Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
20301	Evaluate the Limit	( limit as x approaches 0 of sin(3x))/(4x)	$\frac{lim_{x \to 0} \sin (3 x)}{4 x}$
20302	Evaluate the Limit	( limit as x approaches 0 of sin(3x))/(sin(4x))	$\frac{lim_{x \to 0} \sin (3 x)}{\sin (4 x)}$
20303	Evaluate the Limit	( limit as x approaches 0 of sin(3x))/(tan(4x))	$\frac{lim_{x \to 0} \sin (3 x)}{\tan (4 x)}$
20304	Evaluate the Limit	( limit as x approaches 0 of x+2)/(cot(x))	$\frac{lim_{x \to 0} x + 2}{\cot (x)}$
20305	Evaluate the Limit	( limit as x approaches 0 of tan(x))/(tan(2x))	$\frac{lim_{x \to 0} \tan (x)}{\tan (2 x)}$
20306	Evaluate the Limit	( limit as x approaches 0 of xsin(x))/(3-3cos(x))	$\frac{lim_{x \to 0} x \sin (x)}{3 - 3 \cos (x)}$
20307	Evaluate the Limit	( limit as x approaches 0 of xtan(x))/(1-cos(x))	$\frac{lim_{x \to 0} x \tan (x)}{1 - \cos (x)}$
20308	Evaluate the Limit	( limit as x approaches 0 of x-1)/(x^2(x+2))	$\frac{lim_{x \to 0} x - 1}{x^{2} (x + 2)}$
20309	Evaluate the Limit	( limit as x approaches 0 of x-8)/(x-2)	$\frac{lim_{x \to 0} x - 8}{x - 2}$
20310	Evaluate the Limit	( limit as x approaches 0.001 of 8sin(x))/x	$\frac{lim_{x \to 0.001} 8 \sin (x)}{x}$
20311	Evaluate the Limit	( limit as x approaches 0.5 of 2x-1)/(\|2x^3-x^2\|)	$\frac{lim_{x \to 0.5} 2 x - 1}{\| 2 x^{3} - x^{2} \|}$
20312	Evaluate the Limit	( limit as x approaches 0 of e^x)/(4x^3)	$\frac{lim_{x \to 0} e^{x}}{4 x^{3}}$
20313	Evaluate the Limit	( limit as x approaches 1 of (x^2-4)-(-3))/(x-1)	$\frac{lim_{x \to 1} (x^{2} - 4) - (- 3)}{x - 1}$
20314	Evaluate the Limit	( limit as x approaches 1 of (10x-5)^2-25)/(2x-2)	$\frac{lim_{x \to 1} {(10 x - 5)}^{2} - 25}{2 x - 2}$
20315	Evaluate the Limit	( limit as x approaches 0.5 of 2x^2+3x-1)/(4x+5)	$\frac{lim_{x \to 0.5} 2 x^{2} + 3 x - 1}{4 x + 5}$
20316	Evaluate the Limit	( limit as x approaches 1 of t^4-1)/(t^3-1)	$\frac{lim_{x \to 1} t^{4} - 1}{t^{3} - 1}$
20317	Evaluate the Limit	( limit as x approaches 1 of square root of x^2+8-3)/(x-1)	$\frac{lim_{x \to 1} \sqrt{x^{2} + 8} - 3}{x - 1}$
20318	Evaluate the Limit	( limit as x approaches 1 of square root of 2x+1- square root of 3)/(x-1)	$\frac{lim_{x \to 1} \sqrt{2 x + 1} - \sqrt{3}}{x - 1}$
20319	Evaluate the Limit	( limit as x approaches 0 of 5-cos(x))/x	$\frac{lim_{x \to 0} 5 - \cos (x)}{x}$
20320	Evaluate the Limit	( limit as x approaches 0 of 7x)/(cot(3x))	$\frac{lim_{x \to 0} 7 x}{\cot (3 x)}$
20321	Evaluate the Limit	( limit as x approaches 0 of arcsin(x))/x	$\frac{lim_{x \to 0} \arcsin (x)}{x}$
20322	Evaluate the Limit	( limit as x approaches 0 of 2x-5sin(3x))/x	$\frac{lim_{x \to 0} 2 x - 5 \sin (3 x)}{x}$
20323	Evaluate the Limit	( limit as x approaches 0 of 1-cos(x))/(sin(x)^2)	$\frac{lim_{x \to 0} 1 - \cos (x)}{\sin^{2} (x)}$
20324	Evaluate the Limit	( limit as x approaches 0 of 100)/(50x+1)	$\frac{lim_{x \to 0} 100}{50 x + 1}$
20325	Evaluate the Limit	( limit as x approaches 0 of 2x)/(cot(6x))	$\frac{lim_{x \to 0} 2 x}{\cot (6 x)}$
20326	Evaluate the Limit	( limit as x approaches 0 of 2x)/(tan(x))	$\frac{lim_{x \to 0} 2 x}{\tan (x)}$
20327	Evaluate the Limit	( limit as x approaches 0 of 4x-sin(pix))/(6x^2-1)	$\frac{lim_{x \to 0} 4 x - \sin (π x)}{6 x^{2} - 1}$
20328	Evaluate the Limit	( limit as x approaches 0 of 3xtan(x))/(sin(x))	$\frac{lim_{x \to 0} 3 x \tan (x)}{\sin (x)}$
20329	Evaluate the Limit	( limit as x approaches 0 of 5x^3+8x^2)/(3x^4-16x^2)	$\frac{lim_{x \to 0} 5 x^{3} + 8 x^{2}}{3 x^{4} - 16 x^{2}}$
20330	Evaluate the Limit	( limit as x approaches 0 of sin(2x))/(cos(5x))	$\frac{lim_{x \to 0} \sin (2 x)}{\cos (5 x)}$
20331	Evaluate the Limit	( limit as x approaches 0 of sin(x^2))/(x^2)	$\frac{lim_{x \to 0} \sin (x^{2})}{x^{2}}$
20332	Evaluate the Limit	( limit as x approaches 0 of natural log of cos(x))/(x^2)	$\frac{lim_{x \to 0} \ln (\cos (x))}{x^{2}}$
20333	Evaluate the Limit	( limit as x approaches 0 of sin(x/2))/(sin(x/3))	$\frac{lim_{x \to 0} \sin (\frac{x}{2})}{\sin (\frac{x}{3})}$
20334	Evaluate the Limit	( limit as x approaches 0 of sin(2x))/(xcos(x))	$\frac{lim_{x \to 0} \sin (2 x)}{x \cos (x)}$
20335	Evaluate the Limit	( limit as x approaches 0 of natural log of x)/(csc(x))	$\frac{lim_{x \to 0} \ln (x)}{\csc (x)}$
20336	Evaluate the Limit	( limit as x approaches 0 of natural log of x)/x	$\frac{lim_{x \to 0} \ln (x)}{x}$
20337	Evaluate the Limit	( limit as x approaches 0 of cos(5x)-1)/(2x)	$\frac{lim_{x \to 0} \cos (5 x) - 1}{2 x}$
20338	Evaluate the Limit	limit as x approaches 6 of square root of 36-x^2	$lim_{x \to 6} \sqrt{36 - x^{2}}$
20339	Evaluate the Limit	( limit as x approaches 0 of (cos(x))tan(x))/x	$\frac{lim_{x \to 0} (\cos (x)) \tan (x)}{x}$
20340	Evaluate the Limit	( limit as x approaches 0 of cos(x)-cos(2x))/(x^2)	$\frac{lim_{x \to 0} \cos (x) - \cos (2 x)}{x^{2}}$
20341	Evaluate the Limit	( limit as x approaches 0 of cot(x))/(csc(x))	$\frac{lim_{x \to 0} \cot (x)}{\csc (x)}$
20342	Evaluate the Limit	( limit as x approaches 0 of (1+h)^4-1)/h	$\frac{lim_{x \to 0} {(1 + h)}^{4} - 1}{h}$
20343	Evaluate the Limit	( limit as x approaches 0 of x^2)/(sin(3x)^2)	$\frac{lim_{x \to 0} x^{2}}{\sin^{2} (3 x)}$
20344	Evaluate the Limit	( limit as x approaches 0 of x^2+5x)/x	$\frac{lim_{x \to 0} x^{2} + 5 x}{x}$
20345	Evaluate the Limit	( limit as x approaches 0 of x^2-6x+9)/(x^2)	$\frac{lim_{x \to 0} x^{2} - 6 x + 9}{x^{2}}$
20346	Evaluate the Limit	( limit as x approaches 0 of x^2-2x+sin(x))/x	$\frac{lim_{x \to 0} x^{2} - 2 x + \sin (x)}{x}$
20347	Evaluate the Limit	( limit as x approaches 0 of x^4-x^2)/(x^2)	$\frac{lim_{x \to 0} x^{4} - x^{2}}{x^{2}}$
20348	Evaluate the Limit	( limit as x approaches 0 of 1)/x-1/(x^2+x)	$\frac{lim_{x \to 0} 1}{x} - \frac{1}{x^{2} + x}$
20349	Evaluate the Limit	( limit as x approaches 0 of x^3*sin(1/x))/(tan(x)^2)	$\frac{lim_{x \to 0} x^{3} \cdot \sin (\frac{1}{x})}{\tan^{2} (x)}$
20350	Evaluate the Limit	( limit as x approaches 0 of x^5+3x)/x	$\frac{lim_{x \to 0} x^{5} + 3 x}{x}$
20351	Evaluate the Limit	( limit as x approaches 0 of 10x-3sin(x))/x	$\frac{lim_{x \to 0} 10 x - 3 \sin (x)}{x}$
20352	Evaluate the Limit	( limit as x approaches 0 of 1-cos(2x))/x	$\frac{lim_{x \to 0} 1 - \cos (2 x)}{x}$
20353	Evaluate the Limit	( limit as x approaches 0 of 1-sec(7x)^2)/((3x)^2)	$\frac{lim_{x \to 0} 1 - \sec^{2} (7 x)}{{(3 x)}^{2}}$
20354	Evaluate the Limit	( limit as x approaches 0 of 1-e^(-2x))/(sec(x))	$\frac{lim_{x \to 0} 1 - e^{- 2 x}}{\sec (x)}$
20355	Evaluate the Limit	( limit as x approaches 0 of 1-e^x)/(1-e^(2x))	$\frac{lim_{x \to 0} 1 - e^{x}}{1 - e^{2 x}}$
20356	Evaluate the Limit	( limit as x approaches pi/3 of 2cos(x)^2+3cos(x)-2)/(2cos(x)-1)	$\frac{lim_{x \to \frac{π}{3}} 2 \cos^{2} (x) + 3 \cos (x) - 2}{2 \cos (x) - 1}$
20357	Evaluate the Limit	( limit as x approaches 0 of 1/(x+4)-1/4)/x	$\frac{lim_{x \to 0} \frac{1}{x + 4} - \frac{1}{4}}{x}$
20358	Evaluate the Limit	( limit as x approaches 0 of e^x-1)/(x^3)	$\frac{lim_{x \to 0} e^{x} - 1}{x^{3}}$
20359	Evaluate the Limit	( limit as x approaches 0 of 3^(2x)-1)/(3^x-1)	$\frac{lim_{x \to 0} 3^{2 x} - 1}{3^{x} - 1}$
20360	Evaluate the Limit	( limit as x approaches 0 of (x+3)^3-27)/x	$\frac{lim_{x \to 0} {(x + 3)}^{3} - 27}{x}$
20361	Evaluate the Limit	( limit as x approaches 0 of (x-5)^2-25)/x	$\frac{lim_{x \to 0} {(x - 5)}^{2} - 25}{x}$
20362	Evaluate the Limit	( limit as x approaches 0 of (x+h)^3-x^3)/h	$\frac{lim_{x \to 0} {(x + h)}^{3} - x^{3}}{h}$
20363	Evaluate the Limit	( limit as x approaches 0 of cube root of 8+x-2)/x	$\frac{lim_{x \to 0} \sqrt[3]{8 + x} - 2}{x}$
20364	Evaluate the Limit	( limit as x approaches 0 of square root of 1+3x- square root of 1-2x)/x	$\frac{lim_{x \to 0} \sqrt{1 + 3 x} - \sqrt{1 - 2 x}}{x}$
20365	Evaluate the Limit	( limit as x approaches 0 of cube root of x+1-1)/x	$\frac{lim_{x \to 0} \sqrt[3]{x + 1} - 1}{x}$
20366	Evaluate the Limit	( limit as x approaches 0 of square root of x^2+81-9)/(x^2)	$\frac{lim_{x \to 0} \sqrt{x^{2} + 81} - 9}{x^{2}}$
20367	Evaluate the Limit	( limit as x approaches 0 of square root of 5x+4-2)/x	$\frac{lim_{x \to 0} \sqrt{5 x + 4} - 2}{x}$
20368	Evaluate the Limit	( limit as x approaches 0 of e^(5x)-1-5x)/(x^2)	$\frac{lim_{x \to 0} e^{5 x} - 1 - 5 x}{x^{2}}$
20369	Evaluate the Limit	( limit as x approaches 0 of e^x-e^(-x))/(sin(2x))	$\frac{lim_{x \to 0} e^{x} - e^{- x}}{\sin (2 x)}$
20370	Evaluate the Limit	( limit as x approaches 0 of e^x-1)/(2^x-1)	$\frac{lim_{x \to 0} e^{x} - 1}{2^{x} - 1}$
20371	Evaluate the Limit	( limit as x approaches 0 of sin(x)^7)/x	$\frac{lim_{x \to 0} \sin^{7} (x)}{x}$
20372	Evaluate the Limit	( limit as x approaches 0 of tan(x)^2)/x	$\frac{lim_{x \to 0} \tan^{2} (x)}{x}$
20373	Evaluate the Limit	( limit as x approaches 0 of sin(5x^2)^2+sin(3x)^2)/(x^2)	$\frac{lim_{x \to 0} \sin^{2} (5 x^{2}) + \sin^{2} (3 x)}{x^{2}}$
20374	Evaluate the Limit	( limit as h approaches -1 of square root of h+5-2)/(h+1)	$\frac{lim_{h \to - 1} \sqrt{h + 5} - 2}{h + 1}$
20375	Evaluate the Limit	( limit as h approaches 4 of h^3-64)/(h-4)	$\frac{lim_{h \to 4} h^{3} - 64}{h - 4}$
20376	Evaluate the Limit	limit as n approaches 8 of ((n-3)/n)^n	$lim_{n \to 8} {(\frac{n - 3}{n})}^{n}$
20377	Evaluate the Limit	( limit as n approaches 8 of 5n^2)/(e^(2n)-2n+10)	$\frac{lim_{n \to 8} 5 n^{2}}{e^{2 n} - 2 n + 10}$
20378	Evaluate the Limit	( limit as t approaches 8 of 6-t^3)/(7t^3+3)	$\frac{lim_{t \to 8} 6 - t^{3}}{7 t^{3} + 3}$
20379	Evaluate the Limit	( limit as t approaches 0 of 1-cos(t))/t	$\frac{lim_{t \to 0} 1 - \cos (t)}{t}$
20380	Evaluate the Limit	( limit as t approaches 0 of 1-tan(t))/(sin(t))	$\frac{lim_{t \to 0} 1 - \tan (t)}{\sin (t)}$
20381	Evaluate the Limit	( limit as t approaches 0 of e^(2t)-1)/(sin(t))	$\frac{lim_{t \to 0} e^{2 t} - 1}{\sin (t)}$
20382	Evaluate the Limit	( limit as t approaches 0 of sin(3t))/(3t)	$\frac{lim_{t \to 0} \sin (3 t)}{3 t}$
20383	Evaluate the Limit	limit as x approaches -1 of (x^4-3x)(x^2+5x+3)	$lim_{x \to - 1} (x^{4} - 3 x) (x^{2} + 5 x + 3)$
20384	Evaluate the Limit	( limit as t approaches 1 of t^2+t-2)/(t^2-1)	$\frac{lim_{t \to 1} t^{2} + t - 2}{t^{2} - 1}$
20385	Evaluate the Limit	( limit as t approaches 15 of t^2+3t-270)/(t^2-225)	$\frac{lim_{t \to 15} t^{2} + 3 t - 270}{t^{2} - 225}$
20386	Evaluate the Limit	( limit as t approaches -3 of t^2-9)/(2t^2+7t+3)	$\frac{lim_{t \to - 3} t^{2} - 9}{2 t^{2} + 7 t + 3}$
20387	Evaluate the Limit	( limit as t approaches 3 of t^2-9)/(t-3)	$\frac{lim_{t \to 3} t^{2} - 9}{t - 3}$
20388	Evaluate the Limit	( limit as t approaches 1 of t-1)/(t^2-1)	$\frac{lim_{t \to 1} t - 1}{t^{2} - 1}$
20389	Evaluate the Limit	( limit as t approaches 4 of 4-t)/(2- square root of t)	$\frac{lim_{t \to 4} 4 - t}{2 - \sqrt{t}}$
20390	Evaluate the Limit	( limit as t approaches 8 of 6+0.4^t)/(3-0.7^t)	$\frac{lim_{t \to 8} 6 + {0.4}^{t}}{3 - {0.7}^{t}}$
20391	Evaluate the Limit	( limit as t approaches 9 of square root of t-3)/(t-9)	$\frac{lim_{t \to 9} \sqrt{t} - 3}{t - 9}$
20392	Evaluate the Limit	( limit as t approaches 9 of 9-t)/(3- square root of t)	$\frac{lim_{t \to 9} 9 - t}{3 - \sqrt{t}}$
20393	Evaluate the Limit	limit as x approaches -3 of (x^2-1)/(3-x)	$lim_{x \to - 3} \frac{x^{2} - 1}{3 - x}$
20394	Evaluate the Limit	( limit as x approaches pi/2 of cos(x))/(cot(x))	$\frac{lim_{x \to \frac{π}{2}} \cos (x)}{\cot (x)}$
20395	Evaluate the Limit	( limit as x approaches pi/2 of cos(x)-cos(3x))/((2x-pi)( square root of cos(x)+ square root of cos(3x)))	$\frac{lim_{x \to \frac{π}{2}} \cos (x) - \cos (3 x)}{(2 x - π) (\sqrt{\cos (x)} + \sqrt{\cos (3 x)})}$
20396	Evaluate the Limit	( limit as x approaches pi/2 of cot(pi/2)-cot(x))/(pi/2-x)	$\frac{lim_{x \to \frac{π}{2}} \cot (\frac{π}{2}) - \cot (x)}{\frac{π}{2} - x}$
20397	Evaluate the Limit	( limit as u approaches -2 of u^2-ux+2u-2x)/(u^2-u-6)	$\frac{lim_{u \to - 2} u^{2} - u x + 2 u - 2 x}{u^{2} - u - 6}$
20398	Evaluate the Limit	( limit as u approaches 1 of u^4-1)/(u^3-1)	$\frac{lim_{u \to 1} u^{4} - 1}{u^{3} - 1}$
20399	Evaluate the Limit	( limit as x approaches pi/2 of 2sin(x))/(3x)	$\frac{lim_{x \to \frac{π}{2}} 2 \sin (x)}{3 x}$
20400	Evaluate the Limit	( limit as x approaches pi/2 of 6cos(x))/(cot(x))	$\frac{lim_{x \to \frac{π}{2}} 6 \cos (x)}{\cot (x)}$