Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
32301	Evaluate the Limit	f'(0) = limit as h approaches 0 of (f(0+h)-f*0)/h	$f' (0) = lim_{h \to 0} \frac{f (0 + h) - f \cdot 0}{h}$
32302	Evaluate the Limit	f(h) = limit as h approaches 0 of ( square root of 16+h-4)/h	$f (h) = lim_{h \to 0} \frac{\sqrt{16 + h} - 4}{h}$
32303	Evaluate the Limit	f(x)=(x^2-4)/((x^2-3x-10) limit as x approaches 2 of f(x))	$f (x) = \frac{x^{2} - 4}{(x^{2} - 3 x - 10) lim_{x \to 2} f (x)}$
32304	Evaluate the Limit	f(x)=(5x+11)/((7x^3-2) limit as x approaches 8 of f(x))	$f (x) = \frac{5 x + 11}{(7 x^{3} - 2) lim_{x \to 8} f (x)}$
32305	Evaluate the Limit	limit as x approaches 4 of x(x-8)(x+8)	$lim_{x \to 4} x (x - 8) (x + 8)$
32306	Evaluate the Limit	f(x)=-5x limit as h approaches 0 of f(xth)-f(x)	$f (x) = - 5 x lim_{h \to 0} f (x t h) - f (x)$
32307	Evaluate the Limit	limit as x approaches infinity of 3x	$lim_{x \to \infty} 3 x$
32308	Evaluate the Limit	f(x) = limit as h approaches 0 of 7x-5	$f (x) = lim_{h \to 0} 7 x - 5$
32309	Evaluate the Limit	( limit as x approaches 8 of xsin(7x)^2)/(sin(11x)^2)	$\frac{lim_{x \to 8} x \sin^{2} (7 x)}{\sin^{2} (11 x)}$
32310	Evaluate the Limit	( limit as x approaches 8 of x- square root of x^2+9x+2)/(x^2- square root of x^4+3x^2+5)	$\frac{lim_{x \to 8} x - \sqrt{x^{2} + 9 x + 2}}{x^{2} - \sqrt{x^{4} + 3 x^{2} + 5}}$
32311	Evaluate the Limit	( limit as x approaches 8 of x square root of x)/( square root of x^3+2x^2)	$\frac{lim_{x \to 8} x \sqrt{x}}{\sqrt{x^{3} + 2 x^{2}}}$
32312	Evaluate the Limit	( limit as x approaches 8 of x+x^2)/(9-2x^2)	$\frac{lim_{x \to 8} x + x^{2}}{9 - 2 x^{2}}$
32313	Evaluate the Limit	( limit as x approaches 8 of x+3)/( square root of 16x^2+8x+1)	$\frac{lim_{x \to 8} x + 3}{\sqrt{16 x^{2} + 8 x + 1}}$
32314	Evaluate the Limit	( limit as x approaches 8 of x-3)/( square root of 9x^2+1)	$\frac{lim_{x \to 8} x - 3}{\sqrt{9 x^{2} + 1}}$
32315	Evaluate the Limit	( limit as x approaches 8x of 5x^5+2x^3+6)/(-6x^6+2x^4)	$\frac{lim_{x \to 8 x} 5 x^{5} + 2 x^{3} + 6}{- 6 x^{6} + 2 x^{4}}$
32316	Evaluate the Limit	( limit as x approaches 81 of 81-x)/(9- square root of x)	$\frac{lim_{x \to 81} 81 - x}{9 - \sqrt{x}}$
32317	Evaluate the Limit	( limit as x approaches 9 of 5/x-5/9)/(x-9)	$\frac{lim_{x \to 9} \frac{5}{x} - \frac{5}{9}}{x - 9}$
32318	Evaluate the Limit	( limit as x approaches 9 of 6+8)/(6(6))	$\frac{lim_{x \to 9} 6 + 8}{6 (6)}$
32319	Evaluate the Limit	( limit as x approaches 9 of t^2+3t-108)/(t^2-81)	$\frac{lim_{x \to 9} t^{2} + 3 t - 108}{t^{2} - 81}$
32320	Evaluate the Limit	( limit as x approaches 9 of square root of x^2-3x-28)/(11-2x)	$\frac{lim_{x \to 9} \sqrt{x^{2} - 3 x} - 28}{11 - 2 x}$
32321	Evaluate the Limit	( limit as x approaches 9 of square root of x)/((r-9)^4)	$\frac{lim_{x \to 9} \sqrt{x}}{{(r - 9)}^{4}}$
32322	Evaluate the Limit	( limit as x approaches a of (5-4x+3x^2)-(5-4a+3a^2))/(x-a)	$\frac{lim_{x \to a} (5 - 4 x + 3 x^{2}) - (5 - 4 a + 3 a^{2})}{x - a}$
32323	Evaluate the Limit	( limit as x approaches a of (x^2-(a+1)x)+a)/(x^3-a^3)	$\frac{lim_{x \to a} (x^{2} - (a + 1) x) + a}{x^{3} - a^{3}}$
32324	Evaluate the Limit	( limit as x approaches a of x^5-a^5)/(x-a)	$\frac{lim_{x \to a} x^{5} - a^{5}}{x - a}$
32325	Evaluate the Limit	( limit as x approaches a of f(x))/(g(x))	$\frac{lim_{x \to a} f (x)}{g (x)}$
32326	Evaluate the Limit	limit as x approaches -b of (x+b)^7+((x+b)^10)/(4(x+b))	$lim_{x \to - b} {(x + b)}^{7} + \frac{{(x + b)}^{10}}{4 (x + b)}$
32327	Evaluate the Limit	limit as x approaches c of (-2)^3	$lim_{x \to c} {(- 2)}^{3}$
32328	Evaluate the Limit	( limit as x approaches c of f(x))/(g(x))	$\frac{lim_{x \to c} f (x)}{g (x)}$
32329	Evaluate the Limit	limit as x approaches infinity of (1-4/x)^(3x)	$lim_{x \to \infty} {(1 - \frac{4}{x})}^{3 x}$
32330	Evaluate the Limit	limit as x approaches infinity of (1+4/x)^(3x)	$lim_{x \to \infty} {(1 + \frac{4}{x})}^{3 x}$
32331	Evaluate the Limit	( limit as x approaches infinity of square root of x^4+7x^3+5)/(x^2-8)	$\frac{lim_{x \to \infty} \sqrt{x^{4} + 7 x^{3} + 5}}{x^{2} - 8}$
32332	Evaluate the Limit	( limit as x approaches infinity of 6x+6)/(8x+6)	$\frac{lim_{x \to \infty} 6 x + 6}{8 x + 6}$
32333	Evaluate the Limit	( limit as x approaches infinity of 8+11x)/( square root of 8+9x^2)	$\frac{lim_{x \to \infty} 8 + 11 x}{\sqrt{8 + 9 x^{2}}}$
32334	Evaluate the Limit	( limit as x approaches inf of 7x^4-6x^2)/(5x^5+3)	$\frac{lim_{x \to i n f} 7 x^{4} - 6 x^{2}}{5 x^{5} + 3}$
32335	Evaluate the Limit	( limit as x approaches inf of x+sin(x))/(x+cos(x))	$\frac{lim_{x \to i n f} x + \sin (x)}{x + \cos (x)}$
32336	Evaluate the Limit	( limit as x approaches inf of 9x^2)/(e^(4x))	$\frac{lim_{x \to i n f} 9 x^{2}}{e^{4 x}}$
32337	Evaluate the Limit	( limit as x approaches infinity of 3x^2+x-2)/(-4x^2+3x+1)	$\frac{lim_{x \to \infty} 3 x^{2} + x - 2}{- 4 x^{2} + 3 x + 1}$
32338	Evaluate the Limit	( limit as x approaches infinity of square root of 6+8x^2)/(3+8x)	$\frac{lim_{x \to \infty} \sqrt{6 + 8 x^{2}}}{3 + 8 x}$
32339	Evaluate the Limit	( limit as x approaches infinity of -6x)/(8+2x)	$\frac{lim_{x \to \infty} - 6 x}{8 + 2 x}$
32340	Evaluate the Limit	( limit as x approaches infinity of 2^(-x))/(2^x)	$\frac{lim_{x \to \infty} 2^{- x}}{2^{x}}$
32341	Evaluate the Limit	( limit as x approaches infinity of square root of x^2+1)/(3x+2)	$\frac{lim_{x \to \infty} \sqrt{x^{2}} + 1}{3 x + 2}$
32342	Evaluate the Limit	( limit as x approaches infinity of 3x^2-4)/(2-7x-x^2)	$\frac{lim_{x \to \infty} 3 x^{2} - 4}{2 - 7 x - x^{2}}$
32343	Evaluate the Limit	( limit as x approaches infinity of 5x^2-5)/x	$\frac{lim_{x \to \infty} 5 x^{2} - 5}{x}$
32344	Evaluate the Limit	( limit as x approaches o of cos(t)-cos(t)^2)/t	$\frac{lim_{x \to o} \cos (t) - \cos^{2} (t)}{t}$
32345	Evaluate the Limit	( limit as x approaches o of x^2+3x)/x	$\frac{lim_{x \to o} x^{2} + 3 x}{x}$
32346	Evaluate the Limit	( limit as x approaches o of 6x-9)/(x^2-12x-3)	$\frac{lim_{x \to o} 6 x - 9}{x^{2} - 12 x - 3}$
32347	Evaluate the Limit	( limit as x approaches o of cos(2x))/(sin(2x))	$\frac{lim_{x \to o} \cos (2 x)}{\sin (2 x)}$
32348	Evaluate the Limit	( limit as x approaches pi of sin(x+pi))/(cos(x-pi/2))	$\frac{lim_{x \to π} \sin (x + π)}{\cos (x - \frac{π}{2})}$
32349	Evaluate the Limit	limit as x approaches pi of (x-pi)^2cos(1/(x-pi))+3x^2	$lim_{x \to π} {(x - π)}^{2} \cos (\frac{1}{x - π}) + 3 x^{2}$
32350	Evaluate the Limit	( limit as x approaches pi of sin(x)^2)/(cos(3x)+1)	$\frac{lim_{x \to π} \sin^{2} (x)}{\cos (3 x) + 1}$
32351	Evaluate the Limit	( limit as x approaches pi of 1-x)/(1-cos(x))	$\frac{lim_{x \to π} 1 - x}{1 - \cos (x)}$
32352	Evaluate the Limit	( limit as x approaches pi of cos(x/2))/(x/2-pi/2)	$\frac{lim_{x \to π} \cos (\frac{x}{2})}{\frac{x}{2} - \frac{π}{2}}$
32353	Evaluate the Limit	( limit as x approaches pi of cos(pi))/(sin(pi))	$\frac{lim_{x \to π} \cos (π)}{\sin (π)}$
32354	Evaluate the Limit	( limit as x approaches p of px-p^2)/(2x-2p)	$\frac{lim_{x \to p} p x - p^{2}}{2 x - 2 p}$
32355	Evaluate the Limit	( limit as x approaches pi of x-pi)/(2tan(3x))	$\frac{lim_{x \to π} x - π}{2 \tan (3 x)}$
32356	Evaluate the Limit	( limit as x approaches square root of 3 of x^2-3)/(x^4+x^2+1)	$\frac{lim_{x \to \sqrt{3}} x^{2} - 3}{x^{4} + x^{2} + 1}$
32357	Evaluate the Limit	( limit as x approaches x of 8x)/(3-x)	$\frac{lim_{x \to x} 8 x}{3 - x}$
32358	Evaluate the Limit	( limit as y approaches 0 of -6(x-y)^2-(-6x)^2)/y	$\frac{lim_{y \to 0} - 6 {(x - y)}^{2} - {(- 6 x)}^{2}}{y}$
32359	Evaluate the Limit	( limit as y approaches 0 of square root of y+9-3)/y	$\frac{lim_{y \to 0} \sqrt{y + 9} - 3}{y}$
32360	Evaluate the Limit	( limit as y approaches 0 from the left of y)/y	$\frac{lim_{y \to 0} y}{y}$
32361	Evaluate the Limit	( limit as y approaches 4 of 16-y^2)/(2- square root of y)	$\frac{lim_{y \to 4} 16 - y^{2}}{2 - \sqrt{y}}$
32362	Evaluate the Limit	( limit as y approaches -5 of y^2)/(5-4)	$\frac{lim_{y \to - 5} y^{2}}{5 - 4}$
32363	Evaluate the Limit	( limit as y approaches 8 of 2-y)/( square root of 7+6y^2)	$\frac{lim_{y \to 8} 2 - y}{\sqrt{7 + 6 y^{2}}}$
32364	Evaluate the Limit	( limit as y approaches 8 of 6-7y^2)/(3y^2+4y)	$\frac{lim_{y \to 8} 6 - 7 y^{2}}{3 y^{2} + 4 y}$
32365	Evaluate the Limit	( limit as x approaches 8 of 9x)/(8e^(x^8))	$\frac{lim_{x \to 8} 9 x}{8 e^{x^{8}}}$
32366	Evaluate the Limit	( limit as x approaches 8 of 9x-4)/(8x+7)	$\frac{lim_{x \to 8} 9 x - 4}{8 x + 7}$
32367	Evaluate the Limit	limit as x approaches 8 of (e)^(1/x)	$lim_{x \to 8} {(e)}^{\frac{1}{x}}$
32368	Evaluate the Limit	limit as x approaches 8 of (e)^(-x)+2cos(3x)	$lim_{x \to 8} {(e)}^{- x} + 2 \cos (3 x)$
32369	Evaluate the Limit	( limit as x approaches 8 of natural log of 2+e^(2x))/( natural log of 2+e^(3x))	$\frac{lim_{x \to 8} \ln (2 + e^{2 x})}{\ln (2 + e^{3 x})}$
32370	Evaluate the Limit	( limit as x approaches 8 of natural log of natural log of x^100)/( natural log of x)	$\frac{lim_{x \to 8} \ln (\ln (x^{100}))}{\ln (x)}$
32371	Evaluate the Limit	( limit as x approaches 8 of natural log of natural log of x)/( natural log of x^2+ natural log of x)	$\frac{lim_{x \to 8} \ln (\ln (x))}{\ln (x^{2} + \ln (x))}$
32372	Evaluate the Limit	( limit as x approaches 8 of natural log of x)/(8x)	$\frac{lim_{x \to 8} \ln (x)}{8 x}$
32373	Find dy/dx	ycos(x)=4x^2+2y^2	$y \cos (x) = 4 x^{2} + 2 y^{2}$
32374	Evaluate the Limit	( limit as x approaches -8 of p square root of 3)/(x^2)	$\frac{lim_{x \to - 8} p \sqrt{3}}{x^{2}}$
32375	Evaluate the Limit	( limit as x approaches 8 of r)/(r^2-30 cube root of r)	$\frac{lim_{x \to 8} r}{r^{2} - 30 \sqrt[3]{r}}$
32376	Evaluate the Limit	( limit as x approaches 8 of sin(3x))/(13x)	$\frac{lim_{x \to 8} \sin (3 x)}{13 x}$
32377	Evaluate the Limit	( limit as x approaches 8 of sin(4x))/x	$\frac{lim_{x \to 8} \sin (4 x)}{x}$
32378	Evaluate the Limit	( limit as x approaches 8 of 8)/(n^3)*((n(n+1)(2n+1))/6)	$\frac{lim_{x \to 8} 8}{n^{3}} \cdot (\frac{n (n + 1) (2 n + 1)}{6})$
32379	Evaluate the Limit	( limit as x approaches 8 of 8 square root of x+x^-9)/(2x-8)	$\frac{lim_{x \to 8} 8 \sqrt{x} + x^{- 9}}{2 x - 8}$
32380	Evaluate the Limit	( limit as x approaches 8 of 8x^2+3x-1)/(6x^3+2x)	$\frac{lim_{x \to 8} 8 x^{2} + 3 x - 1}{6 x^{3} + 2 x}$
32381	Find dy/dx	y=tan(pi-7/x)	$y = \tan (π - \frac{7}{x})$
32382	Evaluate the Limit	( limit as x approaches 8 of 9-2x)/(9x-7)	$\frac{lim_{x \to 8} 9 - 2 x}{9 x - 7}$
32383	Evaluate the Limit	( limit as x approaches 7 of x^2+(8-7)x-56)/(x-7)	$\frac{lim_{x \to 7} x^{2} + (8 - 7) x - 56}{x - 7}$
32384	Evaluate the Limit	( limit as x approaches 8 of 11e^(-x)+8)/(8e^(-x)+11)	$\frac{lim_{x \to 8} 11 e^{- x} + 8}{8 e^{- x} + 11}$
32385	Evaluate the Limit	( limit as x approaches 8 of 13)/(17+1/x)	$\frac{lim_{x \to 8} 13}{17 + \frac{1}{x}}$
32386	Evaluate the Limit	( limit as x approaches 8 of 6x^2-3x^4)/(9x^2-5x-6)	$\frac{lim_{x \to 8} 6 x^{2} - 3 x^{4}}{9 x^{2} - 5 x - 6}$
32387	Find dy/dx	y=-x/(4y)	$y = - \frac{x}{4 y}$
32388	Evaluate the Limit	( limit as x approaches -8 of 60x)/(2x)	$\frac{lim_{x \to - 8} 60 x}{2 x}$
32389	Evaluate the Limit	( limit as x approaches 8 of 6x-7)/(4x+3)	$\frac{lim_{x \to 8} 6 x - 7}{4 x + 3}$
32390	Evaluate the Limit	( limit as x approaches 8 of 6x-9)/(5x+6)	$\frac{lim_{x \to 8} 6 x - 9}{5 x + 6}$
32391	Evaluate the Limit	( limit as x approaches 8 of 7x^2+2x)/(2x^2-2x-1)	$\frac{lim_{x \to 8} 7 x^{2} + 2 x}{2 x^{2} - 2 x - 1}$
32392	Evaluate the Limit	( limit as x approaches 8 of 7x^9-4x^5+2x-13)/(-3x^9+x^8-5x^2+2x)	$\frac{lim_{x \to 8} 7 x^{9} - 4 x^{5} + 2 x - 13}{- 3 x^{9} + x^{8} - 5 x^{2} + 2 x}$
32393	Evaluate the Limit	( limit as x approaches 8 of 2x^4+7)/(-3x^2-1)	$\frac{lim_{x \to 8} 2 x^{4} + 7}{- 3 x^{2} - 1}$
32394	Evaluate the Limit	( limit as x approaches 8 of 2x^4-3x-4)/(5x^3-7x-5)	$\frac{lim_{x \to 8} 2 x^{4} - 3 x - 4}{5 x^{3} - 7 x - 5}$
32395	Evaluate the Limit	( limit as x approaches 8 of 20x^2-8x+6)/(3x-4x^2)	$\frac{lim_{x \to 8} 20 x^{2} - 8 x + 6}{3 x - 4 x^{2}}$
32396	Evaluate the Limit	( limit as x approaches 8 of 25x^2-11)/(9x^2+5x)	$\frac{lim_{x \to 8} 25 x^{2} - 11}{9 x^{2} + 5 x}$
32397	Evaluate the Limit	( limit as x approaches 8 of 2x)/(x^2-36)	$\frac{lim_{x \to 8} 2 x}{x^{2} - 36}$
32398	Evaluate the Limit	( limit as x approaches 8 of 2x)/(7x-3)	$\frac{lim_{x \to 8} 2 x}{7 x - 3}$
32399	Evaluate the Limit	( limit as x approaches 8 of 2x+6)/(11x^2-4x+10)	$\frac{lim_{x \to 8} 2 x + 6}{11 x^{2} - 4 x + 10}$
32400	Evaluate the Limit	( limit as x approaches 8 of 2x+7)/(-3x-1)	$\frac{lim_{x \to 8} 2 x + 7}{- 3 x - 1}$