Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
31501	Graph	x^2=8y-4	$x^{2} = 8 y - 4$
31502	Evaluate the Limit	( limit as x approaches 0 of sin(7x)+sin(3x))/(3x^2+5x)	$\frac{lim_{x \to 0} \sin (7 x) + \sin (3 x)}{3 x^{2} + 5 x}$
31503	Evaluate the Limit	( limit as x approaches 0 of sin(3x))/(xcos(x))	$\frac{lim_{x \to 0} \sin (3 x)}{x \cos (x)}$
31504	Evaluate the Limit	( limit as x approaches 0 of sin(4x))/(2x)	$\frac{lim_{x \to 0} \sin (4 x)}{2 x}$
31505	Evaluate the Limit	( limit as x approaches 0 of sin(4x))/(sin(2x))	$\frac{lim_{x \to 0} \sin (4 x)}{\sin (2 x)}$
31506	Find Where Increasing/Decreasing Using Derivatives	f(x)=8x^4-48x^2	$f (x) = 8 x^{4} - 48 x^{2}$
31507	Evaluate the Limit	( limit as x approaches 0 of sin(3x))/(5x)	$\frac{lim_{x \to 0} \sin (3 x)}{5 x}$
31508	Evaluate the Limit	( limit as x approaches 0 of sin(2x)cos(x)-sin(2x))/(x^2)	$\frac{lim_{x \to 0} \sin (2 x) \cos (x) - \sin (2 x)}{x^{2}}$
31509	Find Where Increasing/Decreasing Using Derivatives	4x^(3/5)-x^(4/5)	$4 x^{\frac{3}{5}} - x^{\frac{4}{5}}$
31510	Find the Inflection Points	3x^4+8x^3	$3 x^{4} + 8 x^{3}$
31511	Evaluate the Limit	( limit as x approaches -1 of cube root of x-1)/(x^2+1)	$\frac{lim_{x \to - 1} \sqrt[3]{x} - 1}{x^{2} + 1}$
31512	Evaluate the Limit	( limit as x approaches 1 of x^3-1)/(\|x-1\|)	$\frac{lim_{x \to 1} x^{3} - 1}{\| x - 1 \|}$
31513	Find the Inflection Points	x^3-9x^2-81x	$x^{3} - 9 x^{2} - 81 x$
31514	Evaluate the Limit	( limit as x approaches -1 of x^3-3x-2)/(x^2+2x+1)	$\frac{lim_{x \to - 1} x^{3} - 3 x - 2}{x^{2} + 2 x + 1}$
31515	Find the Critical Points	y=4x^3+12x-7	$y = 4 x^{3} + 12 x - 7$
31516	Evaluate the Limit	( limit as x approaches 1 of x^x-1)/( natural log of x)	$\frac{lim_{x \to 1} x^{x} - 1}{\ln (x)}$
31517	Evaluate the Limit	( limit as x approaches 1 of y^2+y-2)/(y^2-1)	$\frac{lim_{x \to 1} y^{2} + y - 2}{y^{2} - 1}$
31518	Evaluate the Limit	( limit as x approaches 1 of 1- square root of 2x^2-1)/(x-1)	$\frac{lim_{x \to 1} 1 - \sqrt{2 x^{2} - 1}}{x - 1}$
31519	Evaluate the Limit	( limit as x approaches -1 of 10-2x)/(1^x+5)	$\frac{lim_{x \to - 1} 10 - 2 x}{1^{x} + 5}$
31520	Evaluate the Limit	( limit as x approaches 1 of 17x^2-18x+1)/(x^2-2)	$\frac{lim_{x \to 1} 17 x^{2} - 18 x + 1}{x^{2} - 2}$
31521	Evaluate the Limit	( limit as x approaches 1 of x^2-1)/(2x+4)	$\frac{lim_{x \to 1} x^{2} - 1}{2 x + 4}$
31522	Evaluate the Limit	( limit as x approaches 1 of x^2-1)/( natural log of x)	$\frac{lim_{x \to 1} x^{2} - 1}{\ln (x)}$
31523	Evaluate the Limit	( limit as x approaches 1 of x^2-3x-2)/(x^2+1)	$\frac{lim_{x \to 1} x^{2} - 3 x - 2}{x^{2} + 1}$
31524	Evaluate the Limit	( limit as x approaches -1 of x^2-4x)/(x^2*(3x)-4)	$\frac{lim_{x \to - 1} x^{2} - 4 x}{x^{2} \cdot (3 x) - 4}$
31525	Evaluate the Limit	( limit as x approaches -1 of x^2-8)/(1-x)	$\frac{lim_{x \to - 1} x^{2} - 8}{1 - x}$
31526	Find the Antiderivative	3cos(3x)	$3 \cos (3 x)$
31527	Evaluate the Limit	( limit as x approaches 1 of x^3-x^2+x-1)/(x^4-x^3-2x+2)	$\frac{lim_{x \to 1} x^{3} - x^{2} + x - 1}{x^{4} - x^{3} - 2 x + 2}$
31528	Find the Antiderivative	cos(6x)	$\cos (6 x)$
31529	Evaluate the Limit	( limit as x approaches 1 of x^2+6x-7)/(x^2-1)	$\frac{lim_{x \to 1} x^{2} + 6 x - 7}{x^{2} - 1}$
31530	Find the Antiderivative	f(x) = square root of 2	$f (x) = \sqrt{2}$
31531	Evaluate the Limit	( limit as x approaches 1 of cube root of 1+x^2)/( cube root of 1-x^3)	$\frac{lim_{x \to 1} \sqrt[3]{1 + x^{2}}}{\sqrt[3]{1 - x^{3}}}$
31532	Evaluate the Limit	( limit as x approaches 1 of x^3-7x^2+12x)/(4-x)	$\frac{lim_{x \to 1} x^{3} - 7 x^{2} + 12 x}{4 - x}$
31533	Evaluate the Limit	( limit as x approaches 1 of x^53-1)/(x^7-1)	$\frac{lim_{x \to 1} x^{53} - 1}{x^{7} - 1}$
31534	Evaluate the Limit	( limit as x approaches 1 of x^9-1)/(x^5-1)	$\frac{lim_{x \to 1} x^{9} - 1}{x^{5} - 1}$
31535	Evaluate the Limit	( limit as x approaches 1 of 1- cube root of x)/(1-x)	$\frac{lim_{x \to 1} 1 - \sqrt[3]{x}}{1 - x}$
31536	Evaluate the Limit	( limit as x approaches 1 of 1-x+ natural log of x)/(1+cos(pix))	$\frac{lim_{x \to 1} 1 - x + \ln (x)}{1 + \cos (π x)}$
31537	Evaluate the Limit	( limit as x approaches 1 of 2x+7x-8)/(x^2-1)	$\frac{lim_{x \to 1} 2 x + 7 x - 8}{x^{2} - 1}$
31538	Evaluate the Limit	( limit as x approaches -1 of 3x^2-2x-1)/(x^2+1)	$\frac{lim_{x \to - 1} 3 x^{2} - 2 x - 1}{x^{2} + 1}$
31539	Evaluate the Limit	( limit as x approaches -1 of 5x+5)/(x+1)	$\frac{lim_{x \to - 1} 5 x + 5}{x + 1}$
31540	Evaluate the Limit	( limit as x approaches 1 of 6x-6)/(7x-7)	$\frac{lim_{x \to 1} 6 x - 6}{7 x - 7}$
31541	Evaluate the Limit	( limit as x approaches -1 of sin(x^2-x-2))/(x-1)	$\frac{lim_{x \to - 1} \sin (x^{2} - x - 2)}{x - 1}$
31542	Evaluate the Limit	( limit as x approaches -1 of x^3+1)/x+2	$\frac{lim_{x \to - 1} x^{3} + 1}{x} + 2$
31543	Evaluate the Limit	( limit as x approaches 1 of x+1)/(x^2-4x-5)+1	$\frac{lim_{x \to 1} x + 1}{x^{2} - 4 x - 5} + 1$
31544	Evaluate the Limit	( limit as x approaches 1 of x-3)/x	$\frac{lim_{x \to 1} x - 3}{x}$
31545	Evaluate the Limit	( limit as x approaches 1 of 0.990^3-0.990)/(0.990-1)	$\frac{lim_{x \to 1} {0.99}^{3} - 0.99}{0.99 - 1}$
31546	Evaluate the Limit	( limit as x approaches 1 of \|x-2\|-2)/x	$\frac{lim_{x \to 1} \| x - 2 \| - 2}{x}$
31547	Evaluate the Limit	( limit as x approaches 1 of 1.010^3-3)/(1.010-1)	$\frac{lim_{x \to 1} {1.01}^{3} - 3}{1.01 - 1}$
31548	Evaluate the Limit	( limit as x approaches 1 of 1/x-1)/(x-1)	$\frac{lim_{x \to 1} \frac{1}{x} - 1}{x - 1}$
31549	Evaluate the Limit	( limit as x approaches 1 of 1/(x+8)-1/9)/(x-1)	$\frac{lim_{x \to 1} \frac{1}{x + 8} - \frac{1}{9}}{x - 1}$
31550	Evaluate the Limit	( limit as x approaches -1 of 2x^2+7x+5)/(x+1)	$\frac{lim_{x \to - 1} 2 x^{2} + 7 x + 5}{x + 1}$
31551	Evaluate the Limit	( limit as x approaches 1 of fifth root of x-1)/( eighth root of x-1)	$\frac{lim_{x \to 1} \sqrt[5]{x - 1}}{\sqrt[8]{x - 1}}$
31552	Evaluate the Limit	( limit as x approaches 1 of sixth root of x-1)/( cube root of x-1)	$\frac{lim_{x \to 1} \sqrt[6]{x} - 1}{\sqrt[3]{x} - 1}$
31553	Evaluate the Limit	( limit as x approaches 1 of x^100-x^2+x-1)/(x^10-1)	$\frac{lim_{x \to 1} x^{100} - x^{2} + x - 1}{x^{10} - 1}$
31554	Evaluate the Limit	( limit as x approaches 1 of x^100-1)/(x-1)	$\frac{lim_{x \to 1} x^{100} - 1}{x - 1}$
31555	Evaluate the Limit	( limit as x approaches 1 of x^19+x^8-2)/(x-1)	$\frac{lim_{x \to 1} x^{19} + x^{8} - 2}{x - 1}$
31556	Evaluate the Limit	( limit as x approaches -1 of x^(2(2x)+1))/(x^2-3x-4)	$\frac{lim_{x \to - 1} x^{2 (2 x) + 1}}{x^{2} - 3 x - 4}$
31557	Evaluate the Limit	( limit as x approaches 1 of square root of x^2+22- square root of 23)/(x-1)	$\frac{lim_{x \to 1} \sqrt{x^{2} + 22} - \sqrt{23}}{x - 1}$
31558	Evaluate the Limit	( limit as x approaches 1 of square root of x^2-1)/(( square root of x-1)( square root of x-1))	$\frac{lim_{x \to 1} \sqrt{x^{2} - 1}}{(\sqrt{x - 1}) (\sqrt{x - 1})}$
31559	Evaluate the Limit	( limit as x approaches 1 of square root of 2x-1- square root of 3x-2)/(x-1)	$\frac{lim_{x \to 1} \sqrt{2 x - 1} - \sqrt{3 x - 2}}{x - 1}$
31560	Find the Inverse	f(x)=mx	$f (x) = m x$
31561	Evaluate the Limit	( limit as x approaches 0 of sin(9x))/(4x)	$\frac{lim_{x \to 0} \sin (9 x)}{4 x}$
31562	Evaluate the Limit	( limit as x approaches 0 of sin(8x))/(7x)	$\frac{lim_{x \to 0} \sin (8 x)}{7 x}$
31563	Evaluate the Limit	( limit as x approaches 1 of square root of x-1)/( square root of 2x-1-1)	$\frac{lim_{x \to 1} \sqrt{x} - 1}{\sqrt{2 x - 1} - 1}$
31564	Evaluate the Limit	limit as h approaches 0 of ((2+h)^2-4)/h	$lim_{h \to 0} \frac{{(2 + h)}^{2} - 4}{h}$
31565	Evaluate the Limit	( limit as x approaches 0 of sin(x))/(sin(4x))	$\frac{lim_{x \to 0} \sin (x)}{\sin (4 x)}$
31566	Evaluate the Limit	( limit as x approaches 2 of (x^2-2x)-8)/(x^2-5x+6)	$\frac{lim_{x \to 2} (x^{2} - 2 x) - 8}{x^{2} - 5 x + 6}$
31567	Evaluate the Limit	( limit as x approaches 2 of x^2-3x+2)/(x^2+5x-14)	$\frac{lim_{x \to 2} x^{2} - 3 x + 2}{x^{2} + 5 x - 14}$
31568	Evaluate the Limit	( limit as x approaches 2 of x^2-3x+2)/(x-2)	$\frac{lim_{x \to 2} x^{2} - 3 x + 2}{x - 2}$
31569	Evaluate the Limit	limit as h approaches 0 of 5/( square root of 5h+4+4)	$lim_{h \to 0} \frac{5}{\sqrt{5 h + 4} + 4}$
31570	Evaluate the Limit	limit as t approaches 4 of (t^3+9t^2-55t+12)/(t^3-16t)	$lim_{t \to 4} \frac{t^{3} + 9 t^{2} - 55 t + 12}{t^{3} - 16 t}$
31571	Evaluate the Limit	( limit as x approaches 2 of square root of 4x-1-3)/(x-2)	$\frac{lim_{x \to 2} \sqrt{4 x - 1} - 3}{x - 2}$
31572	Evaluate the Limit	limit as x approaches infinity of square root of x^4-7x^2-x^2	$lim_{x \to \infty} \sqrt{x^{4} - 7 x^{2}} - x^{2}$
31573	Evaluate the Limit	limit as x approaches 1/2 of 4x^2tan(pix)	$lim_{x \to \frac{1}{2}} 4 x^{2} \tan (π x)$
31574	Evaluate the Limit	( limit as x approaches 2 of cube root of x^2+4- square root of x^2+6x)/(x^2-4)	$\frac{lim_{x \to 2} \sqrt[3]{x^{2} + 4} - \sqrt{x^{2} + 6 x}}{x^{2} - 4}$
31575	Evaluate the Limit	( limit as x approaches 2 of cube root of 1+13x-3 square root of x-1)/(x-2)	$\frac{lim_{x \to 2} \sqrt[3]{1 + 13 x} - 3 \sqrt{x - 1}}{x - 2}$
31576	Evaluate the Limit	( limit as x approaches 2 of cube root of x- cube root of 2)/(x-2)	$\frac{lim_{x \to 2} \sqrt[3]{x} - \sqrt[3]{2}}{x - 2}$
31577	Evaluate the Limit	( limit as x approaches 2 of ( cube root of x-1)-1)/( square root of 2x+5-3)	$\frac{lim_{x \to 2} (\sqrt[3]{x - 1}) - 1}{\sqrt{2 x + 5} - 3}$
31578	Evaluate the Limit	( limit as x approaches 2 of x^2+2x-5)/(x^2-x+3)	$\frac{lim_{x \to 2} x^{2} + 2 x - 5}{x^{2} - x + 3}$
31579	Evaluate the Limit	( limit as x approaches 2 of x^2+2x-8)/( square root of x^2+5-(x+1))	$\frac{lim_{x \to 2} x^{2} + 2 x - 8}{\sqrt{x^{2}} + 5 - (x + 1)}$
31580	Evaluate the Limit	( limit as x approaches 2 of x^2+3x-4)/(x-2)	$\frac{lim_{x \to 2} x^{2} + 3 x - 4}{x - 2}$
31581	Evaluate the Limit	( limit as x approaches 2 from the left of x^2+x-2)/(\|x+2\|)	$\frac{lim_{x \to 2} x^{2} + x - 2}{\| x + 2 \|}$
31582	Evaluate the Limit	( limit as x approaches -2 of x^3+2x^2-1)/(5-3x)	$\frac{lim_{x \to - 2} x^{3} + 2 x^{2} - 1}{5 - 3 x}$
31583	Evaluate the Limit	( limit as x approaches 2 of x^3+27)/(x-3)	$\frac{lim_{x \to 2} x^{3} + 27}{x - 3}$
31584	Evaluate the Limit	( limit as x approaches 2 of x^2-5x+6)/(x^2+3x-10)	$\frac{lim_{x \to 2} x^{2} - 5 x + 6}{x^{2} + 3 x - 10}$
31585	Evaluate the Limit	( limit as x approaches 2 of x^2-5x+6)/(x^2+6x+8)	$\frac{lim_{x \to 2} x^{2} - 5 x + 6}{x^{2} + 6 x + 8}$
31586	Evaluate the Limit	limit as x approaches 1 of (2x^2-13x-7)/(x^2-7x)	$lim_{x \to 1} \frac{2 x^{2} - 13 x - 7}{x^{2} - 7 x}$
31587	Evaluate the Limit	( limit as x approaches 2 of x^2-x+sin(x))/(2x)	$\frac{lim_{x \to 2} x^{2} - x + \sin (x)}{2 x}$
31588	Evaluate the Limit	( limit as x approaches 2 of x^4-16)/(2x^2-8x+8)	$\frac{lim_{x \to 2} x^{4} - 16}{2 x^{2} - 8 x + 8}$
31589	Evaluate the Limit	( limit as x approaches -2 of x^4-2)/(2x^2-3x+2)	$\frac{lim_{x \to - 2} x^{4} - 2}{2 x^{2} - 3 x + 2}$
31590	Evaluate the Limit	( limit as x approaches -2 of x^4-9)/(2x^2-3x+4)	$\frac{lim_{x \to - 2} x^{4} - 9}{2 x^{2} - 3 x + 4}$
31591	Evaluate the Limit	limit as x approaches 25 of x^(1/2)	$lim_{x \to 25} x^{\frac{1}{2}}$
31592	Evaluate the Limit	( limit as x approaches 2 of xe^2-2e^x)/(x^2-5x+6)	$\frac{lim_{x \to 2} x e^{2} - 2 e^{x}}{x^{2} - 5 x + 6}$
31593	Evaluate the Limit	( limit as x approaches 2 of 1- square root of x+1)/(x-2)	$\frac{lim_{x \to 2} 1 - \sqrt{x + 1}}{x - 2}$
31594	Evaluate the Limit	( limit as x approaches 2 of 2- square root of 2+x)/( square root of 1+4x-3)	$\frac{lim_{x \to 2} 2 - \sqrt{2 + x}}{\sqrt{1 + 4 x - 3}}$
31595	Evaluate the Limit	( limit as x approaches 2 of 2x^2-12x+16)/(x^3+8x^2-48)	$\frac{lim_{x \to 2} 2 x^{2} - 12 x + 16}{x^{3} + 8 x^{2} - 48}$
31596	Evaluate the Limit	limit as x approaches infinity of (arctan(x))/((1/x)-2)	$lim_{x \to \infty} \frac{\arctan (x)}{(\frac{1}{x}) - 2}$
31597	Evaluate the Limit	( limit as x approaches 2 of 2x-1)/(x^2-4)	$\frac{lim_{x \to 2} 2 x - 1}{x^{2} - 4}$
31598	Evaluate the Limit	( limit as x approaches 2 of x-2)/(5- square root of x^2+21)	$\frac{lim_{x \to 2} x - 2}{5 - \sqrt{x^{2} + 21}}$
31599	Evaluate the Limit	( limit as x approaches 2 of x-2)/(x-2)	$\frac{lim_{x \to 2} x - 2}{x - 2}$
31600	Evaluate the Limit	( limit as x approaches 2 of x-3)/(x^2-8)	$\frac{lim_{x \to 2} x - 3}{x^{2} - 8}$