Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
34101	Evaluate the Limit	limit as x approaches -8 of (5x^3+16x^2+45)/(9x^3+6x+11)	$lim_{x \to - 8} \frac{5 x^{3} + 16 x^{2} + 45}{9 x^{3} + 6 x + 11}$
34102	Evaluate the Limit	limit as x approaches -8 of (5x^3+27)/(20x^2+10x+9)	$lim_{x \to - 8} \frac{5 x^{3} + 27}{20 x^{2} + 10 x + 9}$
34103	Evaluate the Limit	limit as x approaches 8 of (5x^3-6x-9)/(6x^2-3x-4)	$lim_{x \to 8} \frac{5 x^{3} - 6 x - 9}{6 x^{2} - 3 x - 4}$
34104	Evaluate the Limit	limit as x approaches 8 of (5x^4+8x^2)/(3x^4-16x^2)	$lim_{x \to 8} \frac{5 x^{4} + 8 x^{2}}{3 x^{4} - 16 x^{2}}$
34105	Evaluate the Limit	limit as x approaches 8 of (-5+5/x)/(9-2/(x^2))	$lim_{x \to 8} \frac{- 5 + \frac{5}{x}}{9 - \frac{2}{x^{2}}}$
34106	Evaluate the Limit	limit as x approaches 8 of (5+4x)/(11-6x)	$lim_{x \to 8} \frac{5 + 4 x}{11 - 6 x}$
34107	Evaluate the Limit	limit as x approaches 8 of (-5x)/( square root of 49x^2+4)	$lim_{x \to 8} \frac{- 5 x}{\sqrt{49 x^{2} + 4}}$
34108	Evaluate the Limit	limit as a approaches 8 of (5a+10)/(5a^2-7a+10)	$lim_{a \to 8} \frac{5 a + 10}{5 a^{2} - 7 a + 10}$
34109	Evaluate the Limit	limit as x approaches -8 of (5x-4)/(x^2+6x+6)	$lim_{x \to - 8} \frac{5 x - 4}{x^{2} + 6 x + 6}$
34110	Evaluate the Limit	limit as x approaches -8 of 6/(e^x-3)	$lim_{x \to - 8} \frac{6}{e^{x} - 3}$
34111	Evaluate the Limit	limit as x approaches -8 of (6x^3+2x^2)/(x-6x^2)	$lim_{x \to - 8} \frac{6 x^{3} + 2 x^{2}}{x - 6 x^{2}}$
34112	Evaluate the Limit	limit as x approaches 8 of (6x^3-3x+2)/(9x^3-5)	$lim_{x \to 8} \frac{6 x^{3} - 3 x + 2}{9 x^{3} - 5}$
34113	Evaluate the Limit	limit as x approaches 8 of (6-2x)/((1-x^2)*(x-3))	$lim_{x \to 8} \frac{6 - 2 x}{(1 - x^{2}) \cdot (x - 3)}$
34114	Evaluate the Limit	limit as x approaches 8 of (6-3x^2)/(6x-4)	$lim_{x \to 8} \frac{6 - 3 x^{2}}{6 x - 4}$
34115	Evaluate the Limit	limit as x approaches 8 of (6-cos(x))/(x^3)	$lim_{x \to 8} \frac{6 - \cos (x)}{x^{3}}$
34116	Evaluate the Limit	limit as x approaches 8 of (6x+1)/(\|6-2x\|)	$lim_{x \to 8} \frac{6 x + 1}{\| 6 - 2 x \|}$
34117	Evaluate the Limit	limit as x approaches 8 of (6x+8)/(5x-6)	$lim_{x \to 8} \frac{6 x + 8}{5 x - 6}$
34118	Evaluate the Limit	limit as x approaches 8 of ((6x-2)(2x-3))/((3x+2)(4x-1)(x-1))	$lim_{x \to 8} \frac{(6 x - 2) (2 x - 3)}{(3 x + 2) (4 x - 1) (x - 1)}$
34119	Evaluate the Limit	limit as x approaches 8 of (6x-8)/(5-x^2)	$lim_{x \to 8} \frac{6 x - 8}{5 - x^{2}}$
34120	Evaluate the Limit	limit as x approaches 8 of (7x^10+5x-4)/(8x^10-10x^2+12)	$lim_{x \to 8} \frac{7 x^{10} + 5 x - 4}{8 x^{10} - 10 x^{2} + 12}$
34121	Evaluate the Limit	limit as x approaches 8 of (7x^2)/(e^x)	$lim_{x \to 8} \frac{7 x^{2}}{e^{x}}$
34122	Evaluate the Limit	limit as x approaches -8 of (7x^3+x+3)/(8x^2-5x+2)	$lim_{x \to - 8} \frac{7 x^{3} + x + 3}{8 x^{2} - 5 x + 2}$
34123	Evaluate the Limit	limit as x approaches 8 of ( square root of x^2+7x)/(2-13x)	$lim_{x \to 8} \frac{\sqrt{x^{2} + 7 x}}{2 - 13 x}$
34124	Evaluate the Limit	limit as x approaches 8 of (x+x^2)/(1-4x^2)	$lim_{x \to 8} \frac{x + x^{2}}{1 - 4 x^{2}}$
34125	Evaluate the Limit	limit as x approaches 8 of (x+x^2)/(3-5x^2)	$lim_{x \to 8} \frac{x + x^{2}}{3 - 5 x^{2}}$
34126	Evaluate the Limit	limit as x approaches 1 of (x^2-4x+3)/(x-1)	$lim_{x \to 1} \frac{x^{2} - 4 x + 3}{x - 1}$
34127	Evaluate the Limit	limit as h approaches 0 of ((3+h)^2-9)/h	$lim_{h \to 0} \frac{{(3 + h)}^{2} - 9}{h}$
34128	Evaluate the Limit	limit as x approaches 8 of (x+2)/( square root of 16x^2+1)	$lim_{x \to 8} \frac{x + 2}{\sqrt{16 x^{2} + 1}}$
34129	Evaluate the Limit	limit as x approaches -8 of (x+2)/( square root of 7+6x^2)	$lim_{x \to - 8} \frac{x + 2}{\sqrt{7 + 6 x^{2}}}$
34130	Evaluate the Limit	limit as x approaches 8 of (x+5)/(15+x)	$lim_{x \to 8} \frac{x + 5}{15 + x}$
34131	Evaluate the Limit	limit as x approaches -8 of (x+sin(x))/(2x+7-5sin(x))	$lim_{x \to - 8} \frac{x + \sin (x)}{2 x + 7 - 5 \sin (x)}$
34132	Evaluate the Limit	limit as x approaches -8 of (x-1)^3	$lim_{x \to - 8} {(x - 1)}^{3}$
34133	Evaluate the Limit	limit as x approaches 8 of ((x-2)(2x-3))/((3x+2)(4x-1))	$lim_{x \to 8} \frac{(x - 2) (2 x - 3)}{(3 x + 2) (4 x - 1)}$
34134	Evaluate the Limit	limit as x approaches -8 of (x-6)/(x^2+4)	$lim_{x \to - 8} \frac{x - 6}{x^{2} + 4}$
34135	Evaluate the Limit	limit as x approaches 8 of (7x^3-5x^2-10x)/(4-3x-5x^3)	$lim_{x \to 8} \frac{7 x^{3} - 5 x^{2} - 10 x}{4 - 3 x - 5 x^{3}}$
34136	Evaluate the Limit	limit as x approaches 8 of (7x^3-6x^2-9x)/(5-4x-4x^3)	$lim_{x \to 8} \frac{7 x^{3} - 6 x^{2} - 9 x}{5 - 4 x - 4 x^{3}}$
34137	Evaluate the Limit	limit as x approaches 8 of (7+5^x+3^(-x))/(13+5^x+9^(-x))	$lim_{x \to 8} \frac{7 + 5^{x} + 3^{- x}}{13 + 5^{x} + 9^{- x}}$
34138	Evaluate the Limit	limit as x approaches 8 of (7+x^3)/(3-x^2-2x^3)	$lim_{x \to 8} \frac{7 + x^{3}}{3 - x^{2} - 2 x^{3}}$
34139	Evaluate the Limit	limit as x approaches 8 of (7sin(x)+3)/(sin(x)-1)	$lim_{x \to 8} \frac{7 \sin (x) + 3}{\sin (x) - 1}$
34140	Evaluate the Limit	limit as x approaches 8 of (7x)/(9x-9)	$lim_{x \to 8} \frac{7 x}{9 x - 9}$
34141	Evaluate the Limit	limit as x approaches 8 of (7x)/( square root of 81x^2+4)	$lim_{x \to 8} \frac{7 x}{\sqrt{81 x^{2} + 4}}$
34142	Evaluate the Limit	limit as x approaches 8 of (7x)/(4x-8)	$lim_{x \to 8} \frac{7 x}{4 x - 8}$
34143	Evaluate the Limit	limit as x approaches -8 of (7x+9)/(3x-11)	$lim_{x \to - 8} \frac{7 x + 9}{3 x - 11}$
34144	Evaluate the Limit	limit as x approaches 8 of (7x-5)/(2x+8)	$lim_{x \to 8} \frac{7 x - 5}{2 x + 8}$
34145	Evaluate the Limit	limit as x approaches 8 of (7x-5)/(4x+9)	$lim_{x \to 8} \frac{7 x - 5}{4 x + 9}$
34146	Evaluate the Limit	limit as x approaches -8 of (7x-6)/x	$lim_{x \to - 8} \frac{7 x - 6}{x}$
34147	Evaluate the Limit	limit as x approaches 8 of (8)^(-1/x)	$lim_{x \to 8} {(8)}^{- \frac{1}{x}}$
34148	Evaluate the Limit	limit as x approaches 8 of (8x^2-7x+9)/(2x^2+1)	$lim_{x \to 8} \frac{8 x^{2} - 7 x + 9}{2 x^{2} + 1}$
34149	Evaluate the Limit	limit as x approaches 8 of (8+5x)/(2x^2+5)	$lim_{x \to 8} \frac{8 + 5 x}{2 x^{2} + 5}$
34150	Evaluate the Limit	limit as x approaches 8 of (8x)/(48x+5)	$lim_{x \to 8} \frac{8 x}{48 x + 5}$
34151	Evaluate the Limit	limit as x approaches -8 of (8x-15)/( square root of 4x^2+11)	$lim_{x \to - 8} \frac{8 x - 15}{\sqrt{4 x^{2} + 11}}$
34152	Evaluate the Limit	limit as x approaches 8 of (8x-2)/(6x+5)	$lim_{x \to 8} \frac{8 x - 2}{6 x + 5}$
34153	Evaluate the Limit	limit as x approaches 8 of (-8x-9)/( square root of x^2+9x+5)	$lim_{x \to 8} \frac{- 8 x - 9}{\sqrt{x^{2} + 9 x + 5}}$
34154	Evaluate the Limit	limit as x approaches -8 of (9x^6-x)/((x^3+1)( square root of 9x^6-x))	$lim_{x \to - 8} \frac{9 x^{6} - x}{(x^{3} + 1) (\sqrt{9 x^{6} - x})}$
34155	Evaluate the Limit	limit as x approaches 8 of (9-4y^2)/(9y^2+2y)	$lim_{x \to 8} \frac{9 - 4 y^{2}}{9 y^{2} + 2 y}$
34156	Evaluate the Limit	limit as x approaches 8 of (9-x)/((x-8)^2)	$lim_{x \to 8} \frac{9 - x}{{(x - 8)}^{2}}$
34157	Evaluate the Limit	limit as x approaches 8 of (3x^3+7x-6)/(7x^4-5x^3-4)	$lim_{x \to 8} \frac{3 x^{3} + 7 x - 6}{7 x^{4} - 5 x^{3} - 4}$
34158	Evaluate the Limit	limit as x approaches 8 of (3x^3+7x-9)/(8x^4-4x^3-2)	$lim_{x \to 8} \frac{3 x^{3} + 7 x - 9}{8 x^{4} - 4 x^{3} - 2}$
34159	Evaluate the Limit	limit as x approaches 8 of (3x^3+x+6)/(2x^2-3)	$lim_{x \to 8} \frac{3 x^{3} + x + 6}{2 x^{2} - 3}$
34160	Evaluate the Limit	limit as x approaches 8 of (3x^4-2x+1)/(7x-8x^5-1)	$lim_{x \to 8} \frac{3 x^{4} - 2 x + 1}{7 x - 8 x^{5} - 1}$
34161	Evaluate the Limit	limit as x approaches infinity of e^(-7x)cos(x)	$lim_{x \to \infty} e^{- 7 x} \cos (x)$
34162	Evaluate the Limit	limit as x approaches 8 of (3x^4-3x^3-60x^2)/(x^4-41x^2+400)	$lim_{x \to 8} \frac{3 x^{4} - 3 x^{3} - 60 x^{2}}{x^{4} - 41 x^{2} + 400}$
34163	Evaluate the Limit	limit as x approaches 8 of (3x^5+1)/(2x^7+3)	$lim_{x \to 8} \frac{3 x^{5} + 1}{2 x^{7} + 3}$
34164	Evaluate the Limit	limit as x approaches 8 of (3-4x-2x^3)/(7x^3-6x-11)	$lim_{x \to 8} \frac{3 - 4 x - 2 x^{3}}{7 x^{3} - 6 x - 11}$
34165	Evaluate the Limit	limit as x approaches 8 of (3-5n^2)/(n^2+n)	$lim_{x \to 8} \frac{3 - 5 n^{2}}{n^{2} + n}$
34166	Evaluate the Limit	limit as x approaches 8 of (38x^3)/(sin(3x)-3x)	$lim_{x \to 8} \frac{38 x^{3}}{\sin (3 x) - 3 x}$
34167	Evaluate the Limit	limit as x approaches -8 of (3x)/( square root of x^2-4)	$lim_{x \to - 8} \frac{3 x}{\sqrt{x^{2} - 4}}$
34168	Evaluate the Limit	limit as x approaches 8 of ((3x+1)(2x-3))/((5x-2)(x+4))	$lim_{x \to 8} \frac{(3 x + 1) (2 x - 3)}{(5 x - 2) (x + 4)}$
34169	Evaluate the Limit	limit as x approaches 9 of natural log of (3- square root of x)/(9-x)	$lim_{x \to 9} \ln (\frac{3 - \sqrt{x}}{9 - x})$
34170	Evaluate the Limit	limit as x approaches 0 of (sin(x))/(4x)	$lim_{x \to 0} \frac{\sin (x)}{4 x}$
34171	Evaluate the Limit	limit as x approaches 8 of ((3x-1)(x^2-4))/((2x+1)^2(x-1))	$lim_{x \to 8} \frac{(3 x - 1) \cdot (x^{2} - 4)}{{(2 x + 1)}^{2} \cdot (x - 1)}$
34172	Evaluate the Limit	limit as x approaches 8 of (3x-2)/( square root of 2x^2-3)	$lim_{x \to 8} \frac{3 x - 2}{\sqrt{2 x^{2} - 3}}$
34173	Evaluate the Limit	limit as x approaches 8 of (3x-8x^3)/(7x-8)	$lim_{x \to 8} \frac{3 x - 8 x^{3}}{7 x - 8}$
34174	Evaluate the Limit	limit as x approaches 8 of (43^20+2^19-4)/(53^19+2^21+1)	$lim_{x \to 8} \frac{4 \cdot 3^{20} + 2^{19} - 4}{5 \cdot 3^{19} + 2^{21} + 1}$
34175	Evaluate the Limit	limit as x approaches 8 of (4x^2)/( square root of 9x^4-1)	$lim_{x \to 8} \frac{4 x^{2}}{\sqrt{9 x^{4} - 1}}$
34176	Evaluate the Limit	limit as x approaches 8 of (4x^2+3x^2-7)/(5x^2+2x+1)	$lim_{x \to 8} \frac{4 x^{2} + 3 x^{2} - 7}{5 x^{2} + 2 x + 1}$
34177	Evaluate the Limit	limit as x approaches 8 of (3x^3-4^2-5x-2x^5)/(6x^5-x-2)	$lim_{x \to 8} \frac{3 x^{3} - 4^{2} - 5 x - 2 x^{5}}{6 x^{5} - x - 2}$
34178	Evaluate the Limit	limit as x approaches -8 of (3x^3+13x^2+12x)/(x^3+3x^2)	$lim_{x \to - 8} \frac{3 x^{3} + 13 x^{2} + 12 x}{x^{3} + 3 x^{2}}$
34179	Evaluate the Limit	limit as x approaches 8 of (3e^(5/x)-3)/(pi-2arctan(x))	$lim_{x \to 8} \frac{3 e^{\frac{5}{x}} - 3}{π - 2 \arctan (x)}$
34180	Evaluate the Limit	limit as x approaches 8 of (3e^(2x))/(-e^(3x))	$lim_{x \to 8} \frac{3 e^{2 x}}{- e^{3 x}}$
34181	Evaluate the Limit	limit as x approaches -8 of (2x^3+3x-2)/(x^2+5)	$lim_{x \to - 8} \frac{2 x^{3} + 3 x - 2}{x^{2} + 5}$
34182	Evaluate the Limit	limit as x approaches 8 of ( square root of 16x^2-5)/(4x-5)	$lim_{x \to 8} \frac{\sqrt{16 x^{2} - 5}}{4 x - 5}$
34183	Evaluate the Limit	limit as x approaches 8 of ( square root of x^3+2x^2+ square root of 3x^5-x)/(x^3+x^4)	$lim_{x \to 8} \frac{\sqrt{x^{3} + 2 x^{2}} + \sqrt{3 x^{5} - x}}{x^{3} + x^{4}}$
34184	Evaluate the Limit	limit as x approaches 8 of 1/x-10/(x+83)	$lim_{x \to 8} \frac{1}{x} - \frac{10}{x + 83}$
34185	Evaluate the Limit	limit as x approaches -8 of 1/x-8/(x+33)	$lim_{x \to - 8} \frac{1}{x} - \frac{8}{x + 33}$
34186	Evaluate the Limit	limit as x approaches 8 of 1/x-9/(x+93)	$lim_{x \to 8} \frac{1}{x} - \frac{9}{x + 93}$
34187	Evaluate the Limit	limit as x approaches 8 of (8x+3x-3)/( square root of 4x^2+x^2+x-2)	$lim_{x \to 8} \frac{8 x + 3 x - 3}{\sqrt{4 x^{2}} + x^{2} + x - 2}$
34188	Evaluate the Limit	limit as x approaches 8 of natural log of (x+1)^x- natural log of (x)^x	$lim_{x \to 8} \ln ({(x + 1)}^{x}) - \ln ({(x)}^{x})$
34189	Evaluate the Limit	limit as x approaches 8 of square root of x^2+5x- square root of x^2-3x	$lim_{x \to 8} \sqrt{x^{2} + 5 x} - \sqrt{x^{2} - 3 x}$
34190	Evaluate the Limit	limit as x approaches 8 of 729-729(2n^3+3n^2+n)/(6n^3)	$lim_{x \to 8} 729 - 729 \frac{2 n^{3} + 3 n^{2} + n}{6 n^{3}}$
34191	Evaluate the Limit	limit as x approaches 7 of (\|x-7\|)/(x-7)	$lim_{x \to 7} \frac{\| x - 7 \|}{x - 7}$
34192	Evaluate the Limit	limit as x approaches 8 of arctan(x)-arctan(1)	$lim_{x \to 8} \arctan (x) - \arctan (1)$
34193	Evaluate the Limit	limit as x approaches 8 of f(x)g(x)	$lim_{x \to 8} f (x) g (x)$
34194	Evaluate the Limit	limit as x approaches 8 of natural log of x^2-1- natural log of 3x^2+3x	$lim_{x \to 8} \ln (x^{2} - 1) - \ln (3 x^{2} + 3 x)$
34195	Evaluate the Limit	limit as x approaches 8 of ((1/(7.999+1))-(1/9))/(7.999-8)	$lim_{x \to 8} \frac{(\frac{1}{7.999 + 1}) - (\frac{1}{9})}{7.999 - 8}$
34196	Evaluate the Limit	limit as x approaches 8 of ((1/x)-(1/8))/(x-8)	$lim_{x \to 8} \frac{(\frac{1}{x}) - (\frac{1}{8})}{x - 8}$
34197	Evaluate the Limit	limit as x approaches 8 of (0.000001x^5+3x-10)/(x^4-2)	$lim_{x \to 8} \frac{0.000001 x^{5} + 3 x - 10}{x^{4} - 2}$
34198	Evaluate the Limit	limit as x approaches 8 of ((1-x^4)/(x^2+8x))^5	$lim_{x \to 8} {(\frac{1 - x^{4}}{x^{2} + 8 x})}^{5}$
34199	Evaluate the Limit	limit as x approaches 8 of ((16x)/(16x+6))^(5x)	$lim_{x \to 8} {(\frac{16 x}{16 x + 6})}^{5 x}$
34200	Evaluate the Limit	limit as x approaches 8 of ((1-x^4)/(x^2+5x))^5	$lim_{x \to 8} {(\frac{1 - x^{4}}{x^{2} + 5 x})}^{5}$