Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
32401	Evaluate the Limit	( limit as x approaches -8 of 3)/x-12	$\frac{lim_{x \to - 8} 3}{x} - 12$
32402	Evaluate the Limit	( limit as x approaches 8 of 3e^(3x)(e^(3x)+1)^(1/x-1))/x	$\frac{lim_{x \to 8} 3 e^{3 x} {(e^{3 x} + 1)}^{\frac{1}{x} - 1}}{x}$
32403	Evaluate the Limit	( limit as x approaches 8 of 3x^2+2x-7)/(x^3-7x+11)	$\frac{lim_{x \to 8} 3 x^{2} + 2 x - 7}{x^{3} - 7 x + 11}$
32404	Evaluate the Limit	( limit as x approaches 8 of 3x^2-2x)/(9x^2-4)	$\frac{lim_{x \to 8} 3 x^{2} - 2 x}{9 x^{2} - 4}$
32405	Evaluate the Limit	( limit as x approaches 8 of 3x^3+2x+1)/(100x^2-1000x-10000)	$\frac{lim_{x \to 8} 3 x^{3} + 2 x + 1}{100 x^{2} - 1000 x - 10000}$
32406	Evaluate the Limit	( limit as x approaches 8 of 3x^3+2x-1)/(5x^3+3x+2)	$\frac{lim_{x \to 8} 3 x^{3} + 2 x - 1}{5 x^{3} + 3 x + 2}$
32407	Evaluate the Limit	( limit as x approaches 8 of 3x^3-5x)/(x^3-2x^2+1)	$\frac{lim_{x \to 8} 3 x^{3} - 5 x}{x^{3} - 2 x^{2} + 1}$
32408	Evaluate the Limit	( limit as x approaches -8 of 3x^5-x^2+7)/(2-x^2)	$\frac{lim_{x \to - 8} 3 x^{5} - x^{2} + 7}{2 - x^{2}}$
32409	Evaluate the Limit	( limit as x approaches 8 of 3x^6)/x	$\frac{lim_{x \to 8} 3 x^{6}}{x}$
32410	Evaluate the Limit	( limit as x approaches 8 of 3x-5)/( square root of 7x^2+4)	$\frac{lim_{x \to 8} 3 x - 5}{\sqrt{7 x^{2} + 4}}$
32411	Evaluate the Limit	( limit as x approaches 8 of 3x-5)/(4x+7)	$\frac{lim_{x \to 8} 3 x - 5}{4 x + 7}$
32412	Evaluate the Limit	( limit as x approaches 8 of 3x-8)/(x+8)	$\frac{lim_{x \to 8} 3 x - 8}{x + 8}$
32413	Evaluate the Limit	( limit as x approaches 8 of 4.1)/(2-3x)	$\frac{lim_{x \to 8} 4.1}{2 - 3 x}$
32414	Evaluate the Limit	( limit as x approaches 8 of 4x^2+10x+4)/(2x^2-6x+9)	$\frac{lim_{x \to 8} 4 x^{2} + 10 x + 4}{2 x^{2} - 6 x + 9}$
32415	Evaluate the Limit	( limit as x approaches 8 of 4x^2+2x)/(2x^2-8x+1)	$\frac{lim_{x \to 8} 4 x^{2} + 2 x}{2 x^{2} - 8 x + 1}$
32416	Evaluate the Limit	( limit as x approaches 8 of 4x^2+5x-16)/(5x^2+7x)	$\frac{lim_{x \to 8} 4 x^{2} + 5 x - 16}{5 x^{2} + 7 x}$
32417	Evaluate the Limit	( limit as x approaches 8 of 4x^3+1)/(2x^3+ square root of 16x^6+1)	$\frac{lim_{x \to 8} 4 x^{3} + 1}{2 x^{3} + \sqrt{16 x^{6} + 1}}$
32418	Evaluate the Limit	( limit as x approaches 8 of 4x^7-x+4)/(4x^2-x-4)	$\frac{lim_{x \to 8} 4 x^{7} - x + 4}{4 x^{2} - x - 4}$
32419	Evaluate the Limit	( limit as x approaches -8 of 4+6x)/(1-7x)	$\frac{lim_{x \to - 8} 4 + 6 x}{1 - 7 x}$
32420	Evaluate the Limit	( limit as x approaches 8 of 4sin(x))/(x^2+2x+1)	$\frac{lim_{x \to 8} 4 \sin (x)}{x^{2} + 2 x + 1}$
32421	Evaluate the Limit	( limit as x approaches 8 of 4x-1)/(2x-5)	$\frac{lim_{x \to 8} 4 x - 1}{2 x - 5}$
32422	Evaluate the Limit	limit as x approaches infinity of (6x^2-9x+8)/(3x^2+2)	$lim_{x \to \infty} \frac{6 x^{2} - 9 x + 8}{3 x^{2} + 2}$
32423	Evaluate the Limit	limit as x approaches infinity of x^4e^(-x^3)	$lim_{x \to \infty} x^{4} e^{- x^{3}}$
32424	Evaluate the Limit	limit as x approaches infinity of (3-2x)/(3x-1)	$lim_{x \to \infty} \frac{3 - 2 x}{3 x - 1}$
32425	Evaluate the Limit	limit as h approaches 0 of (f(5+h)-f*5)/h	$lim_{h \to 0} \frac{f (5 + h) - f \cdot 5}{h}$
32426	Evaluate the Limit	limit as h approaches 0 of 7h-9	$lim_{h \to 0} 7 h - 9$
32427	Evaluate the Limit	limit as h approaches 0 of ((2+h)^5-32)/h	$lim_{h \to 0} \frac{{(2 + h)}^{5} - 32}{h}$
32428	Evaluate the Limit	limit as x approaches 0 of (tan(13x))/(sin(4x))	$lim_{x \to 0} \frac{\tan (13 x)}{\sin (4 x)}$
32429	Evaluate the Limit	limit as x approaches 0 of (x-sin(x))/(x^4)	$lim_{x \to 0} \frac{x - \sin (x)}{x^{4}}$
32430	Evaluate the Limit	limit as x approaches 0.0001 of (11^0.0001-1)/0.0001	$lim_{x \to 0.0001} \frac{11^{0.0001} - 1}{0.0001}$
32431	Evaluate the Limit	limit as x approaches x^6 of (3x^4+4x-5)/(x^6-7x^4-2x+10)	$lim_{x \to x^{6}} \frac{3 x^{4} + 4 x - 5}{x^{6} - 7 x^{4} - 2 x + 10}$
32432	Evaluate the Limit	limit as x approaches 19 of tan((pix)/4)	$lim_{x \to 19} \tan (\frac{π x}{4})$
32433	Evaluate the Limit	limit as x approaches 0 of (2sin(-0.01))/-0.01	$lim_{x \to 0} \frac{2 \sin (- 0.01)}{- 0.01}$
32434	Evaluate the Limit	limit as x approaches 0 of (x^2-3sin(x))/x	$lim_{x \to 0} \frac{x^{2} - 3 \sin (x)}{x}$
32435	Evaluate the Limit	limit as x approaches 0 of (sin(8x))/(sin(9x))	$lim_{x \to 0} \frac{\sin (8 x)}{\sin (9 x)}$
32436	Evaluate the Limit	limit as x approaches 0 of (5x)/(tan(x))	$lim_{x \to 0} \frac{5 x}{\tan (x)}$
32437	Evaluate the Limit	limit as x approaches 0 of e^(7/x)	$lim_{x \to 0} e^{\frac{7}{x}}$
32438	Evaluate the Limit	limit as x approaches pi/2 of (1-sin(x))/(cos(x))	$lim_{x \to \frac{π}{2}} \frac{1 - \sin (x)}{\cos (x)}$
32439	Evaluate the Limit	limit as x approaches pi/2 of (7cos(x))/(cot(x))	$lim_{x \to \frac{π}{2}} \frac{7 \cos (x)}{\cot (x)}$
32440	Evaluate the Limit	limit as x approaches 0 of (1+sin(x))^(1/x)	$lim_{x \to 0} {(1 + \sin (x))}^{\frac{1}{x}}$
32441	Evaluate the Limit	limit as x approaches -3 of square root of (y^2-9)/(2y^2+7y+3)	$lim_{x \to - 3} \sqrt{\frac{y^{2} - 9}{2 y^{2} + 7 y + 3}}$
32442	Evaluate the Limit	limit as x approaches 1.9 of (sin(x-2))/(x^2-4)	$lim_{x \to 1.9} \frac{\sin (x - 2)}{x^{2} - 4}$
32443	Evaluate the Limit	limit as x approaches 11 of ( square root of x+5-4)/(x-11)	$lim_{x \to 11} \frac{\sqrt{x + 5} - 4}{x - 11}$
32444	Evaluate the Limit	limit as x approaches 2 of square root of (3x^2+4)/(5x-1)	$lim_{x \to 2} \sqrt{\frac{3 x^{2} + 4}{5 x - 1}}$
32445	Evaluate the Limit	limit as x approaches 4 of (x^3-7x^2+12x)/(4-x)	$lim_{x \to 4} \frac{x^{3} - 7 x^{2} + 12 x}{4 - x}$
32446	Evaluate the Limit	limit as theta approaches 0 of (cos(6theta)tan(6theta))/theta	$lim_{θ \to 0} \frac{\cos (6 θ) \tan (6 θ)}{θ}$
32447	Evaluate the Limit	limit as x approaches infinity of (x^2-4)/(4x^3-x)	$lim_{x \to \infty} \frac{x^{2} - 4}{4 x^{3} - x}$
32448	Evaluate the Limit	limit as x approaches infinity of (10x^2-3x+1)/(7x^2+3x-3)	$lim_{x \to \infty} \frac{10 x^{2} - 3 x + 1}{7 x^{2} + 3 x - 3}$
32449	Evaluate the Limit	limit as x approaches infinity of (e^(5x)+e^(-5x))/(e^(5x)-e^(-5x))	$lim_{x \to \infty} \frac{e^{5 x} + e^{- 5 x}}{e^{5 x} - e^{- 5 x}}$
32450	Evaluate the Limit	limit as x approaches -pi/2 of sec(x)	$lim_{x \to - \frac{π}{2}} \sec (x)$
32451	Evaluate the Limit	limit as t approaches 0 of sec((-2pit)/(sin(t)))	$lim_{t \to 0} \sec (\frac{- 2 π t}{\sin (t)})$
32452	Evaluate the Limit	limit as t approaches 5 of (t^3+11t^2-84t+20)/(t^3-25t)	$lim_{t \to 5} \frac{t^{3} + 11 t^{2} - 84 t + 20}{t^{3} - 25 t}$
32453	Evaluate the Limit	limit as t approaches -9 of (t^2-81)/(2t^2+19t+9)	$lim_{t \to - 9} \frac{t^{2} - 81}{2 t^{2} + 19 t + 9}$
32454	Evaluate the Limit	limit as r approaches -1 of 1/(t^2-1)	$lim_{r \to - 1} \frac{1}{t^{2} - 1}$
32455	Evaluate the Limit	limit as x approaches -0.25 of square root of (x+9)/(x+2)	$lim_{x \to - 0.25} \sqrt{\frac{x + 9}{x + 2}}$
32456	Evaluate the Limit	limit as x approaches -0.5 of (2x^2+x)/(6x^2+x-1)	$lim_{x \to - 0.5} \frac{2 x^{2} + x}{6 x^{2} + x - 1}$
32457	Evaluate the Limit	limit as x approaches 0 of (3sin(x))/x	$lim_{x \to 0} \frac{3 \sin (x)}{x}$
32458	Evaluate the Limit	limit as x approaches 0 of (tan(13x))/(sin(2x))	$lim_{x \to 0} \frac{\tan (13 x)}{\sin (2 x)}$
32459	Evaluate the Limit	limit as x approaches 0 of (tan(2x))/(sin(2x))	$lim_{x \to 0} \frac{\tan (2 x)}{\sin (2 x)}$
32460	Evaluate the Limit	limit as x approaches 0 of (tan(5x))/(sin(20x))	$lim_{x \to 0} \frac{\tan (5 x)}{\sin (20 x)}$
32461	Evaluate the Limit	limit as x approaches 0 of (sin(4x))/(sin(10x))	$lim_{x \to 0} \frac{\sin (4 x)}{\sin (10 x)}$
32462	Evaluate the Limit	limit as x approaches 0 of (sin(5x))/(sin(7x))	$lim_{x \to 0} \frac{\sin (5 x)}{\sin (7 x)}$
32463	Evaluate the Limit	limit as x approaches 4 of (3x^2-17x+20)/(4x^2-25x+36)	$lim_{x \to 4} \frac{3 x^{2} - 17 x + 20}{4 x^{2} - 25 x + 36}$
32464	Evaluate the Limit	limit as x approaches 5 of (x^2+2x-35)/(x^2-10x+25)	$lim_{x \to 5} \frac{x^{2} + 2 x - 35}{x^{2} - 10 x + 25}$
32465	Evaluate the Limit	limit as x approaches 5 of (x^2+x-30)/(x-5)	$lim_{x \to 5} \frac{x^{2} + x - 30}{x - 5}$
32466	Evaluate the Limit	limit as x approaches infinity of (1+9/x)^x	$lim_{x \to \infty} {(1 + \frac{9}{x})}^{x}$
32467	Evaluate the Limit	limit as x approaches infinity of square root of 2x+cos(x)- square root of 2x	$lim_{x \to \infty} \sqrt{2 x + \cos (x)} - \sqrt{2 x}$
32468	Evaluate the Limit	limit as x approaches infinity of square root of x^2+19x-x	$lim_{x \to \infty} \sqrt{x^{2} + 19 x} - x$
32469	Evaluate the Limit	limit as x approaches 9 of square root of 8x-1	$lim_{x \to 9} \sqrt{8 x - 1}$
32470	Evaluate the Limit	limit as x approaches 10 of square root of x^2-100	$lim_{x \to 10} \sqrt{x^{2} - 100}$
32471	Evaluate the Limit	limit as x approaches 27 of (x-27)/(x^(1/3)-3)	$lim_{x \to 27} \frac{x - 27}{x^{\frac{1}{3}} - 3}$
32472	Evaluate the Limit	limit as a approaches 1 of (a^3-a)/(a^2-1)	$lim_{a \to 1} \frac{a^{3} - a}{a^{2} - 1}$
32473	Evaluate the Limit	limit as a approaches 2b of -(12b^2+3a^2)/(a-2b)	$lim_{a \to 2 b} - \frac{12 b^{2} + 3 a^{2}}{a - 2 b}$
32474	Evaluate the Limit	limit as a approaches 81 of (81-a)/(9- square root of a)	$lim_{a \to 81} \frac{81 - a}{9 - \sqrt{a}}$
32475	Evaluate the Limit	limit as b approaches 16 of (16-b)/(4- square root of b)	$lim_{b \to 16} \frac{16 - b}{4 - \sqrt{b}}$
32476	Evaluate the Limit	limit as b approaches -17 of (\|b+17\|)/(b+17)	$lim_{b \to - 17} \frac{\| b + 17 \|}{b + 17}$
32477	Evaluate the Limit	limit as b approaches 2 of (3b)/( square root of 4b+1-1)	$lim_{b \to 2} \frac{3 b}{\sqrt{4 b + 1} - 1}$
32478	Evaluate the Limit	limit as b approaches 6 of (1/b-1/6)/(b-6)	$lim_{b \to 6} \frac{\frac{1}{b} - \frac{1}{6}}{b - 6}$
32479	Evaluate the Limit	limit as b approaches 8 of -2e^(b^2)+2e	$lim_{b \to 8} - 2 e^{b^{2}} + 2 e$
32480	Evaluate the Limit	limit as b approaches 8 of 2e^(0.1b)	$lim_{b \to 8} 2 e^{0.1 b}$
32481	Evaluate the Limit	limit as c approaches 7 of (1/c-1/7)/(c-7)	$lim_{c \to 7} \frac{\frac{1}{c} - \frac{1}{7}}{c - 7}$
32482	Evaluate the Limit	limit as d approaches 0 of 4/d	$lim_{d \to 0} \frac{4}{d}$
32483	Evaluate the Limit	limit as d approaches 2 of square root of 2d+5	$lim_{d \to 2} \sqrt{2 d + 5}$
32484	Evaluate the Limit	limit as x approaches 4 of (3- square root of 5+x)/(2- square root of 8-x)	$lim_{x \to 4} \frac{3 - \sqrt{5 + x}}{2 - \sqrt{8 - x}}$
32485	Evaluate the Limit	limit as h approaches (3/7) of (7h-3)/(2h)	$lim_{h \to (\frac{3}{7})} \frac{7 h - 3}{2 h}$
32486	Evaluate the Limit	limit as x approaches 4 of (x-4)/( square root of x-2)	$lim_{x \to 4} \frac{x - 4}{\sqrt{x - 2}}$
32487	Evaluate the Limit	limit as x approaches 0 of (3x^2+2x-1)/(4x+1)	$lim_{x \to 0} \frac{3 x^{2} + 2 x - 1}{4 x + 1}$
32488	Evaluate the Limit	limit as x approaches infinity of ((2x+4)^2)/((5x-7)^2)	$lim_{x \to \infty} \frac{{(2 x + 4)}^{2}}{{(5 x - 7)}^{2}}$
32489	Find the Asymptotes	f(x)=(1+x)/(x^2(1-x))	$f (x) = \frac{1 + x}{x^{2} (1 - x)}$
32490	Evaluate the Limit	limit as x approaches infinity of (1-1/x)^x	$lim_{x \to \infty} {(1 - \frac{1}{x})}^{x}$
32491	Evaluate the Limit	limit as x approaches negative infinity of ( cube root of x^6+8)/(4x^2+ square root of 3x^4+1)	$lim_{x \to - \infty} \frac{\sqrt[3]{x^{6} + 8}}{4 x^{2} + \sqrt{3 x^{4} + 1}}$
32492	Evaluate the Limit	limit as x approaches infinity of e^(1/x)	$lim_{x \to \infty} e^{\frac{1}{x}}$
32493	Evaluate the Limit	limit as x approaches negative infinity of (5-e^x)/(1+e^x)	$lim_{x \to - \infty} \frac{5 - e^{x}}{1 + e^{x}}$
32494	Evaluate the Limit	limit as x approaches pi/4 of (tan(2x))/(sec(2x))	$lim_{x \to \frac{π}{4}} \frac{\tan (2 x)}{\sec (2 x)}$
32495	Evaluate the Limit	limit as h approaches 0 of ((1/(4+h))-(1/4))*1/2	$lim_{h \to 0} ((\frac{1}{4 + h}) - (\frac{1}{4})) \cdot \frac{1}{2}$
32496	Evaluate the Limit	limit as h approaches 0 of (cos(h-1))/(h^2)	$lim_{h \to 0} \frac{\cos (h - 1)}{h^{2}}$
32497	Evaluate the Limit	limit as h approaches 0 of (((h^2-4h+4)(h-2)(h-2))-(32))/h	$lim_{h \to 0} \frac{((h^{2} - 4 h + 4) (h - 2) (h - 2)) - (32)}{h}$
32498	Evaluate the Limit	limit as h approaches 0 of (((t+h)^3-(t+h)^2)-(t^3-t^2))/h	$lim_{h \to 0} \frac{({(t + h)}^{3} - {(t + h)}^{2}) - (t^{3} - t^{2})}{h}$
32499	Evaluate the Limit	limit as h approaches 0 of (1/(7+h)-1/7)/h	$lim_{h \to 0} \frac{\frac{1}{7 + h} - \frac{1}{7}}{h}$
32500	Evaluate the Limit	limit as h approaches 0 of ((1/(x+h+3))-(1/(x+3)))/h	$lim_{h \to 0} \frac{(\frac{1}{x + h + 3}) - (\frac{1}{x + 3})}{h}$