Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
34201	Evaluate the Limit	limit as x approaches 8 of natural log of 6x+1- natural log of 9x+1	$lim_{x \to 8} \ln (6 x + 1) - \ln (9 x + 1)$
34202	Evaluate the Limit	limit as x approaches 8 of natural log of 7x- natural log of x+8	$lim_{x \to 8} \ln (7 x - \ln (x + 8))$
34203	Evaluate the Limit	limit as x approaches 8 of - natural log of x	$lim_{x \to 8} - \ln (x)$
34204	Evaluate the Limit	limit as x approaches 8 of MattyLovesYou	$lim_{x \to 8} M a t t y L o v e s Y o u$
34205	Evaluate the Limit	limit as x approaches 8 of x square root of x^2+2x-2 square root of x^2+x+x	$lim_{x \to 8} x \sqrt{x^{2} + 2 x} - 2 \sqrt{x^{2} + x} + x$
34206	Evaluate the Limit	limit as x approaches 0 of x/(sin(x))	$lim_{x \to 0} \frac{x}{\sin (x)}$
34207	Evaluate the Limit	limit as x approaches 8 of natural log of square root of 5x^2+2- natural log of x	$lim_{x \to 8} \ln (\sqrt{5 x^{2} + 2}) - \ln (x)$
34208	Evaluate the Limit	limit as x approaches 8 of natural log of 4x- natural log of x+1	$lim_{x \to 8} \ln (4 x) - \ln (x + 1)$
34209	Evaluate the Limit	limit as x approaches 8 of natural log of 4x- natural log of x+5	$lim_{x \to 8} \ln (4 x) - \ln (x + 5)$
34210	Evaluate the Limit	limit as x approaches 8 of x- square root of x^2-2x	$lim_{x \to 8} x - \sqrt{x^{2} - 2 x}$
34211	Evaluate the Limit	limit as x approaches -8 of x+ square root of x^2+2x	$lim_{x \to - 8} x + \sqrt{x^{2} + 2 x}$
34212	Evaluate the Limit	limit as x approaches 8 of x-9	$lim_{x \to 8} x - 9$
34213	Evaluate the Limit	limit as x approaches 8 of ((20x)/(20x+5))^(5x)	$lim_{x \to 8} {(\frac{20 x}{20 x + 5})}^{5 x}$
34214	Evaluate the Limit	limit as x approaches 8 of (2x^2-7x+3)/(5x^2-3x+7)	$lim_{x \to 8} \frac{2 x^{2} - 7 x + 3}{5 x^{2} - 3 x + 7}$
34215	Evaluate the Limit	limit as theta approaches 0 of (cos(9theta)tan(9theta))/theta	$lim_{θ \to 0} \frac{\cos (9 θ) \tan (9 θ)}{θ}$
34216	Evaluate the Limit	limit as x approaches -7 of (1/7+1/x)/(7+x)	$lim_{x \to - 7} \frac{\frac{1}{7} + \frac{1}{x}}{7 + x}$
34217	Evaluate the Limit	limit as x approaches 8 of (5e^(-3x)+e^(3x))/(4e^(-3x)+5e^(3x))	$lim_{x \to 8} \frac{5 e^{- 3 x} + e^{3 x}}{4 e^{- 3 x} + 5 e^{3 x}}$
34218	Evaluate the Limit	limit as x approaches 8 of (9/x-9/8)/(x-8)	$lim_{x \to 8} \frac{\frac{9}{x} - \frac{9}{8}}{x - 8}$
34219	Evaluate the Limit	limit as x approaches 8 of (e^(9/x)-1)/(9/x)	$lim_{x \to 8} \frac{e^{\frac{9}{x}} - 1}{\frac{9}{x}}$
34220	Evaluate the Limit	limit as x approaches 8 of (e^(-2x))/(1/( square root of x))	$lim_{x \to 8} \frac{e^{- 2 x}}{\frac{1}{\sqrt{x}}}$
34221	Evaluate the Limit	limit as x approaches 8 of (e^(2x)+x^2)/(e^(2x)+x)	$lim_{x \to 8} \frac{e^{2 x} + x^{2}}{e^{2 x} + x}$
34222	Evaluate the Limit	limit as y approaches -3 of (y^2+4y+3)/(y^2-3)	$lim_{y \to - 3} \frac{y^{2} + 4 y + 3}{y^{2} - 3}$
34223	Evaluate the Limit	limit as x approaches 8 of (e^(3x)+1)^(1/x)	$lim_{x \to 8} {(e^{3 x} + 1)}^{\frac{1}{x}}$
34224	Evaluate the Limit	limit as x approaches 8 of (e^x-cos(x)^2)/x	$lim_{x \to 8} \frac{e^{x} - \cos^{2} (x)}{x}$
34225	Evaluate the Limit	limit as x approaches 8 of (e^x-e^x)/(e^x+e^x)	$lim_{x \to 8} \frac{e^{x} - e^{x}}{e^{x} + e^{x}}$
34226	Evaluate the Limit	limit as x approaches 8 of (e^x-x)^(1/x)	$lim_{x \to 8} {(e^{x} - x)}^{\frac{1}{x}}$
34227	Evaluate the Limit	limit as x approaches 2 of square root of (4x+10)/(2x-2)	$lim_{x \to 2} \sqrt{\frac{4 x + 10}{2 x - 2}}$
34228	Evaluate the Limit	limit as x approaches 8 of ( natural log of (x)^2)/(2x)	$lim_{x \to 8} \frac{\ln ({(x)}^{2})}{2 x}$
34229	Evaluate the Limit	limit as x approaches -8 of (s^6-2s^3-5s-1)/(4s^4-3s)	$lim_{x \to - 8} \frac{s^{6} - 2 s^{3} - 5 s - 1}{4 s^{4} - 3 s}$
34230	Evaluate the Limit	limit as x approaches 8 of ( square root of x^2+1-x)/1	$lim_{x \to 8} \frac{\sqrt{x^{2} + 1} - x}{1}$
34231	Evaluate the Limit	limit as x approaches 8 of ( square root of x^2+15x)/(6-11x)	$lim_{x \to 8} \frac{\sqrt{x^{2} + 15 x}}{6 - 11 x}$
34232	Evaluate the Limit	limit as x approaches 8 of ( square root of x^2+2)/( square root of 2x^2+1)	$lim_{x \to 8} \frac{\sqrt{x^{2} + 2}}{\sqrt{2 x^{2} + 1}}$
34233	Evaluate the Limit	limit as x approaches 8 of ((1-x^3)/(x^2+8x))^7	$lim_{x \to 8} {(\frac{1 - x^{3}}{x^{2} + 8 x})}^{7}$
34234	Evaluate the Limit	limit as x approaches -8 of ((1-x^4)/(x^2+6x))^5	$lim_{x \to - 8} {(\frac{1 - x^{4}}{x^{2} + 6 x})}^{5}$
34235	Evaluate the Limit	limit as x approaches 8 of (x^101+9^x-e^( square root of x))/(2*9^x-10^6sin(x)+x^25)	$lim_{x \to 8} \frac{x^{101} + 9^{x} - e^{\sqrt{x}}}{2 \cdot 9^{x} - 10^{6} \sin (x) + x^{25}}$
34236	Evaluate the Limit	limit as x approaches 8 of (x^2+1)/(100x+50)	$lim_{x \to 8} \frac{x^{2} + 1}{100 x + 50}$
34237	Evaluate the Limit	limit as x approaches -8 of (x^2+15x+56)/(x+8)	$lim_{x \to - 8} \frac{x^{2} + 15 x + 56}{x + 8}$
34238	Evaluate the Limit	limit as x approaches (5pi)/6 of sin(x)	$lim_{x \to \frac{5 π}{6}} \sin (x)$
34239	Evaluate the Limit	limit as x approaches 8 of (x^2+24x)/(9x^2-16)	$lim_{x \to 8} \frac{x^{2} + 24 x}{9 x^{2} - 16}$
34240	Evaluate the Limit	limit as x approaches 8 of (x^2+2x-80)/(x^2-64)	$lim_{x \to 8} \frac{x^{2} + 2 x - 80}{x^{2} - 64}$
34241	Evaluate the Limit	limit as x approaches 8 of (x^2+8)/(x^3+11)	$lim_{x \to 8} \frac{x^{2} + 8}{x^{3} + 11}$
34242	Evaluate the Limit	limit as x approaches -8 of (x^2+x-56)/(x^2-x-72)	$lim_{x \to - 8} \frac{x^{2} + x - 56}{x^{2} - x - 72}$
34243	Evaluate the Limit	limit as x approaches 8 of (x^2-11x+24)/(x-8)	$lim_{x \to 8} \frac{x^{2} - 11 x + 24}{x - 8}$
34244	Evaluate the Limit	limit as x approaches 8 of (x^2-11x+30)/(x^3-6x^2)	$lim_{x \to 8} \frac{x^{2} - 11 x + 30}{x^{3} - 6 x^{2}}$
34245	Evaluate the Limit	limit as t approaches -5 of (t^2-25)/(2t^2+11t+5)	$lim_{t \to - 5} \frac{t^{2} - 25}{2 t^{2} + 11 t + 5}$
34246	Evaluate the Limit	limit as x approaches 8 of (x^2-6)/(2+x-3x^2)	$lim_{x \to 8} \frac{x^{2} - 6}{2 + x - 3 x^{2}}$
34247	Evaluate the Limit	limit as x approaches 8 of (x^2-64)/(\|x-8\|)	$lim_{x \to 8} \frac{x^{2} - 64}{\| x - 8 \|}$
34248	Evaluate the Limit	limit as x approaches 8 of (x^2-64)/(8-x)	$lim_{x \to 8} \frac{x^{2} - 64}{8 - x}$
34249	Evaluate the Limit	limit as x approaches -8 of ( square root of 16x^2+x-1)/(3-x)	$lim_{x \to - 8} \frac{\sqrt{16 x^{2} + x - 1}}{3 - x}$
34250	Evaluate the Limit	limit as x approaches 8 of ( square root of 3x^2-1)/(5x-2)	$lim_{x \to 8} \frac{\sqrt{3 x^{2} - 1}}{5 x - 2}$
34251	Evaluate the Limit	limit as x approaches -8 of ( square root of 4x^6-x)/(x^3+1)	$lim_{x \to - 8} \frac{\sqrt{4 x^{6} - x}}{x^{3} + 1}$
34252	Evaluate the Limit	limit as x approaches 8 of ( square root of 5+4x^2)/(6+10x)	$lim_{x \to 8} \frac{\sqrt{5 + 4 x^{2}}}{6 + 10 x}$
34253	Evaluate the Limit	limit as x approaches 8 of ( square root of x^4+3)/(3x^2+4)	$lim_{x \to 8} \frac{\sqrt{x^{4} + 3}}{3 x^{2} + 4}$
34254	Evaluate the Limit	limit as x approaches 8 of (e^x+x)^(3/x)	$lim_{x \to 8} {(e^{x} + x)}^{\frac{3}{x}}$
34255	Evaluate the Limit	limit as x approaches 8 of (1/x-1/8)/(x-8)	$lim_{x \to 8} \frac{\frac{1}{x} - \frac{1}{8}}{x - 8}$
34256	Evaluate the Limit	limit as x approaches 8 of ((18x)/(18x+4))^(5x)	$lim_{x \to 8} {(\frac{18 x}{18 x + 4})}^{5 x}$
34257	Evaluate the Limit	limit as x approaches 8 of (2/3)^x	$lim_{x \to 8} {(\frac{2}{3})}^{x}$
34258	Evaluate the Limit	limit as x approaches -8 of (3x^2+4)/(2x^2+1)	$lim_{x \to - 8} \frac{3 x^{2} + 4}{2 x^{2} + 1}$
34259	Evaluate the Limit	limit as x approaches 8 of (3x^2+4x-3)/(8x^2-3x+2)	$lim_{x \to 8} \frac{3 x^{2} + 4 x - 3}{8 x^{2} - 3 x + 2}$
34260	Evaluate the Limit	limit as x approaches -8 of (3x^2-21x+30)/(x^2+3x-10)	$lim_{x \to - 8} \frac{3 x^{2} - 21 x + 30}{x^{2} + 3 x - 10}$
34261	Evaluate the Limit	limit as x approaches 8 of (3x^2-4x+9)/(17+2x-8x^2)	$lim_{x \to 8} \frac{3 x^{2} - 4 x + 9}{17 + 2 x - 8 x^{2}}$
34262	Evaluate the Limit	limit as x approaches 8 of (2x^2-7x^4)/(4x^2+5x-6)	$lim_{x \to 8} \frac{2 x^{2} - 7 x^{4}}{4 x^{2} + 5 x - 6}$
34263	Evaluate the Limit	limit as x approaches 8 of (2x^2-8x+6)/(x^2-x-6)	$lim_{x \to 8} \frac{2 x^{2} - 8 x + 6}{x^{2} - x - 6}$
34264	Evaluate the Limit	limit as x approaches -8 of (2x^2+1)/(x^2+2x-1)	$lim_{x \to - 8} \frac{2 x^{2} + 1}{x^{2} + 2 x - 1}$
34265	Evaluate the Limit	limit as x approaches 8 of (2x^2+10x-5)/(3x^2+3)	$lim_{x \to 8} \frac{2 x^{2} + 10 x - 5}{3 x^{2} + 3}$
34266	Evaluate the Limit	limit as x approaches 8 of (2x^3-2x-4)/(5x^2-5x-3)	$lim_{x \to 8} \frac{2 x^{3} - 2 x - 4}{5 x^{2} - 5 x - 3}$
34267	Evaluate the Limit	limit as x approaches 8 of (-2+ square root of 5x)/(5x+2)	$lim_{x \to 8} \frac{- 2 + \sqrt{5 x}}{5 x + 2}$
34268	Evaluate the Limit	limit as x approaches 8 of (2+2x)/(5-9x)	$lim_{x \to 8} \frac{2 + 2 x}{5 - 9 x}$
34269	Evaluate the Limit	limit as x approaches 8 of (25x^2+3x+140)/(5x^(2-10))	$lim_{x \to 8} \frac{25 x^{2} + 3 x + 140}{5 x^{2 - 10}}$
34270	Evaluate the Limit	limit as x approaches 8 of (2-x)/( square root of 7+6x^2)	$lim_{x \to 8} \frac{2 - x}{\sqrt{7 + 6 x^{2}}}$
34271	Evaluate the Limit	limit as x approaches -8 of (-2x+5)/(5x- square root of 25x^2+x-5)	$lim_{x \to - 8} \frac{- 2 x + 5}{5 x - \sqrt{25 x^{2} + x - 5}}$
34272	Evaluate the Limit	limit as x approaches 8 of (2x+sin(3x))/(5x^2-2x+1)	$lim_{x \to 8} \frac{2 x + \sin (3 x)}{5 x^{2} - 2 x + 1}$
34273	Evaluate the Limit	limit as x approaches 8 of (11x+9)/(8x^2-7x+5)	$lim_{x \to 8} \frac{11 x + 9}{8 x^{2} - 7 x + 5}$
34274	Evaluate the Limit	limit as x approaches 8 of (12x^2+4x+60)/(4x^2-1)	$lim_{x \to 8} \frac{12 x^{2} + 4 x + 60}{4 x^{2} - 1}$
34275	Evaluate the Limit	limit as x approaches 8 of (12x^8-3)/(3x^8-2x^7)	$lim_{x \to 8} \frac{12 x^{8} - 3}{3 x^{8} - 2 x^{7}}$
34276	Evaluate the Limit	limit as x approaches 8 of (12x-7)/(3x+2)	$lim_{x \to 8} \frac{12 x - 7}{3 x + 2}$
34277	Evaluate the Limit	limit as x approaches 8 of (13-4x)/(9+x)+(6x^2+10)/((2x-5)^2)	$lim_{x \to 8} \frac{13 - 4 x}{9 + x} + \frac{6 x^{2} + 10}{{(2 x - 5)}^{2}}$
34278	Evaluate the Limit	limit as x approaches -8 of (1-3x+x^4)/(2-5x^4)	$lim_{x \to - 8} \frac{1 - 3 x + x^{4}}{2 - 5 x^{4}}$
34279	Evaluate the Limit	limit as x approaches -8 of (13x-7)/(x^3+10x-8)	$lim_{x \to - 8} \frac{13 x - 7}{x^{3} + 10 x - 8}$
34280	Evaluate the Limit	limit as x approaches 8 of (14x^2-4x+9)/(7x^2+3x+1)	$lim_{x \to 8} \frac{14 x^{2} - 4 x + 9}{7 x^{2} + 3 x + 1}$
34281	Evaluate the Limit	limit as x approaches -8 of (14x^4)/(7x^4+18x^3+5x^2)	$lim_{x \to - 8} \frac{14 x^{4}}{7 x^{4} + 18 x^{3} + 5 x^{2}}$
34282	Evaluate the Limit	limit as x approaches 8 of (15e^x-18)/(3e^x)	$lim_{x \to 8} \frac{15 e^{x} - 18}{3 e^{x}}$
34283	Evaluate the Limit	limit as x approaches 8 of (15x^2-2x+3)/(5x^2-7)	$lim_{x \to 8} \frac{15 x^{2} - 2 x + 3}{5 x^{2} - 7}$
34284	Evaluate the Limit	limit as x approaches 8 of (15x^3)/(e^(10x))	$lim_{x \to 8} \frac{15 x^{3}}{e^{10 x}}$
34285	Evaluate the Limit	limit as x approaches -8 of (16+x^2)^6	$lim_{x \to - 8} {(16 + x^{2})}^{6}$
34286	Evaluate the Limit	limit as x approaches 8 of 10/(5-15^(-x/2))	$lim_{x \to 8} \frac{10}{5 - 15^{- \frac{x}{2}}}$
34287	Evaluate the Limit	limit as x approaches -8 of (10-2^x)/(10+2^(-x))	$lim_{x \to - 8} \frac{10 - 2^{x}}{10 + 2^{- x}}$
34288	Evaluate the Limit	limit as x approaches 8 of (10x^2+400x+10)/(4x^6+9)	$lim_{x \to 8} \frac{10 x^{2} + 400 x + 10}{4 x^{6} + 9}$
34289	Evaluate the Limit	limit as x approaches 8 of (10x^3)/(e^x)	$lim_{x \to 8} \frac{10 x^{3}}{e^{x}}$
34290	Evaluate the Limit	limit as x approaches 8 of (10+3x)/( square root of 6+9x^2)	$lim_{x \to 8} \frac{10 + 3 x}{\sqrt{6 + 9 x^{2}}}$
34291	Evaluate the Limit	limit as x approaches 8 of (10x+3)/x	$lim_{x \to 8} \frac{10 x + 3}{x}$
34292	Evaluate the Limit	limit as x approaches -8 of (11x^2-1)/(x+3)	$lim_{x \to - 8} \frac{11 x^{2} - 1}{x + 3}$
34293	Evaluate the Limit	limit as x approaches 8 of (11x^3-4x^2-2x)/(2-11x-5x^3)	$lim_{x \to 8} \frac{11 x^{3} - 4 x^{2} - 2 x}{2 - 11 x - 5 x^{3}}$
34294	Evaluate the Limit	limit as x approaches -8 of (11x+2)/(2x^3-1)	$lim_{x \to - 8} \frac{11 x + 2}{2 x^{3} - 1}$
34295	Evaluate the Limit	limit as x approaches 8 of (1+2x)^(1/(2 natural log of x))	$lim_{x \to 8} {(1 + 2 x)}^{\frac{1}{2 \ln (x)}}$
34296	Evaluate the Limit	limit as x approaches 8 of (1+2x)^(19/(2 natural log of x))	$lim_{x \to 8} {(1 + 2 x)}^{\frac{19}{2 \ln (x)}}$
34297	Evaluate the Limit	limit as x approaches 8 of (1+4n)/n	$lim_{x \to 8} \frac{1 + 4 n}{n}$
34298	Evaluate the Limit	limit as x approaches 8 of (1+8x)/(5-5x)	$lim_{x \to 8} \frac{1 + 8 x}{5 - 5 x}$
34299	Evaluate the Limit	limit as x approaches 3 of (x^2+x-12)/(x-3)	$lim_{x \to 3} \frac{x^{2} + x - 12}{x - 3}$
34300	Evaluate the Limit	limit as x approaches 0 of (tan(7x))/(sin(3x))	$lim_{x \to 0} \frac{\tan (7 x)}{\sin (3 x)}$