Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
5901	Evaluate the Limit	limit as x approaches 6 of (x+6)/((x-6)^2)	$lim_{x \to 6} \frac{x + 6}{{(x - 6)}^{2}}$
5902	Evaluate the Limit	limit as t approaches 8 of ( square root of t+t^2)/(2t-t^2)	$lim_{t \to 8} \frac{\sqrt{t} + t^{2}}{2 t - t^{2}}$
5903	Evaluate the Limit	limit as t approaches 3 of (t^2+3t-18)/(t^2-9)	$lim_{t \to 3} \frac{t^{2} + 3 t - 18}{t^{2} - 9}$
5904	Evaluate the Limit	limit as t approaches 6 of 8(t-5)(t-7)	$lim_{t \to 6} 8 (t - 5) (t - 7)$
5905	Evaluate the Limit	limit as t approaches -2 of (t+2)/(t^2-4)	$lim_{t \to - 2} \frac{t + 2}{t^{2} - 4}$
5906	Evaluate the Limit	limit as t approaches 2 of (t^2-4)/(t^3-8)	$lim_{t \to 2} \frac{t^{2} - 4}{t^{3} - 8}$
5907	Evaluate the Limit	limit as t approaches 0 of 7/t-7/(t^2+t)	$lim_{t \to 0} \frac{7}{t} - \frac{7}{t^{2} + t}$
5908	Evaluate the Limit	limit as t approaches 0 of 2/t-2/(t^2+t)	$lim_{t \to 0} \frac{2}{t} - \frac{2}{t^{2} + t}$
5909	Evaluate the Limit	limit as r approaches 9 of ( square root of r)/((r-9)^4)	$lim_{r \to 9} \frac{\sqrt{r}}{{(r - 9)}^{4}}$
5910	Evaluate the Limit	limit as x approaches 1 of ( cube root of x-1)/( square root of x-1)	$lim_{x \to 1} \frac{\sqrt[3]{x} - 1}{\sqrt{x} - 1}$
5911	Evaluate the Limit	limit as n approaches 8 of nsin(pi/n)	$lim_{n \to 8} n \sin (\frac{π}{n})$
5912	Evaluate the Limit	( limit as x approaches 2 of x^4-16)/(x^3-8)	$\frac{lim_{x \to 2} x^{4} - 16}{x^{3} - 8}$
5913	Evaluate the Limit	( limit as x approaches 2 of x^3-8)/(x^4-16)	$\frac{lim_{x \to 2} x^{3} - 8}{x^{4} - 16}$
5914	Evaluate the Limit	( limit as x approaches 2 of x^3-8)/(x^2-4)	$\frac{lim_{x \to 2} x^{3} - 8}{x^{2} - 4}$
5915	Evaluate the Limit	( limit as x approaches 2 of x^2-4)/(x^3-8)	$\frac{lim_{x \to 2} x^{2} - 4}{x^{3} - 8}$
5916	Evaluate the Limit	limit as x approaches -2 of (3x^2+ax+a+3)/(x^2+x-2)	$lim_{x \to - 2} \frac{3 x^{2} + a x + a + 3}{x^{2} + x - 2}$
5917	Evaluate the Limit	limit as x approaches 3 of (x^2-7x+12)/(x-3)	$lim_{x \to 3} \frac{x^{2} - 7 x + 12}{x - 3}$
5918	Evaluate the Limit	( limit as x approaches -10 of 9x+90)/(\|x+10\|)	$\frac{lim_{x \to - 10} 9 x + 90}{\| x + 10 \|}$
5919	Evaluate the Limit	( limit as x approaches 10 of x^2+100)/(x-10)	$\frac{lim_{x \to 10} x^{2} + 100}{x - 10}$
5920	Evaluate the Limit	( limit as x approaches 1 of 1-x)/(1- square root of x)	$\frac{lim_{x \to 1} 1 - x}{1 - \sqrt{x}}$
5921	Evaluate the Limit	( limit as x approaches 1 of 3x^2+7x-2)/(3x^2-4x-2)	$\frac{lim_{x \to 1} 3 x^{2} + 7 x - 2}{3 x^{2} - 4 x - 2}$
5922	Evaluate the Limit	( limit as x approaches 1 of sin(x-1))/(x^2+x-2)	$\frac{lim_{x \to 1} \sin (x - 1)}{x^{2} + x - 2}$
5923	Evaluate the Limit	( limit as x approaches 1 of natural log of x)/(x-1)	$\frac{lim_{x \to 1} \ln (x)}{x - 1}$
5924	Find the Derivative - d/d@VAR	f(x) = seventh root of x	$f (x) = \sqrt[7]{x}$
5925	Evaluate the Limit	( limit as x approaches -1 of x^2-3x)/(x^2-2x-3)	$\frac{lim_{x \to - 1} x^{2} - 3 x}{x^{2} - 2 x - 3}$
5926	Evaluate the Limit	( limit as x approaches 1 of x^2+3x-4)/(x-1)	$\frac{lim_{x \to 1} x^{2} + 3 x - 4}{x - 1}$
5927	Evaluate the Limit	( limit as x approaches 3 of x)/(x-3)	$\frac{lim_{x \to 3} x}{x - 3}$
5928	Evaluate the Limit	( limit as x approaches 4 of x-4)/( square root of x-2)	$\frac{lim_{x \to 4} x - 4}{\sqrt{x - 2}}$
5929	Evaluate the Limit	( limit as x approaches 3 of x^2+2x-15)/(x^2-9)	$\frac{lim_{x \to 3} x^{2} + 2 x - 15}{x^{2} - 9}$
5930	Evaluate the Limit	( limit as x approaches 3 of x^4-81)/(2x^2-5x-3)	$\frac{lim_{x \to 3} x^{4} - 81}{2 x^{2} - 5 x - 3}$
5931	Evaluate the Limit	( limit as x approaches 3 of x^2+6x-27)/(x^2-9)	$\frac{lim_{x \to 3} x^{2} + 6 x - 27}{x^{2} - 9}$
5932	Evaluate the Limit	( limit as x approaches -3 of x^2-5x-24)/(x^2+5x+6)	$\frac{lim_{x \to - 3} x^{2} - 5 x - 24}{x^{2} + 5 x + 6}$
5933	Evaluate the Limit	( limit as x approaches 3 of x^2-5x+6)/(x-3)	$\frac{lim_{x \to 3} x^{2} - 5 x + 6}{x - 3}$
5934	Evaluate the Limit	( limit as x approaches 3 of x^2-7x+12)/(x^2+2x-15)	$\frac{lim_{x \to 3} x^{2} - 7 x + 12}{x^{2} + 2 x - 15}$
5935	Evaluate the Limit	limit as x approaches 4 of (x^2+3x)/(x^2-x-12)	$lim_{x \to 4} \frac{x^{2} + 3 x}{x^{2} - x - 12}$
5936	Evaluate the Limit	( limit as x approaches 2 of x-2)/( square root of x^2-4)	$\frac{lim_{x \to 2} x - 2}{\sqrt{x^{2} - 4}}$
5937	Evaluate the Limit	( limit as x approaches 2 of x-2)/( square root of x+7-3)	$\frac{lim_{x \to 2} x - 2}{\sqrt{x + 7} - 3}$
5938	Evaluate the Limit	limit as x approaches 7 of (x^2-3x-28)/(x-7)	$lim_{x \to 7} \frac{x^{2} - 3 x - 28}{x - 7}$
5939	Evaluate the Limit	( limit as x approaches -2 of -2x-4)/(x^3+2x^2)	$\frac{lim_{x \to - 2} - 2 x - 4}{x^{3} + 2 x^{2}}$
5940	Evaluate the Limit	( limit as x approaches 2 of 3x^2-7x+2)/(2-x)	$\frac{lim_{x \to 2} 3 x^{2} - 7 x + 2}{2 - x}$
5941	Evaluate the Limit	( limit as x approaches 6 of x^3-36x)/(x-6)	$\frac{lim_{x \to 6} x^{3} - 36 x}{x - 6}$
5942	Evaluate the Limit	( limit as x approaches -7 of 7-\|x\|)/(7+x)	$\frac{lim_{x \to - 7} 7 - \| x \|}{7 + x}$
5943	Evaluate the Limit	( limit as x approaches -6 of 2x+12)/(\|x+6\|)	$\frac{lim_{x \to - 6} 2 x + 12}{\| x + 6 \|}$
5944	Evaluate the Limit	( limit as x approaches 5 of x-7)/((x-5)^2)	$\frac{lim_{x \to 5} x - 7}{{(x - 5)}^{2}}$
5945	Evaluate the Limit	( limit as x approaches 5 of x^2-5x+10)/(x^2-25)	$\frac{lim_{x \to 5} x^{2} - 5 x + 10}{x^{2} - 25}$
5946	Evaluate the Limit	( limit as x approaches 5 of x^2-7x+10)/(x-5)	$\frac{lim_{x \to 5} x^{2} - 7 x + 10}{x - 5}$
5947	Evaluate the Limit	( limit as x approaches -5 of x^2-25)/(x+5)	$\frac{lim_{x \to - 5} x^{2} - 25}{x + 5}$
5948	Evaluate the Limit	( limit as x approaches -8 of 1-x-x^2)/(3x^2-8)	$\frac{lim_{x \to - 8} 1 - x - x^{2}}{3 x^{2} - 8}$
5949	Evaluate the Limit	limit as x approaches 8 of (1+1/x)^x	$lim_{x \to 8} {(1 + \frac{1}{x})}^{x}$
5950	Evaluate the Limit	( limit as x approaches 8 of 8x-5)/(7x+4)	$\frac{lim_{x \to 8} 8 x - 5}{7 x + 4}$
5951	Evaluate the Limit	( limit as x approaches 9 of x^2-3x-54)/(x-9)	$\frac{lim_{x \to 9} x^{2} - 3 x - 54}{x - 9}$
5952	Evaluate the Limit	( limit as x approaches -9 of x^2-81)/(2x^2+19x+9)	$\frac{lim_{x \to - 9} x^{2} - 81}{2 x^{2} + 19 x + 9}$
5953	Evaluate the Limit	( limit as x approaches 9 of x^2-5x-36)/(x-9)	$\frac{lim_{x \to 9} x^{2} - 5 x - 36}{x - 9}$
5954	Evaluate the Limit	( limit as x approaches 9 of x^2-6x-27)/(x-9)	$\frac{lim_{x \to 9} x^{2} - 6 x - 27}{x - 9}$
5955	Evaluate the Limit	( limit as x approaches e of natural log of x-1)/(x-e)	$\frac{lim_{x \to e} \ln (x - 1)}{x - e}$
5956	Evaluate the Limit	( limit as x approaches 8 of 3x^5-2x^2+5)/(7x^5+8x^4-11)	$\frac{lim_{x \to 8} 3 x^{5} - 2 x^{2} + 5}{7 x^{5} + 8 x^{4} - 11}$
5957	Evaluate the Limit	( limit as x approaches 8 of 5x^3-3x^2+10)/(x^2)	$\frac{lim_{x \to 8} 5 x^{3} - 3 x^{2} + 10}{x^{2}}$
5958	Evaluate the Limit	limit as x approaches 0 of (sin(x)+x)/x	$lim_{x \to 0} \frac{\sin (x) + x}{x}$
5959	Evaluate the Limit	limit as x approaches 2 of ( square root of x^2+12-4)/(x-2)	$lim_{x \to 2} \frac{\sqrt{x^{2} + 12} - 4}{x - 2}$
5960	Evaluate the Limit	limit as x approaches 0 of (1+4x)^(3/x)	$lim_{x \to 0} {(1 + 4 x)}^{\frac{3}{x}}$
5961	Evaluate the Limit	limit as x approaches 0 of (2x-1)^3	$lim_{x \to 0} {(2 x - 1)}^{3}$
5962	Evaluate the Limit	limit as x approaches 121 of (x-121)/( square root of x-11)	$lim_{x \to 121} \frac{x - 121}{\sqrt{x} - 11}$
5963	Evaluate the Limit	limit as x approaches 0 of (sin(x)^2)/(1-cos(x))	$lim_{x \to 0} \frac{\sin^{2} (x)}{1 - \cos (x)}$
5964	Evaluate the Limit	limit as x approaches 0 of (1-cos(2x))/(x^2)	$lim_{x \to 0} \frac{1 - \cos (2 x)}{x^{2}}$
5965	Evaluate the Limit	limit as x approaches 0 of 1/(x^(2/3))	$lim_{x \to 0} \frac{1}{x^{\frac{2}{3}}}$
5966	Evaluate the Limit	limit as x approaches 4 of (4x-x^2)/(2- square root of x)	$lim_{x \to 4} \frac{4 x - x^{2}}{2 - \sqrt{x}}$
5967	Find the Critical Points	f(x)=5x^3-15x	$f (x) = 5 x^{3} - 15 x$
5968	Evaluate the Limit	limit as x approaches 0 of (x^2-2x)/x	$lim_{x \to 0} \frac{x^{2} - 2 x}{x}$
5969	Evaluate the Limit	limit as x approaches 0 of (x^2-16)/(x+4)	$lim_{x \to 0} \frac{x^{2} - 16}{x + 4}$
5970	Evaluate the Limit	limit as x approaches 0 of (x^2-16)/(x-4)	$lim_{x \to 0} \frac{x^{2} - 16}{x - 4}$
5971	Evaluate the Limit	limit as x approaches 0 of ((sin(x))/x)^(1/(x^2))	$lim_{x \to 0} {(\frac{\sin (x)}{x})}^{\frac{1}{x^{2}}}$
5972	Evaluate the Limit	limit as x approaches 0 of (3^x-4^x)/x	$lim_{x \to 0} \frac{3^{x} - 4^{x}}{x}$
5973	Evaluate the Limit	limit as x approaches 0 of (sin(5x))/(3x)	$lim_{x \to 0} \frac{\sin (5 x)}{3 x}$
5974	Evaluate the Limit	limit as x approaches negative infinity of x^2+2x^7	$lim_{x \to - \infty} x^{2} + 2 x^{7}$
5975	Evaluate the Limit	limit as x approaches 0 of x^2-1	$lim_{x \to 0} x^{2} - 1$
5976	Evaluate the Limit	limit as x approaches 0 of x^2cos(20pix)	$lim_{x \to 0} x^{2} \cos (20 π x)$
5977	Evaluate the Limit	limit as x approaches 0 of x/( square root of 1+3x-1)	$lim_{x \to 0} \frac{x}{\sqrt{1 + 3 x} - 1}$
5978	Evaluate the Limit	limit as x approaches 0 of 1/x-cot(x)	$lim_{x \to 0} \frac{1}{x} - \cot (x)$
5979	Evaluate the Limit	limit as t approaches 0 of 9/(t square root of 1+t)-9/t	$lim_{t \to 0} \frac{9}{t \sqrt{1 + t}} - \frac{9}{t}$
5980	Evaluate the Limit	limit as x approaches 0 of 1/( natural log of x)-1/(x-1)	$lim_{x \to 0} \frac{1}{\ln (x)} - \frac{1}{x - 1}$
5981	Evaluate the Limit	limit as x approaches infinity of -2x+11	$lim_{x \to \infty} - 2 x + 11$
5982	Evaluate the Limit	limit as x approaches 7 of (x-7)/(x^2-49)	$lim_{x \to 7} \frac{x - 7}{x^{2} - 49}$
5983	Evaluate the Limit	limit as x approaches 0 of square root of x	$lim_{x \to 0} \sqrt{x}$
5984	Evaluate the Limit	limit as x approaches 0 of (sin(3x))/(sin(8x))	$lim_{x \to 0} \frac{\sin (3 x)}{\sin (8 x)}$
5985	Evaluate the Limit	limit as x approaches 0 of (sin(2x))/(8x)	$lim_{x \to 0} \frac{\sin (2 x)}{8 x}$
5986	Evaluate the Limit	limit as x approaches 0 of (sin(2x))/(tan(3x))	$lim_{x \to 0} \frac{\sin (2 x)}{\tan (3 x)}$
5987	Evaluate the Limit	limit as x approaches 0 of (sin(4x))/(tan(3x))	$lim_{x \to 0} \frac{\sin (4 x)}{\tan (3 x)}$
5988	Evaluate the Limit	limit as x approaches 1 of (2x-2)/(x-1)	$lim_{x \to 1} \frac{2 x - 2}{x - 1}$
5989	Evaluate the Limit	limit as x approaches 0 of (sin(4x^2))/(3x)	$lim_{x \to 0} \frac{\sin (4 x^{2})}{3 x}$
5990	Evaluate the Limit	limit as x approaches 0 of (sin(3x))/(x^2)	$lim_{x \to 0} \frac{\sin (3 x)}{x^{2}}$
5991	Evaluate the Limit	limit as x approaches 0 of (sin(4x))/(3x)	$lim_{x \to 0} \frac{\sin (4 x)}{3 x}$
5992	Evaluate the Limit	limit as x approaches 0 of (sin(cos(x)))/(sec(x))	$lim_{x \to 0} \frac{\sin (\cos (x))}{\sec (x)}$
5993	Evaluate the Limit	limit as x approaches 0 of (sin(cos(x)))/(sin(x))	$lim_{x \to 0} \frac{\sin (\cos (x))}{\sin (x)}$
5994	Evaluate the Limit	limit as x approaches 0 of (tan(3x))/(tan(5x))	$lim_{x \to 0} \frac{\tan (3 x)}{\tan (5 x)}$
5995	Evaluate the Limit	limit as x approaches 0 of sin(x)^2	$lim_{x \to 0} \sin^{2} (x)$
5996	Evaluate the Limit	limit as x approaches 0 of (sin(x))/(sin(pix))	$lim_{x \to 0} \frac{\sin (x)}{\sin (π x)}$
5997	Evaluate the Limit	limit as x approaches 0 of x/(arctan(8x))	$lim_{x \to 0} \frac{x}{\arctan (8 x)}$
5998	Evaluate the Limit	limit as x approaches 0 of (tan(3x))/(sin(8x))	$lim_{x \to 0} \frac{\tan (3 x)}{\sin (8 x)}$
5999	Evaluate the Limit	limit as x approaches 0 of (tan(x))/(sin(x))	$lim_{x \to 0} \frac{\tan (x)}{\sin (x)}$
6000	Evaluate the Limit	limit as x approaches 0 of tan(9x)^x	$lim_{x \to 0} {\tan (9 x)}^{x}$