \ln (x^{2} - 8)$ , $(3, 0)$
6121	Find the Tangent Line at the Point	y=5x^3-3x , (1,2)	$y = 5 x^{3} - 3 x$ , $(1, 2)$
6122	Find the Tangent Line at the Point	y=6x^2-x^3 , (1,5)	$y = 6 x^{2} - x^{3}$ , $(1, 5)$
6123	Find the Tangent Line at the Point	y=7x^2+5x , (-1,2)	$y = 7 x^{2} + 5 x$ , $P (- 1, 2)$
6124	Find the Tangent Line at the Point	y=2x^3-2x , (1,0)	$y = 2 x^{3} - 2 x$ , $(1, 0)$
6125	Find the Tangent Line at the Point	y=x^3 , (2,8)	$y = x^{3}$ , $(2, 8)$
6126	Find the Derivative - d/dx	y=(3x+4)^2(x-5)^3	$y = {(3 x + 4)}^{2} {(x - 5)}^{3}$
6127	Evaluate the Limit	( limit as h approaches 0 of square root of 64+h-8)/h	$\frac{lim_{h \to 0} \sqrt{64 + h} - 8}{h}$
6128	Evaluate the Limit	( limit as h approaches 0 of 2.7^h-1)/h	$\frac{lim_{h \to 0} {2.7}^{h} - 1}{h}$
6129	Evaluate the Limit	( limit as h approaches 0 of e^h-1)/h	$\frac{lim_{h \to 0} e^{h} - 1}{h}$
6130	Evaluate the Limit	( limit as h approaches 0 of (2+h)^-1-2^-1)/h	$\frac{lim_{h \to 0} {(2 + h)}^{- 1} - 2^{- 1}}{h}$
6131	Evaluate the Limit	(( limit as x approaches -4 of 1)/4+1/x)/(4+x)	$\frac{\frac{lim_{x \to - 4} 1}{4} + \frac{1}{x}}{4 + x}$
6132	Evaluate	(54 natural log of 8-54)/( natural log of (8)^2)	$\frac{54 \ln (8) - 54}{\ln ({(8)}^{2})}$
6133	Graph	tan( natural log of ax+b)	$\tan (\ln (a x + b))$
6134	Graph	log of 8x	$\log (8 x)$
6135	Graph	sin(x) natural log of x	$\sin (x) \ln (x)$
6136	Graph	log of 7x	$\log (7 x)$
6137	Evaluate	log base 4 of square root of 4	$\log_{4} (\sqrt{4})$
6138	Evaluate	log base 19 of square root of 19	$\log_{19} (\sqrt{19})$
6139	Evaluate	e^( natural log of 3-2 natural log of x)	$e^{\ln (3) - 2 \ln (x)}$
6140	Evaluate	( natural log of 2)/0.059	$\frac{\ln (2)}{0.059}$
6141	Evaluate	( natural log of 6)/6	$\frac{\ln (6)}{6}$
6142	Graph	2x natural log of x	$2 x \ln (x)$
6143	Graph	4- natural log of x	$4 - \ln (x)$
6144	Graph	4x^5 natural log of 6x^2	$4 x^{5} \ln (6 x^{2})$
6145	Graph	natural log of e^(2x)	$\ln (e^{2 x})$
6146	Graph	9x natural log of 8x	$9 x \ln (8 x)$
6147	Graph	natural log of x^2+16	$\ln (x^{2} + 16)$
6148	Graph	natural log of 1+x^2	$\ln (1 + x^{2})$
6149	Graph	natural log of cube root of x	$\ln (\sqrt[3]{x})$
6150	Graph	natural log of 3x^2-2x+1	$\ln (3 x^{2} - 2 x + 1)$
6151	Graph	( natural log of x)/(3x)	$\frac{\ln (x)}{3 x}$
6152	Graph	( natural log of x)/(e^x)	$\frac{\ln (x)}{e^{x}}$
6153	Graph	( natural log of x)/( square root of x)	$\frac{\ln (x)}{\sqrt{x}}$
6154	Graph	square root of x natural log of x	$\sqrt{x} \ln (x)$
6155	Graph	x/(1- natural log of x-2)	$\frac{x}{1 - \ln (x - 2)}$
6156	Graph	e^(1+ natural log of x)	$e^{1 + \ln (x)}$
6157	Graph	e^(3 natural log of x)	$e^{3 \ln (x)}$
6158	Graph	e^(5 natural log of x)	$e^{5 \ln (x)}$
6159	Graph	natural log of (7x^9+4x)^(9/5)	$\ln ({(7 x^{9} + 4 x)}^{\frac{9}{5}})$
6160	Graph	natural log of t	$\ln (t)$
6161	Evaluate	x/( natural log of x)	$\frac{x}{\ln (x)}$
6162	Evaluate	3 natural log of 1	$3 \ln (1)$
6163	Evaluate	8 log base 8 of 19	$8 \log_{8} (19)$
6164	Evaluate	4 natural log of 4	$4 \ln (4)$
6165	Evaluate	natural log of 1/21	$\ln (\frac{1}{21})$
6166	Evaluate	natural log of 2/49	$\ln (\frac{2}{49})$
6167	Evaluate	natural log of 5/4	$\ln (\frac{5}{4})$
6168	Evaluate	natural log of 1.03	$\ln (1.03)$
6169	Evaluate	natural log of 1000	$\ln (1000)$
6170	Evaluate	natural log of 0.94	$\ln (0.94)$
6171	Evaluate	log of cube root of 100	$\log (\sqrt[3]{100})$
6172	Evaluate	log of y/1000000	$\log (\frac{y}{1000000})$
6173	Evaluate	natural log of 2e	$\ln (2 e)$
6174	Expand the Logarithmic Expression	natural log of 4 square root of 3	$\ln (4 \sqrt{3})$
6175	Solve the Function Operation	f(x)=4x-2 , g(x)=3x^2 , g(f(3/2))	$f (x) = 4 x - 2$ , $g (x) = 3 x^{2}$ , $g (f (\frac{3}{2}))$
6176	Find the Area Between the Curves	x=0 , x=3 , y=2e^(3x) , y=e^(3x)+e^6	$x = 0$ , $x = 3$ , $y = 2 e^{3 x}$ , $y = e^{3 x} + e^{6}$
6177	Find the Area Between the Curves	x=0 , x=3 , y=2e^(5x) , y=e^(5x)+e^10	$x = 0$ , $x = 3$ , $y = 2 e^{5 x}$ , $y = e^{5 x} + e^{10}$
6178	Find the Area Between the Curves	q(p)=29-5p , q^2(p)=-7+4p	$q (p) = 29 - 5 p$ , $q^{2} (p) = - 7 + 4 p$
6179	Solve for ?	cos(x)^2=3/4	$\cos^{2} (x) = \frac{3}{4}$
6180	Find the Tangent Line at the Point	x^2+y^2=4 , (0,2)	$x^{2} + y^{2} = 4$ , $(0, 2)$
6181	Evaluate the Limit	limit as x approaches 8 of (x^2-4x-32)/(x-8)	$lim_{x \to 8} \frac{x^{2} - 4 x - 32}{x - 8}$
6182	Solve for a	a=(7-2b)^3	$a = {(7 - 2 b)}^{3}$
6183	Solve for ?	tan(x)=-4/12	$\tan (x) = - \frac{4}{12}$
6184	Solve for ?	tan(x)=-4/12	$\tan (x) = \frac{- 4}{12}$
6185	Solve for t	natural log of 2=0.02t	$\ln (2) = 0.02 t$
6186	Solve for t	s=t^3-27t	$s = t^{3} - 27 t$
6187	Solve for t	x=e^t	$x = e^{t}$
6188	Solve for t	2500=100(1+0.2t+0.02t^2)	$2500 = 100 (1 + 0.2 t + 0.02 t^{2})$
6189	Solve for t	2=e^(0.03t)	$2 = e^{0.03 t}$
6190	Solve for t	-2sin(t)+2cos(2t)=0	$- 2 \sin (t) + 2 \cos (2 t) = 0$
6191	Solve for t	0.18=0.20*0.5^(t/5730)	$0.18 = 0.2 \cdot {0.5}^{\frac{t}{5730}}$
6192	Solve for t	b=pe^(rt)	$b = p e^{r t}$
6193	Solve for t	A/(1+Be^(t/2))=C	$\frac{A}{1 + B e^{\frac{t}{2}}} = C$
6194	Solve for s	2s-27648/(s^2)=0	$2 s - \frac{27648}{s^{2}} = 0$
6195	Solve for s	2s-432/(s^2)=0	$2 s - \frac{432}{s^{2}} = 0$
6196	Solve for q	q=1000-2p^2	$q = 1000 - 2 p^{2}$
6197	Solve for q	q=cos(t/( square root of t+2))	$q = \cos (\frac{t}{\sqrt{t + 2}})$
6198	Solve for x	(x-2)^2=0	${(x - 2)}^{2} = 0$
6199	Solve for w	c=8(w+2l)+5w	$c = 8 (w + 2 l) + 5 w$
6200	Solve for x	(1+x^2)^2=0	${(1 + x^{2})}^{2} = 0$