Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
31201	Evaluate the Limit	( limit as t approaches 8 of e^(5t)+t^2)/(4e^(5t)-t)	$\frac{lim_{t \to 8} e^{5 t} + t^{2}}{4 e^{5 t} - t}$
31202	Evaluate the Limit	( limit as t approaches 8 of square root of 16t^2+9)/(4t+1)	$\frac{lim_{t \to 8} \sqrt{16 t^{2} + 9}}{4 t + 1}$
31203	Solve for x	6x=0	$6 x = 0$
31204	Evaluate the Limit	( limit as t approaches 8 of 36t^3+12t-653)/(7t^5-13t^3+4t^2)	$\frac{lim_{t \to 8} 36 t^{3} + 12 t - 653}{7 t^{5} - 13 t^{3} + 4 t^{2}}$
31205	Evaluate the Limit	( limit as t approaches 8 of t-t square root of t)/(2t^(3/2)+3t-5)	$\frac{lim_{t \to 8} t - t \sqrt{t}}{2 t^{\frac{3}{2}} + 3 t - 5}$
31206	Evaluate the Limit	( limit as t approaches 9 of 3- square root of t)/(9-t)	$\frac{lim_{t \to 9} 3 - \sqrt{t}}{9 - t}$
31207	Evaluate the Limit	( limit as t approaches a of -16a^2+400+16t^2-400)/(a-t)	$\frac{lim_{t \to a} - 16 a^{2} + 400 + 16 t^{2} - 400}{a - t}$
31208	Evaluate the Limit	( limit as t approaches infinity of t^2)/( square root of t^4+1)	$\frac{lim_{t \to \infty} t^{2}}{\sqrt{t^{4} + 1}}$
31209	Solve for x	-3x^2+24x+60=0	$- 3 x^{2} + 24 x + 60 = 0$
31210	Evaluate the Limit	( limit as u approaches 5 of u^2-u-20)/(5-u)	$\frac{lim_{u \to 5} u^{2} - u - 20}{5 - u}$
31211	Evaluate the Limit	( limit as v approaches 0 of 1-sec(v))/(v^2sec(v))	$\frac{lim_{v \to 0} 1 - \sec (v)}{v^{2} \sec (v)}$
31212	Evaluate the Limit	( limit as w approaches -2 of 4-w^2)/(w+2)	$\frac{lim_{w \to - 2} 4 - w^{2}}{w + 2}$
31213	Evaluate the Limit	( limit as W approaches 8 of 4-3a^3)/(a^3-1)	$\frac{lim_{W \to 8} 4 - 3 a^{3}}{a^{3} - 1}$
31214	Evaluate the Limit	( limit as x approaches 1/2 of x^2-1)/((2x)+1)	$\frac{lim_{x \to \frac{1}{2}} x^{2} - 1}{(2 x) + 1}$
31215	Evaluate the Limit	( limit as x approaches 1/2 of \|2x-1\|)/(2x-1)	$\frac{lim_{x \to \frac{1}{2}} \| 2 x - 1 \|}{2 x - 1}$
31216	Evaluate the Limit	( limit as x approaches 1/2 of 8x^3-1)/(6x^2-5x+1)	$\frac{lim_{x \to \frac{1}{2}} 8 x^{3} - 1}{6 x^{2} - 5 x + 1}$
31217	Evaluate the Limit	( limit as n approaches 8 of 4^n-2^n)/(2(4^n)-2^n)	$\frac{lim_{n \to 8} 4^{n} - 2^{n}}{2 (4^{n}) - 2^{n}}$
31218	Evaluate the Limit	( limit as n approaches 8 of square root of n^2+n)/n	$\frac{lim_{n \to 8} \sqrt{n^{2} + n}}{n}$
31219	Evaluate the Limit	( limit as h approaches 3 of h^3-27)/(h-3)	$\frac{lim_{h \to 3} h^{3} - 27}{h - 3}$
31220	Evaluate the Limit	( limit as h approaches 8 of h^3-512)/(h-8)	$\frac{lim_{h \to 8} h^{3} - 512}{h - 8}$
31221	Evaluate the Limit	( limit as h approaches 8 of 3h+2xh^2+x^2h^3)/(4-3xh-2x^3h^3)	$\frac{lim_{h \to 8} 3 h + 2 x h^{2} + x^{2} h^{3}}{4 - 3 x h - 2 x^{3} h^{3}}$
31222	Evaluate the Limit	limit as h approaches 9 of (5(9+h))^3-(9+h)^2+6	$lim_{h \to 9} {(5 (9 + h))}^{3} - {(9 + h)}^{2} + 6$
31223	Evaluate the Limit	( limit as h approaches a of 1/h-1/a)/(h-a)	$\frac{lim_{h \to a} \frac{1}{h} - \frac{1}{a}}{h - a}$
31224	Evaluate the Limit	( limit as h approaches o of (7+h)^3-343)/h	$\frac{lim_{h \to o} {(7 + h)}^{3} - 343}{h}$
31225	Evaluate the Limit	( limit as k approaches 4 of k^2-16)/( square root of k-12)	$\frac{lim_{k \to 4} k^{2} - 16}{\sqrt{k} - 12}$
31226	Evaluate the Limit	( limit as n approaches 0 of \|x\|)/x	$\frac{lim_{n \to 0} \| x \|}{x}$
31227	Evaluate the Limit	limit as n approaches 8 of (n/(n+1))^n	$lim_{n \to 8} {(\frac{n}{n + 1})}^{n}$
31228	Evaluate the Limit	( limit as h approaches 0 of square root of 3h+4-2)/h	$\frac{lim_{h \to 0} \sqrt{3 h + 4} - 2}{h}$
31229	Evaluate the Limit	( limit as h approaches 0 of square root of 5h+4)/h-2	$\frac{lim_{h \to 0} \sqrt{5 h + 4}}{h} - 2$
31230	Evaluate the Limit	( limit as h approaches 0 of square root of 5h+4-2)/h	$\frac{lim_{h \to 0} \sqrt{5 h + 4} - 2}{h}$
31231	Evaluate the Limit	( limit as h approaches 0 of square root of 5x-5h- square root of 5x)/h	$\frac{lim_{h \to 0} \sqrt{5 x - 5 h} - \sqrt{5 x}}{h}$
31232	Evaluate the Limit	( limit as h approaches 0 of square root of 8(x+h)+9)/h-( square root of 8x+9)/h	$\frac{lim_{h \to 0} \sqrt{8 (x + h) + 9}}{h} - \frac{\sqrt{8 x + 9}}{h}$
31233	Evaluate the Limit	( limit as h approaches 0 of square root of 8h+1-1)/h	$\frac{lim_{h \to 0} \sqrt{8 h + 1 - 1}}{h}$
31234	Evaluate the Limit	( limit as h approaches 0 of square root of 9+h-3)/h	$\frac{lim_{h \to 0} \sqrt{9 + h - 3}}{h}$
31235	Solve for x	log base 4 of x+41- log of 2x-5=2	$\log_{4} (x + 41) - \log (2 x - 5) = 2$
31236	Evaluate the Limit	( limit as h approaches 0 of ( square root of h^2+4h+5)- square root of 5)/h	$\frac{lim_{h \to 0} (\sqrt{h^{2} + 4 h + 5}) - \sqrt{5}}{h}$
31237	Evaluate the Limit	( limit as h approaches 0 of 1/(1+h)-1)/h	$\frac{lim_{h \to 0} \frac{1}{1 + h} - 1}{h}$
31238	Evaluate the Limit	( limit as h approaches 0 of 2.8^h-1)/h	$\frac{lim_{h \to 0} {2.8}^{h} - 1}{h}$
31239	Evaluate the Limit	( limit as r approaches 0 of 3r-1)/r	$\frac{lim_{r \to 0} 3 r - 1}{r}$
31240	Evaluate the Limit	( limit as r approaches 0 of r)/(sin(r))	$\frac{lim_{r \to 0} r}{\sin (r)}$
31241	Evaluate the Limit	limit as x approaches infinity of xtan(1/x)	$lim_{x \to \infty} x \tan (\frac{1}{x})$
31242	Evaluate the Limit	( limit as r approaches 9 of square root of r)/((r-9)^4)	$\frac{lim_{r \to 9} \sqrt{r}}{{(r - 9)}^{4}}$
31243	Evaluate the Limit	( limit as s approaches 16 of 4- square root of s)/(s-16)	$\frac{lim_{s \to 16} 4 - \sqrt{s}}{s - 16}$
31244	Evaluate the Limit	( limit as s approaches 4 of 1/s-1/4)/(s-4)	$\frac{lim_{s \to 4} \frac{1}{s} - \frac{1}{4}}{s - 4}$
31245	Evaluate the Limit	( limit as s approaches 5 of 1/s-1/5)/(s-5)	$\frac{lim_{s \to 5} \frac{1}{s} - \frac{1}{5}}{s - 5}$
31246	Evaluate the Limit	( limit as t approaches 0 of 1+cot(t)^2)/(csc(t)^3)	$\frac{lim_{t \to 0} 1 + \cot^{2} (t)}{\csc^{3} (t)}$
31247	Evaluate the Limit	( limit as t approaches 0 of t-t square root of 1+t)/(t^2 square root of 1+t)	$\frac{lim_{t \to 0} t - t \sqrt{1 + t}}{t^{2} \sqrt{1 + t}}$
31248	Evaluate the Limit	( limit as t approaches 0 of (1+t)^5-1)/(t(t+1)^5)	$\frac{lim_{t \to 0} {(1 + t)}^{5} - 1}{t {(t + 1)}^{5}}$
31249	Evaluate the Limit	( limit as n approaches 8 of 3n^2+n-2)/(2n-1)	$\frac{lim_{n \to 8} 3 n^{2} + n - 2}{2 n - 1}$
31250	Evaluate the Limit	( limit as n approaches 8 of 4n^2)/(n^2+10000n)	$\frac{lim_{n \to 8} 4 n^{2}}{n^{2} + 10000 n}$
31251	Evaluate the Limit	limit as n approaches 8 of (e)^(1/n)	$lim_{n \to 8} {(e)}^{\frac{1}{n}}$
31252	Evaluate the Limit	( limit as n approaches 8 of lg(n^2+2n+3))/(2 natural log of n)	$\frac{lim_{n \to 8} l g (n^{2} + 2 n + 3)}{2 \ln (n)}$
31253	Evaluate the Limit	( limit as n approaches 8 of natural log of n^9)/(8n)	$\frac{lim_{n \to 8} \ln (n^{9})}{8 n}$
31254	Evaluate the Limit	( limit as n approaches 8 of natural log of 1+1/n)/n	$\frac{lim_{n \to 8} \ln (1 + \frac{1}{n})}{n}$
31255	Evaluate the Limit	( limit as n approaches 8 of n+ natural log of n)/(n^2+1)	$\frac{lim_{n \to 8} n + \ln (n)}{n^{2} + 1}$
31256	Evaluate the Limit	( limit as n approaches 8 of sin(n))/(n^2+sin(n))	$\frac{lim_{n \to 8} \sin (n)}{n^{2} + \sin (n)}$
31257	Evaluate the Limit	( limit as n approaches 8p of log of 2^n)/( log of 3^n)	$\frac{lim_{n \to 8 p} \log (2^{n})}{\log (3^{n})}$
31258	Evaluate the Limit	( limit as n approaches infinity of 3n^2+4n+1)/( square root of 9n^4+n^3+n+1)	$\frac{lim_{n \to \infty} 3 n^{2} + 4 n + 1}{\sqrt{9 n^{4} + n^{3} + n + 1}}$
31259	Evaluate the Limit	( limit as q approaches 2 of 4q^2-q+2)/8	$\frac{lim_{q \to 2} 4 q^{2} - q + 2}{8}$
31260	Evaluate the Limit	( limit as t approaches 0 of te^t)/(1-t)	$\frac{lim_{t \to 0} t e^{t}}{1 - t}$
31261	Evaluate the Limit	( limit as t approaches 0 of e^(3t^2+4t))/(7t)- limit as t approaches 0 of 1/(7t)	$\frac{lim_{t \to 0} e^{3 t^{2} + 4 t}}{7 t} - lim_{t \to 0} \frac{1}{7 t}$
31262	Evaluate the Limit	( limit as h approaches 0 of ( square root of 1-2(x+h))- square root of 1-2x)/h	$\frac{lim_{h \to 0} (\sqrt{1 - 2 (x + h)}) - \sqrt{1 - 2 x}}{h}$
31263	Evaluate the Limit	( limit as h approaches 0 of square root of 121+h- square root of 121)/h	$\frac{lim_{h \to 0} \sqrt{121 + h} - \sqrt{121}}{h}$
31264	Evaluate the Limit	( limit as h approaches 0 of square root of 13h+1-1)/h	$\frac{lim_{h \to 0} \sqrt{13 h + 1} - 1}{h}$
31265	Evaluate the Limit	( limit as x approaches 0 of 5x)/(tan(2x))	$\frac{lim_{x \to 0} 5 x}{\tan (2 x)}$
31266	Evaluate the Limit	( limit as x approaches 0 of 6sin(x))/(7x)	$\frac{lim_{x \to 0} 6 \sin (x)}{7 x}$
31267	Evaluate the Limit	( limit as x approaches 0 of 6xcos(4x-1))/(sin(9x-9x))	$\frac{lim_{x \to 0} 6 x \cos (4 x - 1)}{\sin (9 x - 9 x)}$
31268	Evaluate the Limit	( limit as x approaches 0 of 6x-sin(6x))/(6x-tan(6x))	$\frac{lim_{x \to 0} 6 x - \sin (6 x)}{6 x - \tan (6 x)}$
31269	Evaluate the Limit	( limit as x approaches 0 of -7)/(1-7x)	$\frac{lim_{x \to 0} - 7}{1 - 7 x}$
31270	Evaluate the Limit	( limit as x approaches 0 of 7sin(-0.1))/-0.1	$\frac{lim_{x \to 0} 7 \sin (- 0.1)}{- 0.1}$
31271	Evaluate the Limit	( limit as x approaches 0 of 7sin(x)cos(x))/(5x)	$\frac{lim_{x \to 0} 7 \sin (x) \cos (x)}{5 x}$
31272	Evaluate the Limit	( limit as x approaches 0 of 8x)/(3sin(x))	$\frac{lim_{x \to 0} 8 x}{3 \sin (x)}$
31273	Evaluate the Limit	( limit as x approaches 0 of 3(x+h)^2-3x^2)/h	$\frac{lim_{x \to 0} 3 {(x + h)}^{2} - 3 x^{2}}{h}$
31274	Evaluate the Limit	( limit as x approaches 0 of 3+3x+sin(x))/(4cos(x))	$\frac{lim_{x \to 0} 3 + 3 x + \sin (x)}{4 \cos (x)}$
31275	Evaluate the Limit	( limit as x approaches 0 of 3-3cos(x)^2)/(21x^2)	$\frac{lim_{x \to 0} 3 - 3 \cos^{2} (x)}{21 x^{2}}$
31276	Evaluate the Limit	( limit as x approaches 0 of 3 natural log of cos(28x))/(28x^2)	$\frac{lim_{x \to 0} 3 \ln (\cos (28 x))}{28 x^{2}}$
31277	Evaluate the Limit	( limit as x approaches 0 of 3 natural log of x)/(x^-1)	$\frac{lim_{x \to 0} 3 \ln (x)}{x^{- 1}}$
31278	Evaluate the Limit	( limit as x approaches 0 of 3sin(-0.1))/-0.1	$\frac{lim_{x \to 0} 3 \sin (- 0.1)}{- 0.1}$
31279	Evaluate the Limit	( limit as x approaches 0 of 4x)/(tan(7x))	$\frac{lim_{x \to 0} 4 x}{\tan (7 x)}$
31280	Evaluate the Limit	( limit as x approaches 0 of cos(x)sin(x))/x	$\frac{lim_{x \to 0} \cos (x) \sin (x)}{x}$
31281	Evaluate the Limit	( limit as x approaches 0 of cot(3x))/(cot(x))	$\frac{lim_{x \to 0} \cot (3 x)}{\cot (x)}$
31282	Evaluate the Limit	( limit as x approaches 0 of cot(5x))/(csc(5x))	$\frac{lim_{x \to 0} \cot (5 x)}{\csc (5 x)}$
31283	Evaluate the Limit	limit as x approaches 0 of (e)^x+5x^(2/x)	$lim_{x \to 0} {(e)}^{x} + 5 x^{\frac{2}{x}}$
31284	Evaluate the Limit	limit as x approaches 0 of (e)^(-x)sin(x)	$lim_{x \to 0} {(e)}^{- x} \sin (x)$
31285	Evaluate the Limit	( limit as x approaches 0 of ex)/(x-2)	$\frac{lim_{x \to 0} e x}{x - 2}$
31286	Evaluate the Limit	( limit as x approaches 0 of f(2+x)-f*2)/x	$\frac{lim_{x \to 0} f (2 + x) - f \cdot 2}{x}$
31287	Evaluate the Limit	( limit as x approaches 0 of f(x))/(g(x))	$\frac{lim_{x \to 0} f (x)}{g (x)}$
31288	Evaluate the Limit	( limit as x approaches 0 of natural log of 1+4x)/(sin(5x))	$\frac{lim_{x \to 0} \ln (1 + 4 x)}{\sin (5 x)}$
31289	Evaluate the Limit	( limit as x approaches 0 of natural log of 1+x)/x	$\frac{lim_{x \to 0} \ln (1 + x)}{x}$
31290	Evaluate the Limit	( limit as x approaches 0 of ( natural log of a+x)- natural log of a)/x	$\frac{lim_{x \to 0} (\ln (a + x)) - \ln (a)}{x}$
31291	Find the Slope of the Tangent Line at (1,1)	(x^2+y^2)^2=4x^2y , (1,1)	$\frac{lim_{x \to 0} \arcsin (\frac{x}{b}) \cdot \ln (1 + a x)}{\tan (a x) \cdot (\sqrt[3]{1 + x - 1})}$
31292	Evaluate the Limit	( limit as x approaches 0 of arcsin(0))/(2(0))	$\frac{lim_{x \to 0} \arcsin (0)}{2 (0)}$
31293	Evaluate the Limit	( limit as x approaches 0 of cos(2x))/(2x)	$\frac{lim_{x \to 0} \cos (2 x)}{2 x}$
31294	Evaluate the Limit	( limit as x approaches 0 of cos(2x))/(cos(3x))	$\frac{lim_{x \to 0} \cos (2 x)}{\cos (3 x)}$
31295	Evaluate the Limit	( limit as x approaches 0 of cos(2x)-1)/(sin(x))	$\frac{lim_{x \to 0} \cos (2 x) - 1}{\sin (x)}$
31296	Evaluate the Limit	( limit as x approaches 0 of cos(3x))/(cos(5x))	$\frac{lim_{x \to 0} \cos (3 x)}{\cos (5 x)}$
31297	Evaluate the Limit	( limit as x approaches 0 of cos(9x)-1)/(x^2)	$\frac{lim_{x \to 0} \cos (9 x) - 1}{x^{2}}$
31298	Evaluate the Limit	limit as x approaches 0 of (cos(x))^(1/(x^2))
31299	Evaluate the Limit	( limit as x approaches 0 of cos(x)-cos(x)^2)/x	$\frac{lim_{x \to 0} \cos (x) - \cos^{2} (x)}{x}$
31300	Evaluate the Limit	( limit as x approaches 0 of 2e^x-2+x)/(5x)	$\frac{lim_{x \to 0} 2 e^{x} - 2 + x}{5 x}$