Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
30301	Evaluate the Limit	limit as x approaches 1 of (x^2-4x+3)/(x^2-5x+4)	$lim_{x \to 1} \frac{x^{2} - 4 x + 3}{x^{2} - 5 x + 4}$
30302	Evaluate the Limit	limit as x approaches -1 of (x^2-8)/(1-x)	$lim_{x \to - 1} \frac{x^{2} - 8}{1 - x}$
30303	Evaluate the Limit	limit as x approaches 1 of (x^2-8x+12)/(x-2)	$lim_{x \to 1} \frac{x^{2} - 8 x + 12}{x - 2}$
30304	Evaluate the Limit	limit as x approaches 1 of (x^2-x)/(2x^2+5x-7)	$lim_{x \to 1} \frac{x^{2} - x}{2 x^{2} + 5 x - 7}$
30305	Evaluate the Limit	limit as x approaches -1 of (x^3-x^2-x+1)/( square root of 0+3x^2+2x-1- square root of 0)	$lim_{x \to - 1} \frac{x^{3} - x^{2} - x + 1}{\sqrt{0} + 3 x^{2} + 2 x - 1 - \sqrt{0}}$
30306	Evaluate the Limit	limit as x approaches 1 of (x^3+x-2)/(x-1)	$lim_{x \to 1} \frac{x^{3} + x - 2}{x - 1}$
30307	Evaluate the Limit	limit as x approaches 1 of 1/(\|x-1\|)	$lim_{x \to 1} \frac{1}{\| x - 1 \|}$
30308	Evaluate the Limit	limit as x approaches -1 of (x^3-1)/(x-1)	$lim_{x \to - 1} \frac{x^{3} - 1}{x - 1}$
30309	Evaluate the Limit	limit as x approaches 1 of (x^3-3x^2+3x-1)/(x^3+x)	$lim_{x \to 1} \frac{x^{3} - 3 x^{2} + 3 x - 1}{x^{3} + x}$
30310	Evaluate the Limit	limit as x approaches 1 of (x^3-3x+2)/(x^4-4x+3)	$lim_{x \to 1} \frac{x^{3} - 3 x + 2}{x^{4} - 4 x + 3}$
30311	Evaluate the Limit	limit as x approaches 1 of (x^3-7x^2+14x-8)/(x^3-6x^2+11x-6)	$lim_{x \to 1} \frac{x^{3} - 7 x^{2} + 14 x - 8}{x^{3} - 6 x^{2} + 11 x - 6}$
30312	Find the Derivative - d/dt	t^7 natural log of t	$t^{7} \ln (t)$
30313	Evaluate the Limit	limit as x approaches 1 of (x^5-1)/(x^3-1)	$lim_{x \to 1} \frac{x^{5} - 1}{x^{3} - 1}$
30314	Evaluate the Limit	limit as x approaches 1 of (x^9-x^8)/(1-x)	$lim_{x \to 1} \frac{x^{9} - x^{8}}{1 - x}$
30315	Find the Derivative - d/dr	square root of r+ eighth root of r	$\sqrt{r} + \sqrt[8]{r}$
30316	Evaluate the Limit	limit as x approaches 1 of \|x\|	$lim_{x \to 1} \| x \|$
30317	Evaluate the Limit	limit as x approaches 1 from the left of \|x+2\|	$lim_{x \to 1} \| x + 2 \|$
30318	Evaluate the Limit	limit as x approaches 1 of (1-x^(-1/3))/(1-x^(-2/3))	$lim_{x \to 1} \frac{1 - x^{- \frac{1}{3}}}{1 - x^{- \frac{2}{3}}}$
30319	Evaluate the Limit	limit as x approaches 1 of (3x^2)-6x+1	$lim_{x \to 1} (3 x^{2}) - 6 x + 1$
30320	Evaluate the Limit	limit as x approaches 1 of (3x-3)/(x-1)	$lim_{x \to 1} \frac{3 x - 3}{x - 1}$
30321	Evaluate the Limit	limit as x approaches 1 of 4/(x^(2-1))	$lim_{x \to 1} \frac{4}{x^{2 - 1}}$
30322	Evaluate the Limit	limit as x approaches 1 of (4 natural log of x+2 natural log of x^3)/( natural log of x- natural log of square root of x)	$lim_{x \to 1} \frac{4 \ln (x) + 2 \ln (x^{3})}{\ln (x) - \ln (\sqrt{x})}$
30323	Evaluate the Limit	limit as x approaches 1 of (5x^2-24x-5)/(x^2+16x-105)	$lim_{x \to 1} \frac{5 x^{2} - 24 x - 5}{x^{2} + 16 x - 105}$
30324	Evaluate the Limit	limit as x approaches 1 from the left of x/(x-1)	$lim_{x \to 1} \frac{x}{x - 1}$
30325	Find the Derivative - d/d@VAR	M(t)=at^be^(-ct)	$M (t) = a t^{b} e^{- c t}$
30326	Evaluate the Limit	( limit as x approaches 1 of (x^2)(x^2-(a+1)x+a))/(x-a)	$\frac{lim_{x \to 1} (x^{2}) (x^{2} - (a + 1) x + a)}{x - a}$
30327	Evaluate the Limit	limit as x approaches 1 of (x^2)+2x	$lim_{x \to 1} (x^{2}) + 2 x$
30328	Evaluate the Limit	limit as x approaches -1 of (10x^2-10)/(2x+2)	$lim_{x \to - 1} \frac{10 x^{2} - 10}{2 x + 2}$
30329	Evaluate the Limit	limit as x approaches 1 of (100x^99-2x+1)/(10x)	$lim_{x \to 1} \frac{100 x^{99} - 2 x + 1}{10 x}$
30330	Evaluate the Limit	limit as x approaches 1 of (2x^2+x-3)/(x^2+4x-5)	$lim_{x \to 1} \frac{2 x^{2} + x - 3}{x^{2} + 4 x - 5}$
30331	Evaluate the Limit	limit as x approaches 1 of (2x^2+x-3)/(x-1)	$lim_{x \to 1} \frac{2 x^{2} + x - 3}{x - 1}$
30332	Evaluate the Limit	limit as x approaches -1 of 5/4x-3/4	$lim_{x \to - 1} \frac{5}{4} x - \frac{3}{4}$
30333	Evaluate the Limit	limit as x approaches 1 of (6x^2+12x-18)/(2x-2)	$lim_{x \to 1} \frac{6 x^{2} + 12 x - 18}{2 x - 2}$
30334	Evaluate the Limit	limit as x approaches 1 from the left of 7/(x^3-1)	$lim_{x \to 1} \frac{7}{x^{3} - 1}$
30335	Evaluate the Limit	limit as x approaches 1 of (cos(3x))/(x^2+2x-1)	$lim_{x \to 1} \frac{\cos (3 x)}{x^{2} + 2 x - 1}$
30336	Evaluate the Limit	limit as x approaches 1 of e^(1/(x-1))	$lim_{x \to 1} e^{\frac{1}{x - 1}}$
30337	Evaluate the Limit	limit as x approaches 1 of e^(0.1x)	$lim_{x \to 1} e^{0.1 x}$
30338	Evaluate the Limit	limit as x approaches 1 of e^(4x^3-4x)	$lim_{x \to 1} e^{4 x^{3} - 4 x}$
30339	Find the Derivative - d/d@VAR	f(x)=2+2/(x^3)+4x^2-(3 square root of x)/4	$f (x) = 2 + \frac{2}{x^{3}} + 4 x^{2} - \frac{3 \sqrt{x}}{4}$
30340	Evaluate the Limit	limit as x approaches 1 of ( natural log of natural log of x)/( natural log of x)	$lim_{x \to 1} \frac{\ln (\ln (x))}{\ln (x)}$
30341	Evaluate the Limit	limit as x approaches 1 of ( natural log of x)/(sin(6pi))	$lim_{x \to 1} \frac{\ln (x)}{\sin (6 π)}$
30342	Find the Derivative - d/d@VAR	f(x)=x^9e^(7x)	$f (x) = x^{9} e^{7 x}$
30343	Evaluate the Limit	limit as x approaches 1 of natural log of (x)^(x-1)	$lim_{x \to 1} \ln ({(x)}^{x - 1})$
30344	Evaluate the Limit	limit as x approaches 1 of (sin(8x))/(tan(7x))	$lim_{x \to 1} \frac{\sin (8 x)}{\tan (7 x)}$
30345	Evaluate the Limit	limit as x approaches 1 of (tan(6x))/(sin(3x))	$lim_{x \to 1} \frac{\tan (6 x)}{\sin (3 x)}$
30346	Evaluate the Limit	limit as x approaches 1 of square root of (x^2+2x-3)/(x-1)	$lim_{x \to 1} \sqrt{\frac{x^{2} + 2 x - 3}{x - 1}}$
30347	Evaluate the Limit	limit as x approaches 1 from the left of square root of (x+4)/(x+9)	$lim_{x \to 1} \sqrt{\frac{x + 4}{x + 9}}$
30348	Evaluate the Limit	limit as x approaches 1 of square root of (x-1)/(x-3)	$lim_{x \to 1} \sqrt{\frac{x - 1}{x - 3}}$
30349	Evaluate the Limit	limit as x approaches 1 of square root of 4x+5	$lim_{x \to 1} \sqrt{4 x + 5}$
30350	Evaluate the Limit	limit as h approaches 0 of ((5+h)^2-25)/h	$lim_{h \to 0} \frac{{(5 + h)}^{2} - 25}{h}$
30351	Evaluate the Limit	limit as x approaches -1 of cube root of x^3-1	$lim_{x \to - 1} \sqrt[3]{x^{3} - 1}$
30352	Evaluate the Limit	limit as x approaches -2 of (x^2-6x+5)/(x^2-7x+10)	$lim_{x \to - 2} \frac{x^{2} - 6 x + 5}{x^{2} - 7 x + 10}$
30353	Evaluate the Limit	limit as x approaches -1 of (x^2+4x+3)/(x^2-3x-4)	$lim_{x \to - 1} \frac{x^{2} + 4 x + 3}{x^{2} - 3 x - 4}$
30354	Evaluate the Limit	limit as x approaches 2 of (x^3-2x^2-6+3x)/(x-2)	$lim_{x \to 2} \frac{x^{3} - 2 x^{2} - 6 + 3 x}{x - 2}$
30355	Evaluate the Limit	limit as x approaches 2 of (x^3-2x-4)/(x-2)	$lim_{x \to 2} \frac{x^{3} - 2 x - 4}{x - 2}$
30356	Evaluate the Limit	limit as x approaches 2 of (x^3-7x+6)/(x^3-5x^2+2x+8)	$lim_{x \to 2} \frac{x^{3} - 7 x + 6}{x^{3} - 5 x^{2} + 2 x + 8}$
30357	Evaluate the Limit	limit as x approaches 2 of (x^3-8)/(x^(2-4))	$lim_{x \to 2} \frac{x^{3} - 8}{x^{2 - 4}}$
30358	Evaluate the Limit	limit as x approaches 2 of 1/(x-2)-((2x)/(x^2-4))	$lim_{x \to 2} \frac{1}{x - 2} - (\frac{2 x}{x^{2} - 4})$
30359	Evaluate the Limit	limit as x approaches 2 of (10-3x-x^2)/(x-2)	$lim_{x \to 2} \frac{10 - 3 x - x^{2}}{x - 2}$
30360	Evaluate the Limit	limit as x approaches -2 of (1-4x)^(3/2)	$lim_{x \to - 2} {(1 - 4 x)}^{\frac{3}{2}}$
30361	Evaluate the Limit	limit as x approaches 2 from the left of (15+x^3)/((x-2)^4)	$lim_{x \to 2} \frac{15 + x^{3}}{{(x - 2)}^{4}}$
30362	Evaluate the Limit	limit as x approaches 2 of ((2.001)-2)/((2.001)^2-13*2.001+22)	$lim_{x \to 2} \frac{(2.001) - 2}{{(2.001)}^{2} - 13 \cdot 2.001 + 22}$
30363	Evaluate the Limit	limit as x approaches 2 of (2x+5)/(11-x^3)	$lim_{x \to 2} \frac{2 x + 5}{11 - x^{3}}$
30364	Evaluate the Limit	limit as x approaches -2 of (3x^2+5x-2)/(x^2)	$lim_{x \to - 2} \frac{3 x^{2} + 5 x - 2}{x^{2}}$
30365	Evaluate the Limit	limit as x approaches -2 of (3x^2+5x-2)/(x+2)	$lim_{x \to - 2} \frac{3 x^{2} + 5 x - 2}{x + 2}$
30366	Evaluate the Limit	limit as x approaches -2 of (3x-2)/(2x^2+x-1)	$lim_{x \to - 2} \frac{3 x - 2}{2 x^{2} + x - 1}$
30367	Evaluate the Limit	limit as x approaches 2 of (4x^2-11x+6)/(3x^2-8x+4)	$lim_{x \to 2} \frac{4 x^{2} - 11 x + 6}{3 x^{2} - 8 x + 4}$
30368	Evaluate the Limit	limit as x approaches 2 of ((52x-16x^2)-40)/(x-2)	$lim_{x \to 2} \frac{(52 x - 16 x^{2}) - 40}{x - 2}$
30369	Evaluate the Limit	limit as x approaches 2 of (6x+3)^2	$lim_{x \to 2} {(6 x + 3)}^{2}$
30370	Evaluate the Limit	limit as x approaches -2 of (sin(5x+10))/(4x+8)	$lim_{x \to - 2} \frac{\sin (5 x + 10)}{4 x + 8}$
30371	Evaluate the Limit	limit as x approaches 2 of (x-2)/(x^2-7x+10)	$lim_{x \to 2} \frac{x - 2}{x^{2} - 7 x + 10}$
30372	Evaluate the Limit	limit as x approaches -2 of (x-4)/(6x^2-8x+4)	$lim_{x \to - 2} \frac{x - 4}{6 x^{2} - 8 x + 4}$
30373	Evaluate the Limit	limit as x approaches 2 of (x-2)/(x^2-18x+32)	$lim_{x \to 2} \frac{x - 2}{x^{2} - 18 x + 32}$
30374	Evaluate the Limit	limit as x approaches -2 of (t^3+8)/(t+2)	$lim_{x \to - 2} \frac{t^{3} + 8}{t + 2}$
30375	Evaluate the Limit	limit as x approaches -2 of (x+2)/(t^2-4)	$lim_{x \to - 2} \frac{x + 2}{t^{2} - 4}$
30376	Evaluate the Limit	limit as x approaches 2 of 3x^3-7x^2+3	$lim_{x \to 2} 3 x^{3} - 7 x^{2} + 3$
30377	Evaluate the Limit	limit as x approaches 2 of 3x+x^2	$lim_{x \to 2} 3 x + x^{2}$
30378	Evaluate the Limit	limit as x approaches 2 of 3x-1	$lim_{x \to 2} 3 x - 1$
30379	Evaluate the Limit	limit as x approaches 2 of 5x^3-3x^2+4	$lim_{x \to 2} 5 x^{3} - 3 x^{2} + 4$
30380	Evaluate the Limit	limit as x approaches -2 of 9x+1	$lim_{x \to - 2} 9 x + 1$
30381	Evaluate the Limit	limit as x approaches 2 of p	$lim_{x \to 2} p$
30382	Evaluate the Limit	limit as x approaches 2 of x-(x)	$lim_{x \to 2} x - (x)$
30383	Evaluate the Limit	limit as x approaches 2 of x square root of x^2-4	$lim_{x \to 2} x \sqrt{x^{2} - 4}$
30384	Evaluate the Limit	limit as x approaches 2 of x+9	$lim_{x \to 2} x + 9$
30385	Evaluate the Limit	limit as x approaches 2 of f(x)+g(x)	$lim_{x \to 2} f (x) + g (x)$
30386	Evaluate the Limit	limit as x approaches 2 of (f(x)-f(x))/(x-2)	$lim_{x \to 2} \frac{f (x) - f (x)}{x - 2}$
30387	Evaluate the Limit	limit as x approaches 2 of ((x^2+5)^(1/2)-3)/(x-2)	$lim_{x \to 2} \frac{{(x^{2} + 5)}^{\frac{1}{2}} - 3}{x - 2}$
30388	Evaluate the Limit	limit as x approaches infinity of x^(6/x)	$lim_{x \to \infty} x^{\frac{6}{x}}$
30389	Evaluate the Limit	limit as x approaches -2 of (5/x+5/2)/(x+2)	$lim_{x \to - 2} \frac{\frac{5}{x} + \frac{5}{2}}{x + 2}$
30390	Evaluate the Limit	limit as x approaches 2 of (t^4-2)/(2t^2-3t+2)	$lim_{x \to 2} \frac{t^{4} - 2}{2 t^{2} - 3 t + 2}$
30391	Evaluate the Limit	limit as x approaches 2 of ( square root of 2+x- square root of 3x-2)/( square root of 4x+1- square root of 5x-1)	$lim_{x \to 2} \frac{\sqrt{2 + x} - \sqrt{3 x - 2}}{\sqrt{4 x + 1} - \sqrt{5 x - 1}}$
30392	Evaluate the Limit	limit as a approaches 2 of (a^2+2a-8)/(a^3-8)	$lim_{a \to 2} \frac{a^{2} + 2 a - 8}{a^{3} - 8}$
30393	Evaluate the Limit	limit as x approaches 2 of (x^2+4x+4)/(x^2-4)	$lim_{x \to 2} \frac{x^{2} + 4 x + 4}{x^{2} - 4}$
30394	Evaluate the Limit	limit as x approaches 2 of (x^2+5x-14)/(x-2)	$lim_{x \to 2} \frac{x^{2} + 5 x - 14}{x - 2}$
30395	Evaluate the Limit	limit as x approaches 2 of (x^2-15x+56)/(x-2)	$lim_{x \to 2} \frac{x^{2} - 15 x + 56}{x - 2}$
30396	Evaluate the Limit	limit as x approaches 2 of (x^2-2x-2)/(x^2-5x+6)	$lim_{x \to 2} \frac{x^{2} - 2 x - 2}{x^{2} - 5 x + 6}$
30397	Evaluate the Limit	limit as x approaches 2 of (x^2-4)/(x^2-8)	$lim_{x \to 2} \frac{x^{2} - 4}{x^{2} - 8}$
30398	Evaluate the Limit	limit as x approaches 1 of (x-1)/( square root of x+3-2)	$lim_{x \to 1} \frac{x - 1}{\sqrt{x + 3 - 2}}$
30399	Evaluate the Limit	limit as x approaches 2 of 3x^2-4x+3	$lim_{x \to 2} 3 x^{2} - 4 x + 3$
30400	Evaluate the Limit	limit as x approaches 16 of (x-4)/(x^2-4x)	$lim_{x \to 16} \frac{x - 4}{x^{2} - 4 x}$