Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
20201	Find f(g(x))	f(x)=2u-3 , g(x)=2e^x	$f (x) = 2 u - 3$ , $g (x) = 2 e^{x}$
20202	Find f(g(x))	f(x)=x-1 , g(x) = square root of x+2	$f (x) = x - 1$ , $g (x) = \sqrt{x + 2}$
20203	Find f(g(x))	f(x)=x-120 , g(x)=0.75x	$f (x) = x - 120$ , $g (x) = 0.75 x$
20204	Find f(g(x))	f(x)=x-2 , g(x)=x^2+3x+4	$f (x) = x - 2$ , $g (x) = x^{2} + 3 x + 4$
20205	Find f(g(x))	f(x)=x^2+1xg(x)=x-9	$f (x) = x^{2} + 1 x g (x) = x - 9$
20206	Find f(g(y))	f(y)=y^2 , g(y)=y+2	$f (y) = y^{2}$ , $g (y) = y + 2$
20207	Evaluate the Limit	limit as x approaches infinity of x^2	$lim_{x \to \infty} x^{2}$
20208	Evaluate the Limit	( limit as x approaches 0 of 1-cos(x))/(xsin(x))	$\frac{lim_{x \to 0} 1 - \cos (x)}{x \sin (x)}$
20209	Evaluate the Limit	( limit as h approaches 0 of ((2+h)^4)-16)/h	$\frac{lim_{h \to 0} ({(2 + h)}^{4}) - 16}{h}$
20210	Evaluate the Limit	( limit as h approaches 0 of (2+h)^4-16)/h	$\frac{lim_{h \to 0} {(2 + h)}^{4} - 16}{h}$
20211	Evaluate the Limit	( limit as h approaches 0 of tan(pi/4+h)-1)/h	$\frac{lim_{h \to 0} \tan (\frac{π}{4} + h) - 1}{h}$
20212	Evaluate the Limit	( limit as x approaches 0 of sin(cos(7x)))/(sec(5x))	$\frac{lim_{x \to 0} \sin (\cos (7 x))}{\sec (5 x)}$
20213	Evaluate the Limit	( limit as x approaches 0 of sin(cos(8x)))/(sec(5x))	$\frac{lim_{x \to 0} \sin (\cos (8 x))}{\sec (5 x)}$
20214	Evaluate the Limit	( limit as h approaches 0 of (1+h)^2-1)/h	$\frac{lim_{h \to 0} {(1 + h)}^{2} - 1}{h}$
20215	Evaluate the Limit	( limit as h approaches 0 of (1+h)^3-1)/h	$\frac{lim_{h \to 0} {(1 + h)}^{3} - 1}{h}$
20216	Evaluate the Limit	( limit as h approaches 0 of (12+h)^2-144)/h	$\frac{lim_{h \to 0} {(12 + h)}^{2} - 144}{h}$
20217	Evaluate the Limit	( limit as h approaches 0 of (15+h)^2-225)/h	$\frac{lim_{h \to 0} {(15 + h)}^{2} - 225}{h}$
20218	Evaluate the Limit	( limit as h approaches 0 of (1-cos(h))^2)/h	$\frac{lim_{h \to 0} {(1 - \cos (h))}^{2}}{h}$
20219	Evaluate the Limit	( limit as h approaches 0 of (6+h)^-1-6^-1)/h	$\frac{lim_{h \to 0} {(6 + h)}^{- 1} - 6^{- 1}}{h}$
20220	Evaluate the Limit	( limit as h approaches 0 of (-6+h)^2-36)/h	$\frac{lim_{h \to 0} {(- 6 + h)}^{2} - 36}{h}$
20221	Evaluate the Limit	( limit as x approaches 0 of csc(x))/(cot(x))	$\frac{lim_{x \to 0} \csc (x)}{\cot (x)}$
20222	Evaluate the Limit	( limit as h approaches 0 of square root of 16+h-4)/h	$\frac{lim_{h \to 0} \sqrt{16 + h} - 4}{h}$
20223	Evaluate the Limit	( limit as h approaches 0 of 2(a+h)^2-2a^2)/h	$\frac{lim_{h \to 0} 2 {(a + h)}^{2} - 2 a^{2}}{h}$
20224	Evaluate the Limit	( limit as h approaches 0 of 2hx+h^2)/h	$\frac{lim_{h \to 0} 2 h x + h^{2}}{h}$
20225	Evaluate the Limit	( limit as h approaches 0 of square root of x+h- square root of x)/h	$\frac{lim_{h \to 0} \sqrt{x + h} - \sqrt{x}}{h}$
20226	Evaluate the Limit	( limit as h approaches 0 of x^2h-xh^2+h^3)/h	$\frac{lim_{h \to 0} x^{2} h - x h^{2} + h^{3}}{h}$
20227	Evaluate the Limit	limit as t approaches 0 of 9/t-9/(t^2+t)	$lim_{t \to 0} \frac{9}{t} - \frac{9}{t^{2} + t}$
20228	Evaluate the Limit	( limit as h approaches 0 of square root of 9+h- square root of 9)/h	$\frac{lim_{h \to 0} \sqrt{9 + h} - \sqrt{9}}{h}$
20229	Evaluate the Limit	( limit as h approaches 0 of (h-1)^3+1)/h	$\frac{lim_{h \to 0} {(h - 1)}^{3} + 1}{h}$
20230	Evaluate the Limit	( limit as h approaches 0 of e^(5+h)-e^5)/h	$\frac{lim_{h \to 0} e^{5 + h} - e^{5}}{h}$
20231	Evaluate the Limit	( limit as h approaches 0 of square root of 2(a+b)- square root of 2a)/h	$\frac{lim_{h \to 0} \sqrt{2 (a + b)} - \sqrt{2 a}}{h}$
20232	Evaluate the Limit	( limit as h approaches 0 of f(x+h)-fx)/h	$\frac{lim_{h \to 0} f (x + h) - f x}{h}$
20233	Evaluate the Limit	( limit as h approaches 0 of 3(a+h)^2-3a^2)/h	$\frac{lim_{h \to 0} 3 {(a + h)}^{2} - 3 a^{2}}{h}$
20234	Find the Tangent Line at the Point	y=x^3-3x+1 , (2,3)	$y = x^{3} - 3 x + 1$ , $(2, 3)$
20235	Find the Tangent Line at the Point	y=x^3-9x+5 , (3,5)	$y = x^{3} - 9 x + 5$ , $(3, 5)$
20236	Find the Tangent Line at the Point	y=x^4+2e^x , (0,2)	$y = x^{4} + 2 e^{x}$ , $(0, 2)$
20237	Find the Tangent Line at the Point	y=1-4tan(h(x)) at, (0,1)	$y = 1 - 4 \tanh (x)$ at, $(0, 1)$
20238	Find the Tangent Line at the Point	y=x^4+8x^2-x , (1,8)	$y = x^{4} + 8 x^{2} - x$ , $(1, 8)$
20239	Find the Tangent Line at the Point	y=-1-4x^2 , (4,-65)	$y = - 1 - 4 x^{2}$ , $(4, - 65)$
20240	Find the Tangent Line at the Point	y=1-6x^2 at, (-4,-95)	$y = 1 - 6 x^{2}$ at, $(- 4, - 95)$
20241	Find the Tangent Line at the Point	y=x^4-3x^2+2 , (1,0)	$y = x^{4} - 3 x^{2} + 2$ , $(1, 0)$
20242	Find the Tangent Line at the Point	y=-2x^3 , (2,-16)	$y = - 2 x^{3}$ , $(2, - 16)$
20243	Find the Tangent Line at the Point	y=2x^3-8x , (2,0)	$y = 2 x^{3} - 8 x$ , $(2, 0)$
20244	Find the Tangent Line at the Point	y=20 square root of x , (4,40)	$y = 20 \sqrt{x}$ , $(4, 40)$
20245	Find the Tangent Line at the Point	y=2xe^x , (0,0)	$y = 2 x e^{x}$ , $(0, 0)$
20246	Find the Tangent Line at the Point	y=3x^2 , (2,12)	$y = 3 x^{2}$ , $(2, 12)$
20247	Find the Tangent Line at the Point	y=3x^2+1 , (-2,13)	$y = 3 x^{2} + 1$ , $(- 2, 13)$
20248	Find the Tangent Line at the Point	y=3x^2+2x , (-2,y)	$y = 3 x^{2} + 2 x$ , $(- 2, y)$
20249	Find the Tangent Line at the Point	y=6x^2+5x , (-4,76)	$y = 6 x^{2} + 5 x$ , $(- 4, 76)$
20250	Find the Tangent Line at the Point	y=64-x^2 , (-8,8)	$y = 64 - x^{2}$ , $(- 8, 8)$
20251	Find the Tangent Line at the Point	y=5x^3-4x , (1,1)	$y = 5 x^{3} - 4 x$ , $(1, 1)$
20252	Find the Antiderivative	2cos(x)	$2 \cos (x)$
20253	Find the Tangent Line at the Point	y=5x^3-5x , (1,0)	$y = 5 x^{3} - 5 x$ , $(1, 0)$
20254	Find the Tangent Line at the Point	y=5x^3-5x , (-1,0)	$y = 5 x^{3} - 5 x$ , $(- 1, 0)$
20255	Find the Tangent Line at the Point	y=4x+5e^x , (0,5)	$y = 4 x + 5 e^{x}$ , $(0, 5)$
20256	Find the Tangent Line at the Point	y=4x-x^2 , (1,3)	$y = 4 x - x^{2}$ , $(1, 3)$
20257	Find the Tangent Line at the Point	y=4-x^2 , (-1,3)	$y = 4 - x^{2}$ , $(- 1, 3)$
20258	Find the Tangent Line at the Point	y=4x^3-2x , (1,2)	$y = 4 x^{3} - 2 x$ , $(1, 2)$
20259	Find the Tangent Line at the Point	y=3x-2 square root of x , (1,1)	$y = 3 x - 2 \sqrt{x}$ , $(1, 1)$
20260	Find the Tangent Line at the Point	y=-3-4x^2 at, (2,-19)	$y = - 3 - 4 x^{2}$ at, $(2, - 19)$
20261	Find the Tangent Line at the Point	y=3x^2+5x , (-6,78)	$y = 3 x^{2} + 5 x$ , $(- 6, 78)$
20262	Find the Tangent Line at the Point	y=2x^3-3x , (1,-1)	$y = 2 x^{3} - 3 x$ , $(1, - 1)$
20263	Find the Tangent Line at the Point	y = natural log of x^2 , (2, natural log of 4)	$y = \ln (x^{2})$ , $(2, \ln (4))$
20264	Find the Tangent Line at the Point	y=7e^xcos(x) , (0,7)	$y = 7 e^{x} \cos (x)$ , $(0, 7)$
20265	Find the Tangent Line at the Point	y=7-x^2 , (2,3)	$y = 7 - x^{2}$ , $P (2, 3)$
20266	Find the Tangent Line at the Point	y=sin(7x)+sin(7x)^2 , (0,0)	$y = \sin (7 x) + \sin^{2} (7 x)$ , $(0, 0)$
20267	Find the Tangent Line at the Point	y=x+6x^2-3x^4 , (1,4)	$y = x + 6 x^{2} - 3 x^{4}$ , $(1, 4)$
20268	Find the Root Using Newton's Method	x^3-7=0 , a=2	$x^{3} - 7 = 0$ , $a = 2$
20269	Find the Tangent Line at the Point	y=sin(x) , ((5pi)/2,1)	$y = \sin (x)$ , $(\frac{5 π}{2}, 1)$
20270	Find the Tangent Line at the Point	y=x-x^2 , (2,-2)	$y = x - x^{2}$ , $(2, - 2)$
20271	Find f(F(x))	f(x)=32x^3 , F(x)=ax^4	$f (x) = 32 x^{3}$ , $F (x) = a x^{4}$
20272	Find f(F(x))	f(x)=14x , F(x)=ax^2	$f (x) = 14 x$ , $F (x) = a x^{2}$
20273	Find f(F(x))	f(x)=5x^4 , F(x)=ax^5	$f (x) = 5 x^{4}$ , $F (x) = a x^{5}$
20274	Find f(g(x))	f(x)=8/x , g(x)=4-x^2	$f (x) = \frac{8}{x}$ , $g (x) = 4 - x^{2}$
20275	Find f(g(x))	f(x)=x^2+3x-1 , g(x)=x+7	$f (x) = x^{2} + 3 x - 1$ , $g (x) = x + 7$
20276	Find f(g(x))	f(x)=cos(x) , g(x)=-2cos(x/3)	$f (x) = \cos (x)$ , $g (x) = - 2 \cos (\frac{x}{3})$
20277	Evaluate the Limit	( limit as x approaches 0 of tan(3x))/(sin(8x))	$\frac{lim_{x \to 0} \tan (3 x)}{\sin (8 x)}$
20278	Evaluate the Limit	( limit as x approaches 0 of tan(2x))/(3x)	$\frac{lim_{x \to 0} \tan (2 x)}{3 x}$
20279	Evaluate the Limit	( limit as x approaches 0 of tan(4x))/(3x)	$\frac{lim_{x \to 0} \tan (4 x)}{3 x}$
20280	Evaluate the Limit	( limit as x approaches 0 of sin(x)-x)/(x^3)	$\frac{lim_{x \to 0} \sin (x) - x}{x^{3}}$
20281	Evaluate the Limit	( limit as x approaches 0 of sin(x)-cos(x))/x	$\frac{lim_{x \to 0} \sin (x) - \cos (x)}{x}$
20282	Evaluate the Limit	( limit as x approaches 0 of x)/( square root of 1+3x-1)	$\frac{lim_{x \to 0} x}{\sqrt{1 + 3 x} - 1}$
20283	Evaluate the Limit	( limit as x approaches 0 of x)/(1-e^x)	$\frac{lim_{x \to 0} x}{1 - e^{x}}$
20284	Evaluate the Limit	( limit as x approaches 0 of x)/(tan(x))	$\frac{lim_{x \to 0} x}{\tan (x)}$
20285	Evaluate the Limit	( limit as x approaches 0 of x- square root of x)/(x+ square root of x)	$\frac{lim_{x \to 0} x - \sqrt{x}}{x + \sqrt{x}}$
20286	Evaluate the Limit	( limit as x approaches 0 of tan(pix))/( natural log of 1+x)	$\frac{lim_{x \to 0} \tan (π x)}{\ln (1 + x)}$
20287	Evaluate the Limit	( limit as x approaches 0 of tan(pix))/x	$\frac{lim_{x \to 0} \tan (π x)}{x}$
20288	Evaluate the Limit	( limit as x approaches 0 of tan(x))/(2x)	$\frac{lim_{x \to 0} \tan (x)}{2 x}$
20289	Evaluate the Limit	( limit as x approaches 0 of tan(h(x)))/(tan(x))	$\frac{lim_{x \to 0} \tanh (x)}{\tan (x)}$
20290	Evaluate the Limit	( limit as x approaches 0 of sin(ax))/(sin(bx))	$\frac{lim_{x \to 0} \sin (a x)}{\sin (b x)}$
20291	Evaluate the Limit	( limit as x approaches 0 of sin(7x))/(sin(9x))	$\frac{lim_{x \to 0} \sin (7 x)}{\sin (9 x)}$
20292	Evaluate the Limit	( limit as x approaches 0 of sin(6x))/(cos(4x))	$\frac{lim_{x \to 0} \sin (6 x)}{\cos (4 x)}$
20293	Evaluate the Limit	( limit as x approaches 0 of sin(6x))/(tan(7x))	$\frac{lim_{x \to 0} \sin (6 x)}{\tan (7 x)}$
20294	Evaluate the Limit	limit as x approaches 0 of xcot(x)	$lim_{x \to 0} x \cot (x)$
20295	Evaluate the Limit	( limit as a approaches 0 of sin(4a))/(sin(2a))	$\frac{lim_{a \to 0} \sin (4 a)}{\sin (2 a)}$
20296	Evaluate the Limit	( limit as x approaches 0 of sin(4x))/( square root of x+1-1)	$\frac{lim_{x \to 0} \sin (4 x)}{\sqrt{x + 1} - 1}$
20297	Evaluate the Limit	( limit as x approaches 0 of sin(4x))/(tan(x))	$\frac{lim_{x \to 0} \sin (4 x)}{\tan (x)}$
20298	Evaluate the Limit	( limit as x approaches 0 of sin(5x))/(7x)	$\frac{lim_{x \to 0} \sin (5 x)}{7 x}$
20299	Evaluate the Limit	( limit as b approaches 0 of sin(2b))/(tan(3b))	$\frac{lim_{b \to 0} \sin (2 b)}{\tan (3 b)}$
20300	Evaluate the Limit	( limit as x approaches 0 of sin(2x))/(tan(5x))	$\frac{lim_{x \to 0} \sin (2 x)}{\tan (5 x)}$