Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
5601	Evaluate the Limit	limit as x approaches 5 of (x^2-7x+10)/(x^2-25)	$lim_{x \to 5} \frac{x^{2} - 7 x + 10}{x^{2} - 25}$
5602	Evaluate the Limit	limit as x approaches 5 of 2x^2-3x+4	$lim_{x \to 5} 2 x^{2} - 3 x + 4$
5603	Evaluate the Limit	limit as x approaches infinity of (x+2)/( square root of 9x^2+1)	$lim_{x \to \infty} \frac{x + 2}{\sqrt{9 x^{2} + 1}}$
5604	Evaluate the Limit	limit as x approaches negative infinity of f(x)	$lim_{x \to - \infty} f (x)$
5605	Evaluate the Limit	limit as x approaches 5 of \|x-5\|	$lim_{x \to 5} \| x - 5 \|$
5606	Evaluate the Limit	limit as x approaches 13 of (x^2+3x-208)/(x^2-169)	$lim_{x \to 13} \frac{x^{2} + 3 x - 208}{x^{2} - 169}$
5607	Evaluate the Limit	limit as x approaches 8 of square root of 9x^2-x-3x	$lim_{x \to 8} \sqrt{9 x^{2} - x - 3 x}$
5608	Evaluate the Limit	limit as x approaches 8 of (x^2-2x-1)e^x	$lim_{x \to 8} (x^{2} - 2 x - 1) e^{x}$
5609	Evaluate the Limit	limit as x approaches 8 of xe^(1/x)-x	$lim_{x \to 8} x e^{\frac{1}{x}} - x$
5610	Evaluate the Limit	limit as x approaches -8 of -3x^16+2	$lim_{x \to - 8} - 3 x^{16} + 2$
5611	Evaluate the Limit	limit as x approaches 8 of 5/x-x/3	$lim_{x \to 8} \frac{5}{x} - \frac{x}{3}$
5612	Evaluate the Limit	limit as x approaches 10 of (x-10)/(x^2-100)	$lim_{x \to 10} \frac{x - 10}{x^{2} - 100}$
5613	Evaluate the Limit	limit as x approaches 8 of square root of x^2+ax- square root of x^2+bx	$lim_{x \to 8} \sqrt{x^{2} + a x} - \sqrt{x^{2} + b x}$
5614	Evaluate the Limit	limit as x approaches -2 of 1/(x+2)	$lim_{x \to - 2} \frac{1}{x + 2}$
5615	Evaluate the Limit	limit as x approaches 7 of (x^2-49)/(\|x-7\|)	$lim_{x \to 7} \frac{x^{2} - 49}{\| x - 7 \|}$
5616	Evaluate the Limit	limit as x approaches 7 from the left of 1/(x-7)	$lim_{x \to 7} \frac{1}{x - 7}$
5617	Evaluate the Limit	limit as x approaches 7 of cos((pix)/3)	$lim_{x \to 7} \cos (\frac{π x}{3})$
5618	Evaluate the Limit	limit as x approaches 3 of (x^2-4x+3)/(x^2-8x+15)	$lim_{x \to 3} \frac{x^{2} - 4 x + 3}{x^{2} - 8 x + 15}$
5619	Evaluate the Limit	limit as x approaches 9 of (9-x)/( square root of x-3)	$lim_{x \to 9} \frac{9 - x}{\sqrt{x} - 3}$
5620	Evaluate the Limit	limit as x approaches 3 of 1/((x-3)^2)	$lim_{x \to 3} \frac{1}{{(x - 3)}^{2}}$
5621	Evaluate the Limit	limit as x approaches 3 of \|x-3\|	$lim_{x \to 3} \| x - 3 \|$
5622	Evaluate the Limit	limit as x approaches 3 of (x^2-x-6)/(x-3)	$lim_{x \to 3} \frac{x^{2} - x - 6}{x - 3}$
5623	Evaluate the Limit	limit as x approaches -2 of (x^2-2x-8)/(x^2+3x+2)	$lim_{x \to - 2} \frac{x^{2} - 2 x - 8}{x^{2} + 3 x + 2}$
5624	Evaluate the Limit	limit as x approaches 9 of (16+ square root of x)/( square root of 16+x)	$lim_{x \to 9} \frac{16 + \sqrt{x}}{\sqrt{16 + x}}$
5625	Evaluate the Limit	limit as x approaches -3 of (1/3+1/x)/(3+x)	$lim_{x \to - 3} \frac{\frac{1}{3} + \frac{1}{x}}{3 + x}$
5626	Evaluate the Limit	limit as x approaches 3 of 2x^3-12x^2+5x+3	$lim_{x \to 3} 2 x^{3} - 12 x^{2} + 5 x + 3$
5627	Evaluate the Limit	limit as x approaches negative infinity of cos(x)	$lim_{x \to - \infty} \cos (x)$
5628	Evaluate the Limit	limit as x approaches 0 of (sin(x))/(3x)	$lim_{x \to 0} \frac{\sin (x)}{3 x}$
5629	Evaluate the Limit	limit as x approaches 3 of square root of 2x-5	$lim_{x \to 3} \sqrt{2 x - 5}$
5630	Evaluate the Limit	limit as x approaches 0 of ((4+x)^2-16)/x	$lim_{x \to 0} \frac{{(4 + x)}^{2} - 16}{x}$
5631	Evaluate the Limit	limit as x approaches infinity of (1-x^2)/(2x)	$lim_{x \to \infty} \frac{1 - x^{2}}{2 x}$
5632	Evaluate the Limit	limit as h approaches 0 of 5x+2h-3	$lim_{h \to 0} 5 x + 2 h - 3$
5633	Graph	f(x)=3x^3-36x	$f (x) = 3 x^{3} - 36 x$
5634	Evaluate the Limit	limit as x approaches infinity of square root of x^2+11	$lim_{x \to \infty} \sqrt{x^{2} + 11}$
5635	Evaluate the Limit	limit as x approaches 3 of 77	$lim_{x \to 3} 77$
5636	Evaluate the Limit	limit as x approaches infinity of 5cos(x)	$lim_{x \to \infty} 5 \cos (x)$
5637	Evaluate the Limit	limit as x approaches 4 of (1/4+1/x)/(4+x)	$lim_{x \to 4} \frac{\frac{1}{4} + \frac{1}{x}}{4 + x}$
5638	Find dy/dx	x^2+5y^2=5	$x^{2} + 5 y^{2} = 5$
5639	Evaluate the Limit	limit as x approaches 4 of x^2+3x-1	$lim_{x \to 4} x^{2} + 3 x - 1$
5640	Evaluate the Limit	limit as x approaches 4 of (x^2+6x-40)/(x-4)	$lim_{x \to 4} \frac{x^{2} + 6 x - 40}{x - 4}$
5641	Find dy/dx	y=2(x^2-3x)	$y = 2 (x^{2} - 3 x)$
5642	Evaluate the Limit	limit as x approaches -4 of f(x)	$lim_{x \to - 4} f (x)$
5643	Evaluate the Limit	limit as x approaches 4 of natural log of x-4	$lim_{x \to 4} \ln (x - 4)$
5644	Evaluate the Limit	limit as x approaches -10 of (x^2+10x)/((x^2+100)(x+10))	$lim_{x \to - 10} \frac{x^{2} + 10 x}{(x^{2} + 100) (x + 10)}$
5645	Evaluate the Limit	limit as x approaches 2 of (x^2-6x+8)/(x-2)	$lim_{x \to 2} \frac{x^{2} - 6 x + 8}{x - 2}$
5646	Find the Local Maxima and Minima	f(x)=3x^4-18x^2+15	$f (x) = 3 x^{4} - 18 x^{2} + 15$
5647	Find the Local Maxima and Minima	f(x)=3x^4-24x^3+30x^2	$f (x) = 3 x^{4} - 24 x^{3} + 30 x^{2}$
5648	Find the Local Maxima and Minima	f(x)=3x^4-4x^3-12x^2+5	$f (x) = 3 x^{4} - 4 x^{3} - 12 x^{2} + 5$
5649	Find the Local Maxima and Minima	f(x)=2x+18/x	$f (x) = 2 x + \frac{18}{x}$
5650	Find the Local Maxima and Minima	f(x)=2x^3+3x^2-12x+5	$f (x) = 2 x^{3} + 3 x^{2} - 12 x + 5$
5651	Find the Local Maxima and Minima	f(x)=2x^3-24x	$f (x) = 2 x^{3} - 24 x$
5652	Find the Local Maxima and Minima	f(x)=3x^5-5x^4	$f (x) = 3 x^{5} - 5 x^{4}$
5653	Find the Local Maxima and Minima	f(x)=3x-36x^(1/3)	$f (x) = 3 x - 36 x^{\frac{1}{3}}$
5654	Find the Local Maxima and Minima	F(X)=4X-X^2	$F (X) = 4 X - X^{2}$
5655	Find the Local Maxima and Minima	f(x)=5x^3-3x^5	$f (x) = 5 x^{3} - 3 x^{5}$
5656	Find the Local Maxima and Minima	f(x)=5x^3-60x+5	$f (x) = 5 x^{3} - 60 x + 5$
5657	Find the Local Maxima and Minima	f(x)=x^4-2x^2+1	$f (x) = x^{4} - 2 x^{2} + 1$
5658	Find the Local Maxima and Minima	f(x)=x^4-32x^2+5	$f (x) = x^{4} - 32 x^{2} + 5$
5659	Find the Local Maxima and Minima	f(x)=x^-4 natural log of x	$f (x) = x^{- 4} \ln (x)$
5660	Find the Local Maxima and Minima	f(x)=x^3-9x^2+27x	$f (x) = x^{3} - 9 x^{2} + 27 x$
5661	Find the Local Maxima and Minima	f(x)=x^4+12x^3+28x^2+2	$f (x) = x^{4} + 12 x^{3} + 28 x^{2} + 2$
5662	Find the Local Maxima and Minima	f(x)=14x^4-84x^2	$f (x) = 14 x^{4} - 84 x^{2}$
5663	Find the Local Maxima and Minima	f(x)=x^2-4	$f (x) = x^{2} - 4$
5664	Find the Local Maxima and Minima	f(x)=x^2-20x+104	$f (x) = x^{2} - 20 x + 104$
5665	Find the Derivative - d/dx	x^11e^x	$x^{11} e^{x}$
5666	Find the Local Maxima and Minima	f(x)=x^2-8x+14	$f (x) = x^{2} - 8 x + 14$
5667	Find the Local Maxima and Minima	f(x)=x^2-4x+8	$f (x) = x^{2} - 4 x + 8$
5668	Find the Local Maxima and Minima	f(x)=x^3-3x^2-24x+5	$f (x) = x^{3} - 3 x^{2} - 24 x + 5$
5669	Find the Local Maxima and Minima	f(x)=x^3-16x^2+64x	$f (x) = x^{3} - 16 x^{2} + 64 x$
5670	Find the Local Maxima and Minima	f(x)=x^3-2x^2+x	$f (x) = x^{3} - 2 x^{2} + x$
5671	Find the Local Maxima and Minima	f(x)=-x^3+9x^2+120x-300	$f (x) = - x^{3} + 9 x^{2} + 120 x - 300$
5672	Find the Domain and Range	f(x)=(x^2-7x+26)/(x-5)	$f (x) = \frac{x^{2} - 7 x + 26}{x - 5}$
5673	Find the Domain and Range	f(x)=1/((x+1)^2)	$f (x) = \frac{1}{{(x + 1)}^{2}}$
5674	Find the Domain and Range	f(x)=2/(x-5)	$f (x) = \frac{2}{x - 5}$
5675	Find the Domain and Range	f(x)=5/(x-6)	$f (x) = \frac{5}{x - 6}$
5676	Find the Domain and Range	f(x)=2t^3-9t^2	$f (x) = 2 t^{3} - 9 t^{2}$
5677	Find the Local Maxima and Minima	y=3x^3-36x-5	$y = 3 x^{3} - 36 x - 5$
5678	Find the Local Maxima and Minima	y=3x^3-36x-1	$y = 3 x^{3} - 36 x - 1$
5679	Find the Local Maxima and Minima	y=2x^3-24x-9	$y = 2 x^{3} - 24 x - 9$
5680	Find the Local Maxima and Minima	y=2sin(x)-cos(x)^2	$y = 2 \sin (x) - \cos^{2} (x)$
5681	Find the Local Maxima and Minima	y=x^3-3x^2-24x+32	$y = x^{3} - 3 x^{2} - 24 x + 32$
5682	Find the Local Maxima and Minima	y=x^3-3x^2+1	$y = x^{3} - 3 x^{2} + 1$
5683	Find the Local Maxima and Minima	y=x^3-12x^2+36x	$y = x^{3} - 12 x^{2} + 36 x$
5684	Find the Local Maxima and Minima	y=x^4-3x^2	$y = x^{4} - 3 x^{2}$
5685	Find the Local Maxima and Minima	y=x^3-6x^2-96x	$y = x^{3} - 6 x^{2} - 96 x$
5686	Find the Local Maxima and Minima	y=x^3-5x^2-8x+5	$y = x^{3} - 5 x^{2} - 8 x + 5$
5687	Find the Local Maxima and Minima	y=1/3x^3-2x^2+3x+2	$y = \frac{1}{3} x^{3} - 2 x^{2} + 3 x + 2$
5688	Find the Local Maxima and Minima	p(x)=33-x/24	$p (x) = 33 - \frac{x}{24}$
5689	Find the Local Maxima and Minima	sin(x)	$\sin (x)$
5690	Find the Local Maxima and Minima	u(y)=100x+40y-5x^2-2y^2	$u (y) = 100 x + 40 y - 5 x^{2} - 2 y^{2}$
5691	Find the Local Maxima and Minima	g(y)=(y-1)/(y^2-y+1)	$g (y) = \frac{y - 1}{y^{2} - y + 1}$
5692	Find the Local Maxima and Minima	g(x)=x^3-27x	$g (x) = x^{3} - 27 x$
5693	Find the Local Maxima and Minima	f(x)=x+sin(x)	$f (x) = x + \sin (x)$
5694	Find the Derivative - d/d@VAR	f(x)=1/(x+2)	$f (x) = \frac{1}{x + 2}$
5695	Find the Local Maxima and Minima	g(x)=-(24x)/(x^2+16)	$g (x) = - \frac{24 x}{x^{2} + 16}$
5696	Find the Derivative - d/dx	(x^2)/(x^2-16)	$\frac{x^{2}}{x^{2} - 16}$
5697	Find the Local Maxima and Minima	f(x)=x+64/x	$f (x) = x + \frac{64}{x}$
5698	Find the Local Maxima and Minima	f(x)=x+81/x	$f (x) = x + \frac{81}{x}$
5699	Find the Local Maxima and Minima	f(x)=x square root of 4-x^2	$f (x) = x \sqrt{4 - x^{2}}$
5700	Find the Derivative - d/dx	-(9x)/y	$- \frac{9 x}{y}$