Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
21201	Evaluate the Limit	( limit as x approaches 2 of x^2+5x+6)/(x+2)	$\frac{lim_{x \to 2} x^{2} + 5 x + 6}{x + 2}$
21202	Evaluate the Limit	( limit as x approaches 2 of x^2+6x-16)/(x^2-4)	$\frac{lim_{x \to 2} x^{2} + 6 x - 16}{x^{2} - 4}$
21203	Evaluate the Limit	( limit as x approaches -2 of x^2+7x+10)/(x^2+3x+2)	$\frac{lim_{x \to - 2} x^{2} + 7 x + 10}{x^{2} + 3 x + 2}$
21204	Evaluate the Limit	( limit as x approaches 2 of x^2+7x-18)/(x^2-4)	$\frac{lim_{x \to 2} x^{2} + 7 x - 18}{x^{2} - 4}$
21205	Evaluate the Limit	( limit as x approaches 2 of x^2-2x)/(4-x^2)	$\frac{lim_{x \to 2} x^{2} - 2 x}{4 - x^{2}}$
21206	Evaluate the Limit	( limit as x approaches -2 of x^2-2x-3)/(x^2+5x+6)	$\frac{lim_{x \to - 2} x^{2} - 2 x - 3}{x^{2} + 5 x + 6}$
21207	Evaluate the Limit	( limit as x approaches 2 of x^2-4x+3)/((x-2)^2)	$\frac{lim_{x \to 2} x^{2} - 4 x + 3}{{(x - 2)}^{2}}$
21208	Evaluate the Limit	( limit as x approaches 2 of x^2-4x+4)/(x^3+5x^2-14x)	$\frac{lim_{x \to 2} x^{2} - 4 x + 4}{x^{3} + 5 x^{2} - 14 x}$
21209	Evaluate the Limit	( limit as x approaches -2 of x^3+8)/(x^2+3x+2)	$\frac{lim_{x \to - 2} x^{3} + 8}{x^{2} + 3 x + 2}$
21210	Evaluate the Limit	( limit as x approaches 2 of x^2-6x+8)/(x-2)	$\frac{lim_{x \to 2} x^{2} - 6 x + 8}{x - 2}$
21211	Evaluate the Limit	( limit as x approaches 2 of x^2-6x+8)/(x^2-4)	$\frac{lim_{x \to 2} x^{2} - 6 x + 8}{x^{2} - 4}$
21212	Evaluate the Limit	( limit as x approaches 2 of x^3-4x)/(x+2)	$\frac{lim_{x \to 2} x^{3} - 4 x}{x + 2}$
21213	Evaluate the Limit	( limit as x approaches 2 of x^4-16)/(8-x^3)	$\frac{lim_{x \to 2} x^{4} - 16}{8 - x^{3}}$
21214	Evaluate the Limit	( limit as x approaches -2 of -x^4+3x^3+9x^2-23x+12)/(x^4-12x^2-16x)	$\frac{lim_{x \to - 2} - x^{4} + 3 x^{3} + 9 x^{2} - 23 x + 12}{x^{4} - 12 x^{2} - 16 x}$
21215	Evaluate the Limit	limit as n approaches 8 of 1/n-1/(n+1)	$lim_{n \to 8} \frac{1}{n} - \frac{1}{n + 1}$
21216	Evaluate the Limit	limit as n approaches 8 of (1-(-1)^n)/( square root of n)	$lim_{n \to 8} \frac{1 - {(- 1)}^{n}}{\sqrt{n}}$
21217	Evaluate the Limit	limit as n approaches 8 of fourth root of n^4-3n^3- fourth root of n^4+5n^3+1	$lim_{n \to 8} \sqrt[4]{n^{4} - 3 n^{3}} - \sqrt[4]{n^{4} + 5 n^{3} + 1}$
21218	Evaluate the Limit	limit as n approaches 8 of n^(1/n)	$lim_{n \to 8} n^{\frac{1}{n}}$
21219	Evaluate the Limit	limit as n approaches 8 of (4i)/n	$lim_{n \to 8} \frac{4 i}{n}$
21220	Evaluate the Limit	limit as n approaches 8 of (2n^3)/(n^2+4n)	$lim_{n \to 8} \frac{2 n^{3}}{n^{2} + 4 n}$
21221	Evaluate the Limit	limit as n approaches 8 of (n^3)/(n+1)	$lim_{n \to 8} \frac{n^{3}}{n + 1}$
21222	Evaluate the Limit	limit as n approaches 8 of ( square root of n+1)/( square root of n+2)	$lim_{n \to 8} \frac{\sqrt{n + 1}}{\sqrt{n + 2}}$
21223	Evaluate the Limit	limit as n approaches 8 of 1/(n^2)	$lim_{n \to 8} \frac{1}{n^{2}}$
21224	Evaluate the Limit	limit as t approaches 0 of (sin(2sin(t)))/t	$lim_{t \to 0} \frac{\sin (2 \sin (t))}{t}$
21225	Evaluate the Limit	limit as t approaches 0 of (sin(3t))/t	$lim_{t \to 0} \frac{\sin (3 t)}{t}$
21226	Evaluate the Limit	limit as t approaches 0 of 1/(tsec(t)csc(4)t)	$lim_{t \to 0} \frac{1}{t \sec (t) \csc (4) t}$
21227	Evaluate the Limit	limit as x approaches 1 of (3x^2-3)/(x-1)	$lim_{x \to 1} \frac{3 x^{2} - 3}{x - 1}$
21228	Evaluate the Limit	limit as t approaches 0 of (tan(6t))/(sin(6t))	$lim_{t \to 0} \frac{\tan (6 t)}{\sin (6 t)}$
21229	Evaluate the Limit	limit as t approaches 0 of (sin(4t))/(tcos(t))	$lim_{t \to 0} \frac{\sin (4 t)}{t \cos (t)}$
21230	Evaluate the Limit	limit as x approaches infinity of x^3-x	$lim_{x \to \infty} x^{3} - x$
21231	Evaluate the Limit	limit as t approaches 0 of (e^t-1)/(t^7)	$lim_{t \to 0} \frac{e^{t} - 1}{t^{7}}$
21232	Evaluate the Limit	limit as t approaches 0 of (te^t)/(1-e^t)	$lim_{t \to 0} \frac{t e^{t}}{1 - e^{t}}$
21233	Evaluate the Limit	limit as t approaches 0 of ( square root of t+9-3)/(t^2)	$lim_{t \to 0} \frac{\sqrt{t + 9} - 3}{t^{2}}$
21234	Evaluate the Limit	limit as t approaches 0 of (tan(4t))/(sin(2t))	$lim_{t \to 0} \frac{\tan (4 t)}{\sin (2 t)}$
21235	Evaluate the Limit	limit as x approaches 1 of (x-1)/( square root of x^2+3-2)	$lim_{x \to 1} \frac{x - 1}{\sqrt{x^{2} + 3} - 2}$
21236	Evaluate the Limit	limit as n approaches 8 of nsin(pi/(2n))	$lim_{n \to 8} n \sin (\frac{π}{2 n})$
21237	Evaluate the Limit	limit as n approaches 8 of cos(2/n)	$lim_{n \to 8} \cos (\frac{2}{n})$
21238	Evaluate the Limit	limit as t approaches 0 of (2^t-1)cos(1/t)	$lim_{t \to 0} (2^{t} - 1) \cos (\frac{1}{t})$
21239	Evaluate the Limit	limit as t approaches 3/2 of (2sin(t))/(3cos(t))	$lim_{t \to \frac{3}{2}} \frac{2 \sin (t)}{3 \cos (t)}$
21240	Evaluate the Limit	limit as x approaches infinity of (sin(x))/x	$lim_{x \to \infty} \frac{(\sin (x))}{x}$
21241	Evaluate the Limit	limit as n approaches 8 of cos(npi)	$lim_{n \to 8} \cos (n π)$
21242	Evaluate the Limit	limit as s approaches 2/3 of 3s(2s-1)	$lim_{s \to \frac{2}{3}} 3 s (2 s - 1)$
21243	Evaluate the Limit	limit as t approaches -2 of (t+1)^9(t^2-1)	$lim_{t \to - 2} {(t + 1)}^{9} (t^{2} - 1)$
21244	Evaluate the Limit	limit as x approaches 1 of (x^2-7x+6)/(x-1)	$lim_{x \to 1} \frac{x^{2} - 7 x + 6}{x - 1}$
21245	Evaluate the Limit	limit as t approaches 0 of tan(1-(sin(t))/t)	$lim_{t \to 0} \tan (1 - \frac{\sin (t)}{t})$
21246	Evaluate the Limit	limit as t approaches -1 of (t^2+1)^4(t+3)^5	$lim_{t \to - 1} {(t^{2} + 1)}^{4} {(t + 3)}^{5}$
21247	Evaluate the Limit	limit as t approaches -2 of (5t)/(t+2)+10/(t+2)	$lim_{t \to - 2} \frac{5 t}{t + 2} + \frac{10}{t + 2}$
21248	Evaluate the Limit	limit as t approaches 10 of 150(0.90)^t	$lim_{t \to 10} 150 {(0.9)}^{t}$
21249	Evaluate the Limit	limit as t approaches 0 of g(t)	$lim_{t \to 0} g (t)$
21250	Evaluate the Limit	limit as x approaches negative infinity of x^2e^x	$lim_{x \to - \infty} x^{2} e^{x}$
21251	Evaluate the Limit	limit as t approaches -1 of (t^2+3t+2)/(t^2-t-2)	$lim_{t \to - 1} \frac{t^{2} + 3 t + 2}{t^{2} - t - 2}$
21252	Evaluate the Limit	limit as t approaches 3 of (t^3+19t^2-68t+6)/(t^3-9t)	$lim_{t \to 3} \frac{t^{3} + 19 t^{2} - 68 t + 6}{t^{3} - 9 t}$
21253	Evaluate the Limit	limit as t approaches 3 of (t^3-27)/(t^2-9)	$lim_{t \to 3} \frac{t^{3} - 27}{t^{2} - 9}$
21254	Evaluate the Limit	limit as t approaches -2 of (t^4-2)/(2t^2-3t+2)	$lim_{t \to - 2} \frac{t^{4} - 2}{2 t^{2} - 3 t + 2}$
21255	Evaluate the Limit	limit as t approaches -5 of t^2-5	$lim_{t \to - 5} t^{2} - 5$
21256	Evaluate the Limit	limit as t approaches 8 of ( square root of 4t^2+4)/(2t+1)	$lim_{t \to 8} \frac{\sqrt{4 t^{2} + 4}}{2 t + 1}$
21257	Evaluate the Limit	limit as x approaches 0 of 4sin(x)-1	$lim_{x \to 0} 4 \sin (x) - 1$
21258	Evaluate the Limit	limit as t approaches 8 of ( square root of t+t^2)/(7t-t^2)	$lim_{t \to 8} \frac{\sqrt{t} + t^{2}}{7 t - t^{2}}$
21259	Evaluate the Limit	limit as t approaches 8 of ( square root of t+t^2)/(8t-t^2)	$lim_{t \to 8} \frac{\sqrt{t} + t^{2}}{8 t - t^{2}}$
21260	Evaluate the Limit	limit as u approaches 3 of ( square root of u+1-2)/(u-3)	$lim_{u \to 3} \frac{\sqrt{u + 1} - 2}{u - 3}$
21261	Evaluate the Limit	limit as u approaches 64 of ( square root of u-8)/(u-64)	$lim_{u \to 64} \frac{\sqrt{u} - 8}{u - 64}$
21262	Evaluate the Limit	limit as v approaches 0 of (v)csc(v)	$lim_{v \to 0} (v) \csc (v)$
21263	Evaluate the Limit	limit as x approaches infinity of ( square root of 9x^6-x)/(x^3+5)	$lim_{x \to \infty} \frac{\sqrt{9 x^{6} - x}}{x^{3} + 5}$
21264	Evaluate the Limit	limit as u approaches 1 of (u^3-1)/(u^4-1)	$lim_{u \to 1} \frac{u^{3} - 1}{u^{4} - 1}$
21265	Evaluate the Limit	limit as x approaches 1/2 of x/(2x-1)	$lim_{x \to \frac{1}{2}} \frac{x}{2 x - 1}$
21266	Evaluate the Limit	limit as x approaches 1/2 of (6x-3)/(2x-1)	$lim_{x \to \frac{1}{2}} \frac{6 x - 3}{2 x - 1}$
21267	Evaluate the Limit	limit as x approaches negative infinity of (7x+2)/( square root of 4x^2+5x-3)	$lim_{x \to - \infty} \frac{7 x + 2}{\sqrt{4 x^{2} + 5 x - 3}}$
21268	Evaluate the Limit	limit as x approaches 1/2 of (6x^2+x-1)/(4x^2-4x-3)	$lim_{x \to \frac{1}{2}} \frac{6 x^{2} + x - 1}{4 x^{2} - 4 x - 3}$
21269	Evaluate the Limit	limit as x approaches 3 of ( square root of x^2-2x+6- square root of x^2+2x-6)/(x^2-4x+3)	$lim_{x \to 3} \frac{\sqrt{x^{2} - 2 x + 6} - \sqrt{x^{2} + 2 x - 6}}{x^{2} - 4 x + 3}$
21270	Evaluate the Limit	limit as x approaches infinity of (3x^3-x+1)/(x+3)	$lim_{x \to \infty} \frac{3 x^{3} - x + 1}{x + 3}$
21271	Evaluate the Limit	limit as x approaches 3 of (x^2-3x)/(x^2-9)	$lim_{x \to 3} \frac{x^{2} - 3 x}{x^{2} - 9}$
21272	Evaluate the Limit	limit as u approaches -5 of square root of u^4+3u+15	$lim_{u \to - 5} \sqrt{u^{4} + 3 u + 15}$
21273	Evaluate the Limit	limit as x approaches negative infinity of ((1-x^3)/(x^2+7x))^5	$lim_{x \to - \infty} {(\frac{1 - x^{3}}{x^{2} + 7 x})}^{5}$
21274	Evaluate the Limit	limit as x approaches infinity of (6x^3-2x^2-5)/(5x-3x^2-12x^3)	$lim_{x \to \infty} \frac{6 x^{3} - 2 x^{2} - 5}{5 x - 3 x^{2} - 12 x^{3}}$
21275	Evaluate the Limit	limit as x approaches 2 of -x^2+5x-2	$lim_{x \to 2} - x^{2} + 5 x - 2$
21276	Evaluate the Limit	limit as x approaches 4 of ((x/(x+1))-(4/5))/(x-4)	$lim_{x \to 4} \frac{(\frac{x}{(x + 1)}) - (\frac{4}{5})}{x - 4}$
21277	Evaluate the Limit	limit as x approaches 5/2 of -x+2	$lim_{x \to \frac{5}{2}} - x + 2$
21278	Evaluate the Limit	limit as x approaches infinity of (x+2)/( square root of 16x^2+1)	$lim_{x \to \infty} \frac{x + 2}{\sqrt{16 x^{2} + 1}}$
21279	Evaluate the Limit	limit as x approaches 10/3 of 10/3*2/3	$lim_{x \to \frac{10}{3}} \frac{10}{3} \cdot \frac{2}{3}$
21280	Evaluate the Limit	limit as x approaches 1/2 of xtan(pix)	$lim_{x \to \frac{1}{2}} x \tan (π x)$
21281	Evaluate the Limit	limit as x approaches 1/2 of intx	$lim_{x \to \frac{1}{2}} i n t x$
21282	Evaluate the Limit	limit as x approaches 1/3 of (3x^2+5x-2)/(6x^2+x-1)	$lim_{x \to \frac{1}{3}} \frac{3 x^{2} + 5 x - 2}{6 x^{2} + x - 1}$
21283	Evaluate the Limit	limit as x approaches (11pi)/2 of 8tan(x)	$lim_{x \to \frac{11 π}{2}} 8 \tan (x)$
21284	Evaluate the Limit	limit as x approaches -2/3 of (6x^3-17x^2-5x+6)/(9x^3+36x^2-4x-16)	$lim_{x \to \frac{- 2}{3}} \frac{6 x^{3} - 17 x^{2} - 5 x + 6}{9 x^{3} + 36 x^{2} - 4 x - 16}$
21285	Evaluate the Limit	limit as x approaches pi/6 of (sin(x)-1/2)/(x-pi/6)	$lim_{x \to \frac{π}{6}} \frac{\sin (x) - \frac{1}{2}}{x - \frac{π}{6}}$
21286	Evaluate the Limit	limit as x approaches -1 of (x^2+8x+7)/(x^2-3x-4)	$lim_{x \to - 1} \frac{x^{2} + 8 x + 7}{x^{2} - 3 x - 4}$
21287	Evaluate the Limit	limit as t approaches 0 of ( square root of 9-t-3)/t	$lim_{t \to 0} \frac{\sqrt{9 - t} - 3}{t}$
21288	Evaluate the Limit	limit as x approaches x/4 of (sin(x+pi/4)-1)/(x-pi/4)	$lim_{x \to \frac{x}{4}} \frac{\sin (x + \frac{π}{4}) - 1}{x - \frac{π}{4}}$
21289	Evaluate the Limit	limit as x approaches square root of 2 of x^2+3	$lim_{x \to \sqrt{2}} x^{2} + 3$
21290	Evaluate the Limit	limit as x approaches 0 of 5+7x-3x^2	$lim_{x \to 0} 5 + 7 x - 3 x^{2}$
21291	Evaluate the Limit	limit as X approaches 5 of (X^2+X-30)/(\|X-5\|)	$lim_{X \to 5} \frac{X^{2} + X - 30}{\| X - 5 \|}$
21292	Evaluate the Limit	limit as x approaches pi/2 of cos(sin(x))	$lim_{x \to \frac{π}{2}} \cos (\sin (x))$
21293	Evaluate the Limit	limit as x approaches 8 of 3x-2/x	$lim_{x \to 8} 3 x - \frac{2}{x}$
21294	Evaluate the Limit	limit as x approaches 0 of 8/x-8/(x^2+x)	$lim_{x \to 0} \frac{8}{x} - \frac{8}{x^{2} + x}$
21295	Evaluate the Limit	limit as x approaches pi/2 of (x-pi/2)tan(x)	$lim_{x \to \frac{π}{2}} (x - \frac{π}{2}) \tan (x)$
21296	Evaluate the Limit	limit as x approaches pi/2 of (8cos(x))/(cot(x))	$lim_{x \to \frac{π}{2}} \frac{8 \cos (x)}{\cot (x)}$
21297	Evaluate the Limit	limit as x approaches 3/2 of - square root of 2x+4	$lim_{x \to \frac{3}{2}} - \sqrt{2 x + 4}$
21298	Evaluate the Limit	limit as x approaches a/2 of (4x^2-4ax+2x+a^2-a)/(4x^2+2x-a^2-a)	$lim_{x \to \frac{a}{2}} \frac{4 x^{2} - 4 a x + 2 x + a^{2} - a}{4 x^{2} + 2 x - a^{2} - a}$
21299	Evaluate the Limit	limit as x approaches pi/2 of (cos(x))/(x-pi/2)	$lim_{x \to \frac{π}{2}} \frac{\cos (x)}{x - \frac{π}{2}}$
21300	Evaluate the Limit	limit as x approaches infinity of (x^3)/(e^(x^2))	$lim_{x \to \infty} \frac{x^{3}}{e^{x^{2}}}$