Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
35201	Find Where Increasing/Decreasing Using Derivatives	2x^3-3x^2-336x	$2 x^{3} - 3 x^{2} - 336 x$
35202	Evaluate the Limit	limit as x approaches -8 of 5x^2+6x	$lim_{x \to - 8} 5 x^{2} + 6 x$
35203	Evaluate the Limit	limit as x approaches 8 of -5x^6-6x^4-x^3+7x	$lim_{x \to 8} - 5 x^{6} - 6 x^{4} - x^{3} + 7 x$
35204	Evaluate the Limit	limit as x approaches 8 of 5xe^(1/x)-5x	$lim_{x \to 8} 5 x e^{\frac{1}{x}} - 5 x$
35205	Evaluate the Limit	limit as x approaches 8 of 5xe^(-x)-5x	$lim_{x \to 8} 5 x e^{- x} - 5 x$
35206	Evaluate the Limit	limit as x approaches -8 of 5+100/x+(x^3sin(4))/(x^2)	$lim_{x \to - 8} 5 + \frac{100}{x} + \frac{x^{3} \sin (4)}{x^{2}}$
35207	Evaluate the Limit	limit as x approaches 8 of 5+8/x	$lim_{x \to 8} 5 + \frac{8}{x}$
35208	Evaluate the Limit	limit as x approaches 8 of 5x+\|x-8\|	$lim_{x \to 8} 5 x + \| x - 8 \|$
35209	Evaluate the Limit	limit as x approaches 8 of (5x+1)- square root of 25x^2-10x+2	$lim_{x \to 8} (5 x + 1) - \sqrt{25 x^{2} - 10 x + 2}$
35210	Evaluate the Limit	limit as x approaches 8 of cube root of (3x^2+5)/(6x-8)	$lim_{x \to 8} \sqrt[3]{\frac{3 x^{2} + 5}{6 x - 8}}$
35211	Evaluate the Limit	limit as x approaches 8 of cube root of x^3-8x^2-x	$lim_{x \to 8} \sqrt[3]{x^{3} - 8 x^{2} - x}$
35212	Evaluate the Limit	limit as x approaches 8 of square root of x^2-mx- square root of x^2-nx	$lim_{x \to 8} \sqrt{x^{2} - m x} - \sqrt{x^{2} - n x}$
35213	Evaluate the Limit	limit as x approaches 8 of square root of 4x^2+5x-2x	$lim_{x \to 8} \sqrt{4 x^{2} + 5 x} - 2 x$
35214	Evaluate the Limit	limit as x approaches 8 of square root of 4x^4+9x^3-2x^2	$lim_{x \to 8} \sqrt{4 x^{4} + 9 x^{3}} - 2 x^{2}$
35215	Evaluate the Limit	limit as x approaches 8 of ( square root of 18x^2+1*1)/( square root of 32x^2-3)	$lim_{x \to 8} \frac{\sqrt{18 x^{2} + 1} \cdot 1}{\sqrt{32 x^{2} - 3}}$
35216	Evaluate the Limit	limit as x approaches 8 of natural log of (x)^(1/x)	$lim_{x \to 8} \ln ({(x)}^{\frac{1}{x}})$
35217	Evaluate the Limit	limit as x approaches 8 of pi/2-arctan(x) natural log of x	$lim_{x \to 8} \frac{π}{2} - \arctan (x) \ln (x)$
35218	Evaluate the Limit	limit as x approaches infinity of ( square root of 1+4x^6)/(2-x^3)	$lim_{x \to \infty} \frac{\sqrt{1 + 4 x^{6}}}{2 - x^{3}}$
35219	Evaluate the Limit	limit as x approaches 8 of (p+3x)/(px-3)	$lim_{x \to 8} \frac{p + 3 x}{p x - 3}$
35220	Evaluate the Limit	limit as x approaches 8 of (sin(13x))/(16x)	$lim_{x \to 8} \frac{\sin (13 x)}{16 x}$
35221	Evaluate the Limit	limit as x approaches 8 of (sin(13x))/(9x)	$lim_{x \to 8} \frac{\sin (13 x)}{9 x}$
35222	Evaluate the Limit	limit as x approaches 8 of (sin(17x))/(15x)	$lim_{x \to 8} \frac{\sin (17 x)}{15 x}$
35223	Evaluate the Limit	limit as x approaches 8 of (sin(20x))/(15x)	$lim_{x \to 8} \frac{\sin (20 x)}{15 x}$
35224	Evaluate the Limit	limit as x approaches 8 of (tan(x))/x	$lim_{x \to 8} \frac{\tan (x)}{x}$
35225	Evaluate the Limit	limit as x approaches 8 of square root of ((-3)^(x-1))/( square root of x)	$lim_{x \to 8} \sqrt{\frac{{(- 3)}^{x - 1}}{\sqrt{x}}}$
35226	Evaluate the Limit	limit as x approaches 8 of square root of (49x^2)/(6+9x^2)	$lim_{x \to 8} \sqrt{\frac{49 x^{2}}{6 + 9 x^{2}}}$
35227	Evaluate the Limit	limit as x approaches 8 of ( square root of 5/(x+3))(x^2+1)	$lim_{x \to 8} (\sqrt{\frac{5}{x + 3}}) (x^{2} + 1)$
35228	Evaluate the Limit	limit as x approaches 8 of ( square root of x^2+11)-( square root of x^2-9)	$lim_{x \to 8} (\sqrt{x^{2} + 11}) - (\sqrt{x^{2} - 9})$
35229	Evaluate the Limit	limit as x approaches 8 of square root of x^2+16- square root of x^2-9	$lim_{x \to 8} \sqrt{x^{2} + 16} - \sqrt{x^{2} - 9}$
35230	Evaluate the Limit	limit as x approaches 8 of ( square root of x^2+3)-x	$lim_{x \to 8} (\sqrt{x^{2} + 3}) - x$
35231	Evaluate the Limit	limit as x approaches 8 of square root of x^2+3-x	$lim_{x \to 8} \sqrt{x^{2} + 3} - x$
35232	Evaluate the Limit	limit as x approaches 8 of square root of x^2+4- square root of x^2-6	$lim_{x \to 8} \sqrt{x^{2} + 4} - \sqrt{x^{2} - 6}$
35233	Evaluate the Limit	limit as x approaches 8 of (sin(5x))/(14x)	$lim_{x \to 8} \frac{\sin (5 x)}{14 x}$
35234	Evaluate the Limit	limit as x approaches 8 of square root of x^2-2x-1- square root of x^2-7x+3	$lim_{x \to 8} \sqrt{x^{2} - 2 x - 1} - \sqrt{x^{2} - 7 x + 3}$
35235	Find the Concavity	f(x)=(x^2)/(x^2-25)	$f (x) = \frac{x^{2}}{x^{2} - 25}$
35236	Evaluate the Limit	limit as x approaches 8 of square root of x^2+ax- square root of x^2+bx	$lim_{x \to 8} \sqrt{x^{2} + a x} - \sqrt{x^{2} + b} x$
35237	Evaluate the Limit	limit as x approaches 8 of square root of x^2+sx- square root of x^2+tx	$lim_{x \to 8} \sqrt{x^{2} + s x} - \sqrt{x^{2} + t x}$
35238	Find the Concavity	f(x)=(x+5)^(6/7)	$f (x) = {(x + 5)}^{\frac{6}{7}}$
35239	Evaluate the Limit	limit as x approaches 8 of (3x)/(7x-1)	$lim_{x \to 8} \frac{3 x}{7 x - 1}$
35240	Evaluate the Limit	limit as x approaches 8 of (3x+2)/(x-1)	$lim_{x \to 8} \frac{3 x + 2}{x - 1}$
35241	Evaluate the Limit	limit as x approaches 8 of (3x-8)/(x^2+2x-6)	$lim_{x \to 8} \frac{3 x - 8}{x^{2} + 2 x - 6}$
35242	Evaluate the Limit	limit as x approaches 8 of (4-e^x)/(4+3e^x)	$lim_{x \to 8} \frac{4 - e^{x}}{4 + 3 e^{x}}$
35243	Evaluate the Limit	limit as x approaches 8 of (4e^x+8)/(3e^x+7)	$lim_{x \to 8} \frac{4 e^{x} + 8}{3 e^{x} + 7}$
35244	Evaluate the Limit	limit as x approaches 8 of (4n^2)/(n^2+10000n)	$lim_{x \to 8} \frac{4 n^{2}}{n^{2} + 10000 n}$
35245	Evaluate the Limit	limit as x approaches 8 of (3x^3+5x^2)/(4+9x^3)	$lim_{x \to 8} \frac{3 x^{3} + 5 x^{2}}{4 + 9 x^{3}}$
35246	Evaluate the Limit	limit as x approaches 8 of (3x^4-6x^2)/(7x^4+15)	$lim_{x \to 8} \frac{3 x^{4} - 6 x^{2}}{7 x^{4} + 15}$
35247	Evaluate the Limit	limit as x approaches 8 of (3x^4-7x-8)/(7x^3-3x-9)	$lim_{x \to 8} \frac{3 x^{4} - 7 x - 8}{7 x^{3} - 3 x - 9}$
35248	Evaluate the Limit	limit as x approaches -8 of 3/x-x/5	$lim_{x \to - 8} \frac{3}{x} - \frac{x}{5}$
35249	Evaluate the Limit	limit as x approaches 8 of 3^(-2x)+3	$lim_{x \to 8} 3^{- 2 x} + 3$
35250	Evaluate the Limit	limit as x approaches 8 of (32x^4-x^3+x+12)/(8x^4+2x^3+x^2+5x+2)	$lim_{x \to 8} \frac{32 x^{4} - x^{3} + x + 12}{8 x^{4} + 2 x^{3} + x^{2} + 5 x + 2}$
35251	Evaluate the Limit	limit as x approaches 8 of (3e^(2x))/(2e^(2x)-e^(3x))	$lim_{x \to 8} \frac{3 e^{2 x}}{2 e^{2 x} - e^{3 x}}$
35252	Evaluate the Limit	limit as x approaches 8 of (3n^3-5n)/(n^3-2n^2+1)	$lim_{x \to 8} \frac{3 n^{3} - 5 n}{n^{3} - 2 n^{2} + 1}$
35253	Evaluate the Limit	limit as x approaches 8 of (3x^2+2x-7)/(x^2-4)	$lim_{x \to 8} \frac{3 x^{2} + 2 x - 7}{x^{2} - 4}$
35254	Evaluate the Limit	limit as x approaches 8 of (-3x^2+5-7)/(4x^2-2x+100)	$lim_{x \to 8} \frac{- 3 x^{2} + 5 - 7}{4 x^{2} - 2 x + 100}$
35255	Evaluate the Limit	limit as x approaches 8 of (3x^2-5x^3+600)/(15x^3+25x^2-13x+2120)	$lim_{x \to 8} \frac{3 x^{2} - 5 x^{3} + 600}{15 x^{3} + 25 x^{2} - 13 x + 2120}$
35256	Evaluate the Limit	limit as x approaches 0 of (5^(2x)-1)/(5^x-1)	$lim_{x \to 0} \frac{5^{2 x} - 1}{5^{x} - 1}$
35257	Evaluate the Limit	limit as x approaches 8 of (2x+tan(2x))/(3x-tan(5x))	$lim_{x \to 8} \frac{2 x + \tan (2 x)}{3 x - \tan (5 x)}$
35258	Evaluate the Limit	limit as x approaches 8 of (2x-5)/(3x+7)	$lim_{x \to 8} \frac{2 x - 5}{3 x + 7}$
35259	Evaluate the Limit	limit as x approaches 8 of (-10x^2+85x+40)/(x-8)	$lim_{x \to 8} \frac{- 10 x^{2} + 85 x + 40}{x - 8}$
35260	Evaluate the Limit	limit as x approaches 8 of (10x^3-8x^2-7x)/(8-2x-6x^3)	$lim_{x \to 8} \frac{10 x^{3} - 8 x^{2} - 7 x}{8 - 2 x - 6 x^{3}}$
35261	Evaluate the Limit	limit as x approaches 8 of (10x^4-x^3+x+14)/(2x^2+2x^3+x^2+5x+12)	$lim_{x \to 8} \frac{10 x^{4} - x^{3} + x + 14}{2 x^{2} + 2 x^{3} + x^{2} + 5 x + 12}$
35262	Evaluate the Limit	limit as x approaches 8 of (10-2x)/(x^2-5x)	$lim_{x \to 8} \frac{10 - 2 x}{x^{2} - 5 x}$
35263	Evaluate the Limit	limit as x approaches -8 of (-11x^2+4x-3)/(18x^2+10x+14)	$lim_{x \to - 8} \frac{- 11 x^{2} + 4 x - 3}{18 x^{2} + 10 x + 14}$
35264	Evaluate the Limit	limit as x approaches 8 of (1-2x^3)/(x+1)	$lim_{x \to 8} \frac{1 - 2 x^{3}}{x + 1}$
35265	Evaluate the Limit	limit as x approaches 8 of (12x^3-5x+3)/(1+4x^2+3x^3)	$lim_{x \to 8} \frac{12 x^{3} - 5 x + 3}{1 + 4 x^{2} + 3 x^{3}}$
35266	Evaluate the Limit	limit as x approaches -8 of (12x^5-3)/(2x^5-4x^4)	$lim_{x \to - 8} \frac{12 x^{5} - 3}{2 x^{5} - 4 x^{4}}$
35267	Evaluate the Limit	limit as x approaches 8 of (1-2x)/(3x+5)	$lim_{x \to 8} \frac{1 - 2 x}{3 x + 5}$
35268	Evaluate the Limit	limit as x approaches -8 of (-14x^2-3x+17)/(-6x^2+8x+13)	$lim_{x \to - 8} \frac{- 14 x^{2} - 3 x + 17}{- 6 x^{2} + 8 x + 13}$
35269	Evaluate the Limit	limit as x approaches 8 of (17x^3*(2x)-13)/(14x^3+5x+25)	$lim_{x \to 8} \frac{17 x^{3} \cdot (2 x) - 13}{14 x^{3} + 5 x + 25}$
35270	Evaluate the Limit	limit as x approaches -8 of (18x)/(x-3)-(2x)/(x+6)	$lim_{x \to - 8} \frac{18 x}{x - 3} - \frac{2 x}{x + 6}$
35271	Evaluate the Limit	limit as x approaches 8 of (2x^2+3x-5)/(7x^3-2x^2+1)	$lim_{x \to 8} \frac{2 x^{2} + 3 x - 5}{7 x^{3} - 2 x^{2} + 1}$
35272	Evaluate the Limit	limit as x approaches -8 of (2x^2+7)/(x-5)+(3-4x^2)/(2x+7)	$lim_{x \to - 8} \frac{2 x^{2} + 7}{x - 5} + \frac{3 - 4 x^{2}}{2 x + 7}$
35273	Evaluate the Limit	limit as x approaches 8 of (2x^2-4x-3)/(x^2+x-3)	$lim_{x \to 8} \frac{2 x^{2} - 4 x - 3}{x^{2} + x - 3}$
35274	Evaluate the Limit	limit as x approaches 8 of (2x^2-6)/(3x^2+96x)	$lim_{x \to 8} \frac{2 x^{2} - 6}{3 x^{2} + 96 x}$
35275	Evaluate the Limit	limit as x approaches 8 of (2x^2-7x)/(9x^2+5x-6)	$lim_{x \to 8} \frac{2 x^{2} - 7 x}{9 x^{2} + 5 x - 6}$
35276	Evaluate the Limit	limit as x approaches 8 of (2x^2-7x+6)/(3x^2+5x-4)	$lim_{x \to 8} \frac{2 x^{2} - 7 x + 6}{3 x^{2} + 5 x - 4}$
35277	Evaluate the Limit	limit as x approaches 8 of (2x^3)/(x^2+1)	$lim_{x \to 8} \frac{2 x^{3}}{x^{2} + 1}$
35278	Evaluate the Limit	limit as x approaches 8 of (2x^3+3)/(4-x-3x^2)	$lim_{x \to 8} \frac{2 x^{3} + 3}{4 - x - 3 x^{2}}$
35279	Evaluate the Limit	limit as x approaches 8 of (2x^3+8)/(4x^3+ square root of 64x^6+3)	$lim_{x \to 8} \frac{2 x^{3} + 8}{4 x^{3} + \sqrt{64 x^{6} + 3}}$
35280	Evaluate the Limit	limit as x approaches 8 of (2x^3-3x+2)/((3x^2+1)^3)	$lim_{x \to 8} \frac{2 x^{3} - 3 x + 2}{{(3 x^{2} + 1)}^{3}}$
35281	Evaluate the Limit	limit as x approaches -8 of (2x^4+20x^3)/(1000x^3+7)	$lim_{x \to - 8} \frac{2 x^{4} + 20 x^{3}}{1000 x^{3} + 7}$
35282	Evaluate the Limit	limit as x approaches 8 of 2/x-x/9	$lim_{x \to 8} \frac{2}{x} - \frac{x}{9}$
35283	Evaluate the Limit	limit as x approaches 8 of 2/x-15	$lim_{x \to 8} \frac{2}{x} - 15$
35284	Evaluate the Limit	limit as x approaches 8 of (2+4(3^x))/(3-6*3^x)	$lim_{x \to 8} \frac{2 + 4 (3^{x})}{3 - 6 \cdot 3^{x}}$
35285	Evaluate the Limit	limit as x approaches 8 of (20x^4-x^3+x+9)/(5x^4+2x^3+x^2+5x+9)	$lim_{x \to 8} \frac{20 x^{4} - x^{3} + x + 9}{5 x^{4} + 2 x^{3} + x^{2} + 5 x + 9}$
35286	Evaluate the Limit	limit as x approaches 8 of (x^2-11x+24)/(x^2-12x+32)	$lim_{x \to 8} \frac{x^{2} - 11 x + 24}{x^{2} - 12 x + 32}$
35287	Evaluate the Limit	limit as x approaches -8 of (x^2-2x+5)/(3x-2)	$lim_{x \to - 8} \frac{x^{2} - 2 x + 5}{3 x - 2}$
35288	Evaluate the Limit	limit as x approaches 8 of (x^2-4x+3)/(x-1)	$lim_{x \to 8} \frac{x^{2} - 4 x + 3}{x - 1}$
35289	Evaluate the Limit	limit as x approaches -8 of (x^2-5)/(8-x)	$lim_{x \to - 8} \frac{x^{2} - 5}{8 - x}$
35290	Evaluate the Limit	limit as x approaches 8 of (x^2-64)/(x^2-8x)	$lim_{x \to 8} \frac{x^{2} - 64}{x^{2} - 8 x}$
35291	Evaluate the Limit	limit as x approaches -8 of (x^2+2x)/( square root of 1+x^2)-x	$lim_{x \to - 8} \frac{x^{2} + 2 x}{\sqrt{1 + x^{2}}} - x$
35292	Evaluate the Limit	limit as x approaches 8 of (x^2+2x-15)/(x-3)	$lim_{x \to 8} \frac{x^{2} + 2 x - 15}{x - 3}$
35293	Evaluate the Limit	limit as x approaches 8 of (x^2+3x+5)/(4x+1+x^k)	$lim_{x \to 8} \frac{x^{2} + 3 x + 5}{4 x + 1 + x^{k}}$
35294	Evaluate the Limit	limit as x approaches 8 of (x^2+64)/(x-8)	$lim_{x \to 8} \frac{x^{2} + 64}{x - 8}$
35295	Evaluate the Limit	limit as x approaches 8 of ( square root of 9x^2+2)/(4x+3)	$lim_{x \to 8} \frac{\sqrt{9 x^{2} + 2}}{4 x + 3}$
35296	Evaluate the Limit	limit as x approaches 8 of ( square root of 81x^2-2)/(6-3x^2)	$lim_{x \to 8} \frac{\sqrt{81 x^{2} - 2}}{6 - 3 x^{2}}$
35297	Evaluate the Limit	limit as x approaches 8 of ( square root of x+28-6)/(x-8)	$lim_{x \to 8} \frac{\sqrt{x + 28} - 6}{x - 8}$
35298	Evaluate the Limit	limit as x approaches -8 of ( cube root of x^6+64)/(4x^2+ square root of 7x^4+16)	$lim_{x \to - 8} \frac{\sqrt[3]{x^{6} + 64}}{4 x^{2} + \sqrt{7 x^{4} + 16}}$
35299	Evaluate the Limit	limit as x approaches -8 of ( cube root of x)/p+(x^3)/( square root of x+44)	$lim_{x \to - 8} \frac{\sqrt[3]{x}}{p} + \frac{x^{3}}{\sqrt{x + 44}}$
35300	Evaluate the Limit	limit as x approaches 1 of (x^6-1)/(x^10-1)	$lim_{x \to 1} \frac{x^{6} - 1}{x^{10} - 1}$