Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
34601	Evaluate the Limit	limit as x approaches 2 of (x^2-7x+12)/(x-2)	$lim_{x \to 2} \frac{x^{2} - 7 x + 12}{x - 2}$
34602	Evaluate the Limit	limit as x approaches -8 of (6x^2+5x)/((1-x)(2x-3))	$lim_{x \to - 8} \frac{6 x^{2} + 5 x}{(1 - x) (2 x - 3)}$
34603	Evaluate the Limit	limit as x approaches 8 of (5-2x)/(6-7x^2)	$lim_{x \to 8} \frac{5 - 2 x}{6 - 7 x^{2}}$
34604	Evaluate the Limit	limit as x approaches 8 of (5-2x)/(9-7x^2)	$lim_{x \to 8} \frac{5 - 2 x}{9 - 7 x^{2}}$
34605	Evaluate the Limit	limit as x approaches 8 of (5-3x)/(6-5x^2)	$lim_{x \to 8} \frac{5 - 3 x}{6 - 5 x^{2}}$
34606	Evaluate the Limit	limit as x approaches 8 of (5-7x^2)/(6x^2+23x+513)	$lim_{x \to 8} \frac{5 - 7 x^{2}}{6 x^{2} + 23 x + 513}$
34607	Evaluate the Limit	limit as x approaches 8 of (5-8x-5x^2)/(3+3x-12x^2)	$lim_{x \to 8} \frac{5 - 8 x - 5 x^{2}}{3 + 3 x - 12 x^{2}}$
34608	Evaluate the Limit	limit as x approaches 8 of (5s- square root of 4s^2+3s-2)/(s+1)	$lim_{x \to 8} \frac{5 s - \sqrt{4 s^{2} + 3 s - 2}}{s + 1}$
34609	Evaluate the Limit	limit as x approaches -8 of (5x)/( fourth root of 5x^4+3)	$lim_{x \to - 8} \frac{5 x}{\sqrt[4]{5 x^{4} + 3}}$
34610	Evaluate the Limit	limit as x approaches 8 of (5x)/(3x+9)	$lim_{x \to 8} \frac{5 x}{3 x + 9}$
34611	Evaluate the Limit	limit as x approaches 8 of (5x)/(7x-9)	$lim_{x \to 8} \frac{5 x}{7 x - 9}$
34612	Evaluate the Limit	limit as x approaches 8 of (5x+1)/( square root of 4x^2+7)	$lim_{x \to 8} \frac{5 x + 1}{\sqrt{4 x^{2} + 7}}$
34613	Evaluate the Limit	limit as x approaches 8 of 5^(-x)	$lim_{x \to 8} 5^{- x}$
34614	Evaluate the Limit	limit as x approaches 8 of (5+e^(4x))/(1+ natural log of x)	$lim_{x \to 8} \frac{5 + e^{4 x}}{1 + \ln (x)}$
34615	Evaluate the Limit	limit as x approaches 8 of (5+e^(4x))/(3+ natural log of x)	$lim_{x \to 8} \frac{5 + e^{4 x}}{3 + \ln (x)}$
34616	Evaluate the Limit	limit as x approaches 8 of (5+10x)/( square root of 10+8x^2)	$lim_{x \to 8} \frac{5 + 10 x}{\sqrt{10 + 8 x^{2}}}$
34617	Evaluate the Limit	limit as x approaches 8 of (5+25)/(x-70)	$lim_{x \to 8} \frac{5 + 25}{x - 70}$
34618	Evaluate the Limit	limit as x approaches 8 of (6x^2-7x+8)/(3x^2+2)	$lim_{x \to 8} \frac{6 x^{2} - 7 x + 8}{3 x^{2} + 2}$
34619	Evaluate the Limit	limit as x approaches 8 of (6x^3)/(e^x)	$lim_{x \to 8} \frac{6 x^{3}}{e^{x}}$
34620	Evaluate the Limit	limit as x approaches 8 of (5x^3)/(e^(2x))	$lim_{x \to 8} \frac{5 x^{3}}{e^{2 x}}$
34621	Evaluate the Limit	limit as x approaches 8 of (5x^3+5x-2)/(5x^4-2x^3-8)	$lim_{x \to 8} \frac{5 x^{3} + 5 x - 2}{5 x^{4} - 2 x^{3} - 8}$
34622	Evaluate the Limit	limit as x approaches 8 of (5x^3+8)/(20x^3-4x^2+5)	$lim_{x \to 8} \frac{5 x^{3} + 8}{20 x^{3} - 4 x^{2} + 5}$
34623	Evaluate the Limit	limit as x approaches 8 of (5x^3+9x-5)/(5x^4-6x^3-7)	$lim_{x \to 8} \frac{5 x^{3} + 9 x - 5}{5 x^{4} - 6 x^{3} - 7}$
34624	Evaluate the Limit	limit as x approaches 8 of (5x^3-2x-8)/(8x^2-8x-5)	$lim_{x \to 8} \frac{5 x^{3} - 2 x - 8}{8 x^{2} - 8 x - 5}$
34625	Evaluate the Limit	limit as x approaches 8 of (5x^3-3x^2+10x)/(x^3)	$lim_{x \to 8} \frac{5 x^{3} - 3 x^{2} + 10 x}{x^{3}}$
34626	Evaluate the Limit	limit as x approaches 8 of (5x^3-6x)/(7x^3+7)	$lim_{x \to 8} \frac{5 x^{3} - 6 x}{7 x^{3} + 7}$
34627	Find the Derivative - d/d@VAR	f(x)=x^3-3x^2-9x+10	$f (x) = x^{3} - 3 x^{2} - 9 x + 10$
34628	Evaluate the Limit	limit as x approaches 8 of (5x^3-7x-8)/(7x^2-2x-2)	$lim_{x \to 8} \frac{5 x^{3} - 7 x - 8}{7 x^{2} - 2 x - 2}$
34629	Evaluate the Limit	limit as x approaches 8 of (5x^3-9x-6x^2)/(3-2x-3x^3)	$lim_{x \to 8} \frac{5 x^{3} - 9 x - 6 x^{2}}{3 - 2 x - 3 x^{3}}$
34630	Evaluate the Limit	limit as x approaches 8 of (5x^4-7x-8)/(4x^3-3x-2)	$lim_{x \to 8} \frac{5 x^{4} - 7 x - 8}{4 x^{3} - 3 x - 2}$
34631	Evaluate the Limit	limit as x approaches -8 of (5x^8-2x^3+9)/(3+x-4x^5)	$lim_{x \to - 8} \frac{5 x^{8} - 2 x^{3} + 9}{3 + x - 4 x^{5}}$
34632	Evaluate the Limit	limit as x approaches -8 of 5/(x^4)	$lim_{x \to - 8} \frac{5}{x^{4}}$
34633	Evaluate the Limit	limit as x approaches -8 of 5/4*(16x-20)	$lim_{x \to - 8} \frac{5}{4} \cdot (16 x - 20)$
34634	Evaluate the Limit	limit as x approaches 8 of (4x-x^3)/(5x^3+2)	$lim_{x \to 8} \frac{4 x - x^{3}}{5 x^{3} + 2}$
34635	Evaluate the Limit	limit as x approaches -8 of (4x)/( square root of 3x^2+7)	$lim_{x \to - 8} \frac{4 x}{\sqrt{3 x^{2} + 7}}$
34636	Evaluate the Limit	limit as x approaches 8 of (4 natural log of x)/x	$lim_{x \to 8} \frac{4 \ln (x)}{x}$
34637	Evaluate the Limit	limit as x approaches 8 of (4+100000sin(100000))/(2100000-3)	$lim_{x \to 8} \frac{4 + 100000 \cdot \sin (100000)}{2 \cdot 100000 - 3}$
34638	Evaluate the Limit	limit as x approaches 8 of (4+9x)/(4-9x)	$lim_{x \to 8} \frac{4 + 9 x}{4 - 9 x}$
34639	Evaluate the Limit	limit as x approaches 8 of (40x^7+2x^2)/(17x^6-3x)	$lim_{x \to 8} \frac{40 x^{7} + 2 x^{2}}{17 x^{6} - 3 x}$
34640	Evaluate the Limit	limit as x approaches 8 of (41x^7+4x^2)/(17x^6-3x)	$lim_{x \to 8} \frac{41 x^{7} + 4 x^{2}}{17 x^{6} - 3 x}$
34641	Evaluate the Limit	limit as x approaches 8 of (4-3x+9x^2)/(3x^2+8x+6)	$lim_{x \to 8} \frac{4 - 3 x + 9 x^{2}}{3 x^{2} + 8 x + 6}$
34642	Evaluate the Limit	limit as x approaches infinity of square root of x^2+7	$lim_{x \to \infty} \sqrt{x^{2} + 7}$
34643	Evaluate the Limit	limit as x approaches 8 of 5/(5x-4)	$lim_{x \to 8} \frac{5}{5 x - 4}$
34644	Evaluate the Limit	limit as x approaches 8 of (5x^2-3x+5)/(14^2+3x-2)	$lim_{x \to 8} \frac{5 x^{2} - 3 x + 5}{14^{2} + 3 x - 2}$
34645	Evaluate the Limit	limit as x approaches 8 of (5x^2-4)/( square root of 4x^4+2)	$lim_{x \to 8} \frac{5 x^{2} - 4}{\sqrt{4 x^{4} + 2}}$
34646	Evaluate the Limit	limit as x approaches -8 of (4x-1)/( square root of 2+3x^2)	$lim_{x \to - 8} \frac{4 x - 1}{\sqrt{2 + 3 x^{2}}}$
34647	Evaluate the Limit	limit as x approaches 8 of (-4x-7)/(6x^2+4)	$lim_{x \to 8} \frac{- 4 x - 7}{6 x^{2} + 4}$
34648	Evaluate the Limit	limit as x approaches 8 of (4x-8)/(x^2+4x+4)	$lim_{x \to 8} \frac{4 x - 8}{x^{2} + 4 x + 4}$
34649	Evaluate the Limit	limit as x approaches 8 of (4x-9)/(3x+4)	$lim_{x \to 8} \frac{4 x - 9}{3 x + 4}$
34650	Evaluate the Limit	limit as x approaches 8 of (5e^(4x)-4e^(-4x))/(3e^(4x)+8e^(-4x))	$lim_{x \to 8} \frac{5 e^{4 \cdot x} - 4 e^{- 4 \cdot x}}{3 e^{4 \cdot x} + 8 e^{- 4 \cdot x}}$
34651	Evaluate the Limit	limit as x approaches 8 of (5e^(-x)+10)/(6e^x-1)	$lim_{x \to 8} \frac{5 e^{- x} + 10}{6 e^{x} - 1}$
34652	Evaluate the Limit	limit as x approaches -5 of (1/5+1/x)/(5+x)	$lim_{x \to - 5} \frac{\frac{1}{5} + \frac{1}{x}}{5 + x}$
34653	Evaluate the Limit	limit as x approaches 8 of (5x^(3/2))/(4 square root of x+1)	$lim_{x \to 8} \frac{5 x^{\frac{3}{2}}}{4 \sqrt{x} + 1}$
34654	Evaluate the Limit	limit as x approaches 8 of (5x^(3/2))/(4 square root of x+5)	$lim_{x \to 8} \frac{5 x^{\frac{3}{2}}}{4 \sqrt{x} + 5}$
34655	Evaluate the Limit	limit as x approaches 8 of (5x^(3/2))/(7x^2+5)	$lim_{x \to 8} \frac{5 x^{\frac{3}{2}}}{7 x^{2} + 5}$
34656	Evaluate the Limit	limit as x approaches 8 of (4x^5+8x^3-9)/(-x^3+7x^2+4)	$lim_{x \to 8} \frac{4 x^{5} + 8 x^{3} - 9}{- x^{3} + 7 x^{2} + 4}$
34657	Evaluate the Limit	limit as x approaches 8 of (4x^7-5x^5)/(3x^8+4)	$lim_{x \to 8} \frac{4 x^{7} - 5 x^{5}}{3 x^{8} + 4}$
34658	Evaluate the Limit	limit as x approaches 8 of 4/(x^r)	$lim_{x \to 8} \frac{4}{x^{r}}$
34659	Evaluate the Limit	limit as x approaches 8 of (4x^2-3x^2+1)/(2x^4+x^3+x^2+x+1)	$lim_{x \to 8} \frac{4 x^{2} - 3 x^{2} + 1}{2 x^{4} + x^{3} + x^{2} + x + 1}$
34660	Evaluate the Limit	limit as x approaches -8 of (4x^2-3x-x-5x^3)/(9x^2+9x+7)	$lim_{x \to - 8} \frac{4 x^{2} - 3 x - x - 5 x^{3}}{9 x^{2} + 9 x + 7}$
34661	Evaluate the Limit	limit as x approaches 8 of (4x^21-5x^19+7x-8)/(5x-34x^21+8)	$lim_{x \to 8} \frac{4 x^{21} - 5 x^{19} + 7 x - 8}{5 x - 34 x^{21} + 8}$
34662	Evaluate the Limit	limit as x approaches 0 of (sin(8x))/x	$lim_{x \to 0} \frac{\sin (8 x)}{x}$
34663	Evaluate the Limit	limit as x approaches 8 of 4/(9+1/x)	$lim_{x \to 8} \frac{4}{9 + \frac{1}{x}}$
34664	Evaluate the Limit	limit as x approaches -8 of (4/x)-12	$lim_{x \to - 8} (\frac{4}{x}) - 12$
34665	Evaluate the Limit	( limit as x approaches -6 of (x+10)(\|x+6\|))/(x+6)	$\frac{lim_{x \to - 6} (x + 10) (\| x + 6 \|)}{x + 6}$
34666	Evaluate the Limit	limit as x approaches -6 of (x+6)((\|x+6\|)/(x+6))	$lim_{x \to - 6} (x + 6) (\frac{\| x + 6 \|}{x + 6})$
34667	Evaluate the Limit	limit as x approaches 6 of x-5	$lim_{x \to 6} x - 5$
34668	Evaluate the Limit	limit as x approaches 6 of (6)(8*-6)	$lim_{x \to 6} (6) (8 \cdot - 6)$
34669	Evaluate the Limit	limit as x approaches 6 of 15-8	$lim_{x \to 6} 15 - 8$
34670	Evaluate the Limit	limit as x approaches 6 of ((x/(x+1))-(6/7))/(x-6)	$lim_{x \to 6} \frac{(\frac{x}{x + 1}) - (\frac{6}{7})}{x - 6}$
34671	Evaluate the Limit	limit as x approaches 6 of ( square root of 2x-4- square root of x+2)/(2-12)	$lim_{x \to 6} \frac{\sqrt{2 x - 4} - \sqrt{x + 2}}{2 - 12}$
34672	Evaluate the Limit	limit as x approaches 6 of (( square root of x+30)-6)/(x-6)	$lim_{x \to 6} \frac{(\sqrt{x + 30}) - 6}{x - 6}$
34673	Evaluate the Limit	limit as x approaches 6 of (x^2+13x+42)/(x+6)	$lim_{x \to 6} \frac{x^{2} + 13 x + 42}{x + 6}$
34674	Evaluate the Limit	limit as x approaches -6 of (x^2+3x-18)/(x+6)	$lim_{x \to - 6} \frac{x^{2} + 3 x - 18}{x + 6}$
34675	Evaluate the Limit	limit as x approaches 6 of (x^2-10x+24)/(x^2-8x+12)	$lim_{x \to 6} \frac{x^{2} - 10 x + 24}{x^{2} - 8 x + 12}$
34676	Evaluate the Limit	limit as x approaches 6 of (x^2-10x+24)/(x^3-6x^2)	$lim_{x \to 6} \frac{x^{2} - 10 x + 24}{x^{3} - 6 x^{2}}$
34677	Evaluate the Limit	limit as x approaches 6 of x/5	$lim_{x \to 6} \frac{x}{5}$
34678	Evaluate the Limit	limit as x approaches 6 of -x^2+8x-3	$lim_{x \to 6} - x^{2} + 8 x - 3$
34679	Evaluate the Limit	limit as x approaches 6 of -x^2+x-6	$lim_{x \to 6} - x^{2} + x - 6$
34680	Evaluate the Limit	limit as x approaches 6 of (4x^2-144)/(x^2-12x+36)	$lim_{x \to 6} \frac{4 x^{2} - 144}{x^{2} - 12 x + 36}$
34681	Evaluate the Limit	limit as x approaches -6 of (7x+42)/(\|x+6\|)	$lim_{x \to - 6} \frac{7 x + 42}{\| x + 6 \|}$
34682	Evaluate the Limit	limit as x approaches -6 of (-8x^2-45x+18)/(x+6)	$lim_{x \to - 6} \frac{- 8 x^{2} - 45 x + 18}{x + 6}$
34683	Evaluate the Limit	limit as x approaches 6 of square root of x^2+14x+49	$lim_{x \to 6} \sqrt{x^{2} + 14 x + 49}$
34684	Evaluate the Limit	limit as x approaches 6 of ((x^2-36)(sin(x-6)))/(x^2-12x+36)	$lim_{x \to 6} \frac{(x^{2} - 36) (\sin (x - 6))}{x^{2} - 12 x + 36}$
34685	Evaluate the Limit	limit as x approaches 6 of -((x^2-8x+12)/(x^3-6x^2))	$lim_{x \to 6} - (\frac{x^{2} - 8 x + 12}{x^{3} - 6 x^{2}})$
34686	Evaluate the Limit	limit as x approaches 6 of (3x)/4+2	$lim_{x \to 6} \frac{3 x}{4} + 2$
34687	Evaluate the Limit	limit as x approaches 6 of (x+2)/(x^2-4x-12)	$lim_{x \to 6} \frac{x + 2}{x^{2} - 4 x - 12}$
34688	Evaluate the Limit	limit as x approaches -6 of ((x+6)^2)/(x^2-36)	$lim_{x \to - 6} \frac{{(x + 6)}^{2}}{x^{2} - 36}$
34689	Evaluate the Limit	limit as x approaches 6 of ( square root of 6.001+2)/(6.001-6)	$lim_{x \to 6} \frac{\sqrt{6.001} + 2}{6.001 - 6}$
34690	Evaluate the Limit	limit as x approaches 6 of ( square root of 6.1+2)/(6.1-6)	$lim_{x \to 6} \frac{\sqrt{6.1} + 2}{6.1 - 6}$
34691	Evaluate the Limit	limit as x approaches 8 of 7x+6-(2x^3)÷3+14x+x^2	$lim_{x \to 8} 7 x + 6 - 2 x^{3} \div 3 + 14 x + x^{2}$
34692	Evaluate the Limit	limit as x approaches 8 of 7x-8 square root of x	$lim_{x \to 8} 7 x - 8 \sqrt{x}$
34693	Evaluate the Limit	limit as x approaches 8 of (5-2x^(3/2))/(3x^2-4)	$lim_{x \to 8} \frac{5 - 2 x^{\frac{3}{2}}}{3 x^{2} - 4}$
34694	Evaluate the Limit	limit as x approaches 8 of (-5x)/(9+2x)	$lim_{x \to 8} \frac{- 5 x}{9 + 2 x}$
34695	Evaluate the Limit	limit as x approaches 8 of (5x)/(x-1)-5/( natural log of x)	$lim_{x \to 8} \frac{5 x}{x - 1} - \frac{5}{\ln (x)}$
34696	Evaluate the Limit	limit as x approaches 8 of (-6x^2+46x+16)/(x-8)	$lim_{x \to 8} \frac{- 6 x^{2} + 46 x + 16}{x - 8}$
34697	Evaluate the Limit	limit as x approaches 8 of (6x^3+3x^2*(8x)+8)/(2x^3-3x^2-10x+2)	$lim_{x \to 8} \frac{6 x^{3} + 3 x^{2} \cdot (8 x) + 8}{2 x^{3} - 3 x^{2} - 10 x + 2}$
34698	Evaluate the Limit	limit as x approaches 8 of 6/x-x/4	$lim_{x \to 8} \frac{6}{x} - \frac{x}{4}$
34699	Evaluate the Limit	limit as x approaches 8 of 6/x-7	$lim_{x \to 8} \frac{6}{x} - 7$
34700	Evaluate the Limit	limit as x approaches 8 of (6000x^2)/(2x^2+3000)	$lim_{x \to 8} \frac{6000 x^{2}}{2 x^{2} + 3000}$