Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
20901	Evaluate the Limit	limit as x approaches 0 of (sin(7x))/(3x)	$lim_{x \to 0} \frac{\sin (7 x)}{3 x}$
20902	Evaluate the Limit	limit as x approaches 0 of (sin(8x))/(tan(3x))	$lim_{x \to 0} \frac{\sin (8 x)}{\tan (3 x)}$
20903	Evaluate the Limit	limit as x approaches 0 of (sin(mx))/(nx)	$lim_{x \to 0} \frac{\sin (m x)}{n x}$
20904	Evaluate the Limit	limit as x approaches 0 of (sin(9(-0.001)))/-0.001	$lim_{x \to 0} \frac{\sin (9 (- 0.001))}{- 0.001}$
20905	Evaluate the Limit	limit as x approaches 0 of (sin(x)(1-cos(x)))/(x^2)	$lim_{x \to 0} \frac{\sin (x) (1 - \cos (x))}{x^{2}}$
20906	Evaluate the Limit	limit as x approaches 0 of (sin(x))/(20x)	$lim_{x \to 0} \frac{\sin (x)}{20 x}$
20907	Evaluate the Limit	limit as x approaches 0 of (sin(x))/(1-cos(x))	$lim_{x \to 0} \frac{\sin (x)}{1 - \cos (x)}$
20908	Evaluate the Limit	limit as x approaches 0 of (sin(x))/(14x)	$lim_{x \to 0} \frac{\sin (x)}{14 x}$
20909	Evaluate the Limit	limit as x approaches 0 of (sin(x))/(10x)	$lim_{x \to 0} \frac{\sin (x)}{10 x}$
20910	Evaluate the Limit	limit as x approaches 0 of (sin(x))/(11 square root of x)	$lim_{x \to 0} \frac{\sin (x)}{11 \sqrt{x}}$
20911	Evaluate the Limit	limit as x approaches 0 of (sin(6x))/(sin(7x))	$lim_{x \to 0} \frac{\sin (6 x)}{\sin (7 x)}$
20912	Evaluate the Limit	limit as x approaches 0 of (sin(6x))/(sin(9x))	$lim_{x \to 0} \frac{\sin (6 x)}{\sin (9 x)}$
20913	Evaluate the Limit	limit as x approaches 0 of (sin(6x))/(sin(x))	$lim_{x \to 0} \frac{\sin (6 x)}{\sin (x)}$
20914	Evaluate the Limit	limit as x approaches 0 of (sin(6x))/(sin(12x))	$lim_{x \to 0} \frac{\sin (6 x)}{\sin (12 x)}$
20915	Evaluate the Limit	limit as x approaches 0 of (sin(6x))/(sin(3x))	$lim_{x \to 0} \frac{\sin (6 x)}{\sin (3 x)}$
20916	Evaluate the Limit	limit as x approaches 0 of (sin(5x^2))/(x^2)	$lim_{x \to 0} \frac{\sin (5 x^{2})}{x^{2}}$
20917	Evaluate the Limit	limit as x approaches 0 of (sin(2x))/(tan(9x))	$lim_{x \to 0} \frac{\sin (2 x)}{\tan (9 x)}$
20918	Evaluate the Limit	limit as x approaches 2 of (x-2)/( square root of x- square root of 4-x)	$lim_{x \to 2} \frac{x - 2}{\sqrt{x} - \sqrt{4 - x}}$
20919	Evaluate the Limit	limit as x approaches 0 of (sin(2x))/(sin(6x))	$lim_{x \to 0} \frac{\sin (2 x)}{\sin (6 x)}$
20920	Evaluate the Limit	limit as x approaches 0 of (sin(x^2))/x	$lim_{x \to 0} \frac{\sin (x^{2})}{x}$
20921	Evaluate the Limit	limit as x approaches 0 of (sin(2x))/(sin(x))	$lim_{x \to 0} \frac{\sin (2 x)}{\sin (x)}$
20922	Evaluate the Limit	limit as x approaches 0 of (sin(2x))/(cos(5x))	$lim_{x \to 0} \frac{\sin (2 x)}{\cos (5 x)}$
20923	Evaluate the Limit	limit as x approaches 0 of (sin(3x))/(sin(6x))	$lim_{x \to 0} \frac{\sin (3 x)}{\sin (6 x)}$
20924	Evaluate the Limit	limit as x approaches 0 of (sin(3x)cos(x))/x	$lim_{x \to 0} \frac{\sin (3 x) \cos (x)}{x}$
20925	Evaluate the Limit	limit as x approaches 0 of (sin(3x)cot(4x))/(cot(5x))	$lim_{x \to 0} \frac{\sin (3 x) \cot (4 x)}{\cot (5 x)}$
20926	Evaluate the Limit	limit as x approaches 0 of (sin(3y))/(4y)	$lim_{x \to 0} \frac{\sin (3 y)}{4 y}$
20927	Evaluate the Limit	limit as x approaches 0 of (sin(3x))/(sin(2x))	$lim_{x \to 0} \frac{\sin (3 x)}{\sin (2 x)}$
20928	Evaluate the Limit	limit as x approaches 0 of (sin(3x))/(sin(4x))	$lim_{x \to 0} \frac{\sin (3 x)}{\sin (4 x)}$
20929	Evaluate the Limit	limit as x approaches 0 of (sin(3x))/(3x)	$lim_{x \to 0} \frac{\sin (3 x)}{3 x}$
20930	Evaluate the Limit	limit as x approaches 0 of (sin(2x))/(x+tan(7x))	$lim_{x \to 0} \frac{\sin (2 x)}{x + \tan (7 x)}$
20931	Evaluate the Limit	limit as x approaches 0 of 6/x-6/(\|x\|)	$lim_{x \to 0} \frac{6}{x} - \frac{6}{\| x \|}$
20932	Evaluate the Limit	limit as x approaches 0 of 9/x-9/(\|x\|)	$lim_{x \to 0} \frac{9}{x} - \frac{9}{\| x \|}$
20933	Evaluate the Limit	limit as x approaches 0 of (2x^2-5x-3)/(x^2+x-12)	$lim_{x \to 0} \frac{2 x^{2} - 5 x - 3}{x^{2} + x - 12}$
20934	Evaluate the Limit	limit as x approaches 0 of (2x)/(tan(x))	$lim_{x \to 0} \frac{2 x}{\tan (x)}$
20935	Evaluate the Limit	limit as x approaches 0 of (4x)/(5- square root of x+25)	$lim_{x \to 0} \frac{4 x}{5 - \sqrt{x + 25}}$
20936	Evaluate the Limit	limit as x approaches 0 of 3/x-3/(\|x\|)	$lim_{x \to 0} \frac{3}{x} - \frac{3}{\| x \|}$
20937	Evaluate the Limit	limit as x approaches 0 of ( square root of 81+h-9)/h	$lim_{x \to 0} \frac{\sqrt{81 + h} - 9}{h}$
20938	Evaluate the Limit	limit as x approaches 5 of (x+3)/(5-x)	$lim_{x \to 5} \frac{x + 3}{5 - x}$
20939	Evaluate the Limit	limit as x approaches 0 of ( square root of 5x+4-2)/x	$lim_{x \to 0} \frac{\sqrt{5 x + 4 - 2}}{x}$
20940	Evaluate the Limit	limit as x approaches 0 of (sin(x)^2)/(4x^2)	$lim_{x \to 0} \frac{\sin^{2} (x)}{4 x^{2}}$
20941	Evaluate the Limit	limit as x approaches 0 of 1/(sin(x))-cot(x)	$lim_{x \to 0} \frac{1}{\sin (x)} - \cot (x)$
20942	Evaluate the Limit	limit as x approaches 0 of ( square root of 16x+1-1)/x	$lim_{x \to 0} \frac{\sqrt{16 x + 1} - 1}{x}$
20943	Evaluate the Limit	limit as x approaches 6 of (x+6)/(x^2-36)	$lim_{x \to 6} \frac{x + 6}{x^{2} - 36}$
20944	Evaluate the Limit	limit as x approaches 8 of (100x^2-5)/(5x^2-100)	$lim_{x \to 8} \frac{100 x^{2} - 5}{5 x^{2} - 100}$
20945	Evaluate the Limit	limit as x approaches 0 of ( square root of x+7- square root of 7)/x	$lim_{x \to 0} \frac{\sqrt{x + 7} - \sqrt{7}}{x}$
20946	Evaluate the Limit	limit as x approaches -4 of (x^2-16)/(2x^2+9x+4)	$lim_{x \to - 4} \frac{x^{2} - 16}{2 x^{2} + 9 x + 4}$
20947	Evaluate the Limit	limit as x approaches pi/2 of (sin(4x))/x	$lim_{x \to \frac{π}{2}} \frac{\sin (4 x)}{x}$
20948	Evaluate the Limit	limit as x approaches 8 of cube root of x^3+1- fourth root of x^4+1	$lim_{x \to 8} \sqrt[3]{x^{3} + 1} - \sqrt[4]{x^{4} + 1}$
20949	Evaluate the Limit	limit as x approaches negative infinity of (1-x)/(x^2)	$lim_{x \to - \infty} \frac{1 - x}{x^{2}}$
20950	Evaluate the Limit	limit as x approaches 0 of 1+sin(4x)^(cot(x))	$lim_{x \to 0} 1 + {\sin (4 x)}^{\cot (x)}$
20951	Evaluate the Limit	limit as x approaches 0 of (x-8)/(x^2-8x)	$lim_{x \to 0} \frac{x - 8}{x^{2} - 8 x}$
20952	Evaluate the Limit	limit as x approaches 0 of (x-sin(x))/(x-tan(x))	$lim_{x \to 0} \frac{x - \sin (x)}{x - \tan (x)}$
20953	Evaluate the Limit	limit as h approaches 0 of (f(3+h)-f(3))/h	$lim_{h \to 0} \frac{f (3 + h) - f (3)}{h}$
20954	Evaluate the Limit	limit as x approaches 0 of x^2cot(2x)csc(3x)	$lim_{x \to 0} x^{2} \cot (2 x) \csc (3 x)$
20955	Evaluate the Limit	limit as x approaches 0 of x^5-6x^4+7	$lim_{x \to 0} x^{5} - 6 x^{4} + 7$
20956	Evaluate the Limit	limit as x approaches 0 of 1/x-1/(\|x\|)	$lim_{x \to 0} \frac{1}{x} - \frac{1}{\| x \|}$
20957	Evaluate the Limit	limit as x approaches 0 of ((e^x-x-1)cos(2/x)^2)+x+1	$lim_{x \to 0} ((e^{x} - x - 1) \cos^{2} (\frac{2}{x})) + x + 1$
20958	Evaluate the Limit	limit as x approaches 0 of (sin(-(pix)/2))/(2x)	$lim_{x \to 0} \frac{\sin (- \frac{π x}{2})}{2 x}$
20959	Evaluate the Limit	limit as x approaches 0 of (xcsc(2x))/(cos(5x))	$lim_{x \to 0} \frac{x \csc (2 x)}{\cos (5 x)}$
20960	Evaluate the Limit	limit as x approaches 0 of (sin(18x))/(4x)	$lim_{x \to 0} \frac{\sin (18 x)}{4 x}$
20961	Evaluate the Limit	limit as x approaches 0 of (sin(x))/(3x)+(2x)/(3sin(x))	$lim_{x \to 0} \frac{\sin (x)}{3 x} + \frac{2 x}{3 \sin (x)}$
20962	Evaluate the Limit	limit as x approaches 0 of (sin(6x))/(sin(2x))	$lim_{x \to 0} \frac{\sin (6 x)}{\sin (2 x)}$
20963	Evaluate the Limit	limit as x approaches 0 of (cos(x))/x	$lim_{x \to 0} \frac{\cos (x)}{x}$
20964	Evaluate the Limit	limit as x approaches 9 of (x^2-3x-54)/(x-9)	$lim_{x \to 9} \frac{x^{2} - 3 x - 54}{x - 9}$
20965	Evaluate the Limit	limit as x approaches 0 of (sin(2x))/(2x)	$lim_{x \to 0} \frac{\sin (2 x)}{2 x}$
20966	Evaluate the Limit	limit as x approaches 0 of (sin(x))/(9x)	$lim_{x \to 0} \frac{\sin (x)}{9 x}$
20967	Evaluate the Limit	limit as x approaches 0 of (sin(3x))/(sin(7x))	$lim_{x \to 0} \frac{\sin (3 x)}{\sin (7 x)}$
20968	Evaluate the Limit	limit as x approaches 3 of (x^3-27)/(x^2-9)	$lim_{x \to 3} \frac{x^{3} - 27}{x^{2} - 9}$
20969	Evaluate the Limit	limit as x approaches 0 of (sin(7x))/(tan(x))	$lim_{x \to 0} \frac{\sin (7 x)}{\tan (x)}$
20970	Evaluate the Limit	limit as x approaches 0 of sin(x+2pi)+cos(x)	$lim_{x \to 0} \sin (x + 2 π) + \cos (x)$
20971	Evaluate the Limit	limit as x approaches 0 of 1/(x square root of 1+x)-1/x	$lim_{x \to 0} \frac{1}{x \sqrt{1} + x} - \frac{1}{x}$
20972	Evaluate the Limit	limit as x approaches 0 of x-10/x	$lim_{x \to 0} x - \frac{10}{x}$
20973	Evaluate the Limit	limit as x approaches 0 of (x-5)cos(x)	$lim_{x \to 0} (x - 5) \cos (x)$
20974	Evaluate the Limit	limit as x approaches 2 of (x^3-4x)/(x-2)	$lim_{x \to 2} \frac{x^{3} - 4 x}{x - 2}$
20975	Evaluate the Limit	limit as x approaches 0 of 5x-4	$lim_{x \to 0} 5 x - 4$
20976	Evaluate the Limit	limit as x approaches 5 of 3x^2-4x-1	$lim_{x \to 5} 3 x^{2} - 4 x - 1$
20977	Evaluate the Limit	limit as x approaches 0 of (2^0-1)/0	$lim_{x \to 0} \frac{2^{0} - 1}{0}$
20978	Evaluate the Limit	limit as x approaches 0 of (e^(ax)+x)^(1/x)	$lim_{x \to 0} {(e^{a x} + x)}^{\frac{1}{x}}$
20979	Evaluate the Limit	limit as x approaches infinity of (2x-3)/(4x+5)	$lim_{x \to \infty} \frac{2 x - 3}{4 x + 5}$
20980	Evaluate the Limit	limit as x approaches negative infinity of square root of 5-x	$lim_{x \to - \infty} \sqrt{5 - x}$
20981	Evaluate the Limit	limit as x approaches 0 of xcos(x^2+1/x)	$lim_{x \to 0} x \cos (x^{2} + \frac{1}{x})$
20982	Evaluate the Limit	limit as x approaches 0 of (9^(2x)-1)/(9^x-1)	$lim_{x \to 0} \frac{9^{2 x} - 1}{9^{x} - 1}$
20983	Evaluate the Limit	limit as x approaches 0 of (x^2-5x)/(x^2+2x)	$lim_{x \to 0} \frac{x^{2} - 5 x}{x^{2} + 2 x}$
20984	Evaluate the Limit	limit as x approaches 0 of (sin(2x))/(sin(8x))	$lim_{x \to 0} \frac{\sin (2 x)}{\sin (8 x)}$
20985	Evaluate the Limit	limit as x approaches 0 of (x^3)/(x-arctan(x))	$lim_{x \to 0} \frac{x^{3}}{x - \arctan (x)}$
20986	Evaluate the Limit	limit as x approaches 0 of (x^4+3x)/x	$lim_{x \to 0} \frac{x^{4} + 3 x}{x}$
20987	Evaluate the Limit	limit as x approaches 0 of \|x\|cos(pi/x)	$lim_{x \to 0} \| x \| \cos (\frac{π}{x})$
20988	Evaluate the Limit	limit as x approaches 0 of 1/(sin(x))	$lim_{x \to 0} \frac{1}{\sin (x)}$
20989	Evaluate the Limit	limit as x approaches 0 of 1/(tsec(t)csc(4t))	$lim_{x \to 0} \frac{1}{t \sec (t) \csc (4 t)}$
20990	Evaluate the Limit	limit as x approaches 0 of (12(1-cos(x)))/(x^2)	$lim_{x \to 0} \frac{12 (1 - \cos (x))}{x^{2}}$
20991	Evaluate the Limit	limit as x approaches 0 of 1/x-2/(x^2+2x)	$lim_{x \to 0} \frac{1}{x} - \frac{2}{x^{2} + 2 x}$
20992	Evaluate the Limit	limit as x approaches 0 of (1/(x+6))-1/(6/x)	$lim_{x \to 0} (\frac{1}{x + 6}) - \frac{1}{\frac{6}{x}}$
20993	Evaluate the Limit	limit as x approaches -6 of (x^2-36)/(2x^2+13x+6)	$lim_{x \to - 6} \frac{x^{2} - 36}{2 x^{2} + 13 x + 6}$
20994	Evaluate the Limit	limit as x approaches 0 of \|x/x\|	$lim_{x \to 0} \| \frac{x}{x} \|$
20995	Evaluate the Limit	limit as x approaches infinity of ( square root of t+t^2)/(2t-t^2)	$lim_{x \to \infty} \frac{\sqrt{t} + t^{2}}{2 t - t^{2}}$
20996	Evaluate the Limit	limit as x approaches 0 of (1+(x-1)cos(x))/(4x)	$lim_{x \to 0} \frac{1 + (x - 1) \cos (x)}{4 x}$
20997	Evaluate the Limit	limit as x approaches 0 of (tan(x)^2)/(xsin(x))	$lim_{x \to 0} \frac{\tan^{2} (x)}{x \sin (x)}$
20998	Evaluate the Limit	limit as x approaches 0 of (tan(3x)^2)/(2x)	$lim_{x \to 0} \frac{\tan^{2} (3 x)}{2 x}$
20999	Evaluate the Limit	limit as x approaches 0 of (5x^4+8x^2)/(3x^4-16x^2)	$lim_{x \to 0} \frac{5 x^{4} + 8 x^{2}}{3 x^{4} - 16 x^{2}}$
21000	Evaluate the Limit	limit as x approaches 0 of (8^x-5^x)/x	$lim_{x \to 0} \frac{8^{x} - 5^{x}}{x}$