Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
30701	Evaluate the Limit	limit as x approaches 0 from the right of ( natural log of 1+x^2)/(x^3)	$lim_{x \to 0} \frac{\ln (1 + x^{2})}{x^{3}}$
30702	Evaluate the Limit	limit as x approaches 0 from the right of (sin(x))/((x^(1/5))/1)	$lim_{x \to 0} \frac{\sin (x)}{\frac{x^{\frac{1}{5}}}{1}}$
30703	Evaluate the Limit	limit as x approaches 0 from the right of sin(h(x)^(tan(x)))	$lim_{x \to 0} \sinh ({(x)}^{\tan (x)})$
30704	Evaluate the Limit	limit as x approaches 0 from the right of ( square root of x)e^(cos(pi/x))	$lim_{x \to 0} (\sqrt{x}) e^{\cos (\frac{π}{x})}$
30705	Evaluate the Limit	limit as x approaches 0 from the right of square root of x*4^(cos(pi/x))	$lim_{x \to 0} \sqrt{x} \cdot 4^{\cos (\frac{π}{x})}$
30706	Evaluate the Limit	limit as x approaches 2 of (2x^3-5x^2-4x+12)/(x^3-12x+16)	$lim_{x \to 2} \frac{2 x^{3} - 5 x^{2} - 4 x + 12}{x^{3} - 12 x + 16}$
30707	Evaluate the Limit	limit as x approaches 0 of 7sin(x-1)	$lim_{x \to 0} 7 \sin (x - 1)$
30708	Evaluate the Limit	limit as x approaches infinity of square root of x^6-5x^3-x^3	$lim_{x \to \infty} \sqrt{x^{6} - 5 x^{3}} - x^{3}$
30709	Evaluate the Limit	limit as t approaches 0 of (1+2t)^(1/(3t))	$lim_{t \to 0} {(1 + 2 t)}^{\frac{1}{3 t}}$
30710	Evaluate the Limit	limit as x approaches -0.25 of square root of (x+4)/(x+1)	$lim_{x \to - 0.25} \sqrt{\frac{x + 4}{x + 1}}$
30711	Evaluate the Limit	limit as x approaches 1 of (e^x-e)/(6x^3+7x^2-4x-9)	$lim_{x \to 1} \frac{e^{x} - e}{6 x^{3} + 7 x^{2} - 4 x - 9}$
30712	Evaluate the Limit	limit as x approaches 1 of (x^2-1)/(cos(pix)+1)	$lim_{x \to 1} \frac{x^{2} - 1}{\cos (π x) + 1}$
30713	Evaluate the Limit	( limit as x approaches 0 of (x)(2x-1))/(2x+1)	$\frac{lim_{x \to 0} (x) (2 x - 1)}{2 x + 1}$
30714	Evaluate the Limit	limit as x approaches -0.001 of ( square root of x+2- square root of 2)/x	$lim_{x \to - 0.001} \frac{\sqrt{x + 2} - \sqrt{2}}{x}$
30715	Evaluate the Limit	limit as x approaches 0.001 of (x^2-12x)/x	$lim_{x \to 0.001} \frac{x^{2} - 12 x}{x}$
30716	Evaluate the Limit	limit as x approaches 0.001 of (8x^2)/(1-cos(x))	$lim_{x \to 0.001} \frac{8 x^{2}}{1 - \cos (x)}$
30717	Evaluate the Limit	limit as x approaches -0.01 of ( square root of x+2- square root of 2)/x	$lim_{x \to - 0.01} \frac{\sqrt{x + 2} - \sqrt{2}}{x}$
30718	Evaluate the Limit	limit as x approaches 0.01 of x/(arctan(x))	$lim_{x \to 0.01} \frac{x}{\arctan (x)}$
30719	Evaluate the Limit	limit as x approaches 0.2 from the right of square root of (x+5)/(x+1)	$lim_{x \to 0.2} \sqrt{\frac{x + 5}{x + 1}}$
30720	Evaluate the Limit	limit as x approaches 0.5 from the left of (2x-1)/(-(2x^3-x^2))	$lim_{x \to 0.5} \frac{2 x - 1}{- (2 x^{3} - x^{2})}$
30721	Evaluate the Limit	limit as x approaches -0.5 from the left of square root of (x+2)/(x+1)	$lim_{x \to - 0.5} \sqrt{\frac{x + 2}{x + 1}}$
30722	Evaluate the Limit	limit as x approaches 0.5 of x natural log of x	$lim_{x \to 0.5} x \ln (x)$
30723	Evaluate the Limit	limit as x approaches 0.785 of (4x)/(tan(x))	$lim_{x \to 0.785} \frac{4 x}{\tan (x)}$
30724	Evaluate the Limit	limit as x approaches -0.9 of (3(-0.9)^2+2(-0.9)-1)/(-0.9+1)	$lim_{x \to - 0.9} \frac{3 {(- 0.9)}^{2} + 2 (- 0.9) - 1}{- 0.9 + 1}$
30725	Find the Derivative - d/d@VAR	f(x)=(64x)/(x^2+64)	$f (x) = \frac{64 x}{x^{2} + 64}$
30726	Evaluate the Limit	limit as x approaches -1 of ( cube root of x+1)/(x^3+1)	$lim_{x \to - 1} \frac{\sqrt[3]{x} + 1}{x^{3} + 1}$
30727	Evaluate the Limit	limit as x approaches -1 of (x^100-1)/(x+1)	$lim_{x \to - 1} \frac{x^{100} - 1}{x + 1}$
30728	Evaluate the Limit	limit as x approaches -1 of (x^11+1)/(x+1)	$lim_{x \to - 1} \frac{x^{11} + 1}{x + 1}$
30729	Evaluate the Limit	limit as x approaches 1 of (1/(x-1)-1)/(x-1)	$lim_{x \to 1} \frac{\frac{1}{x - 1} - 1}{x - 1}$
30730	Evaluate the Limit	limit as x approaches 1 of ( square root of 10-x+ square root of 8+x)/(x-1)	$lim_{x \to 1} \frac{\sqrt{10 - x} + \sqrt{8 + x}}{x - 1}$
30731	Evaluate the Limit	limit as x approaches 1 from the left of ( square root of 2*x(x-1))/(\|x-1\|)	$lim_{x \to 1} \frac{\sqrt{2 \cdot x} (x - 1)}{\| x - 1 \|}$
30732	Evaluate the Limit	limit as x approaches 1 of ( square root of 2x+1- square root of 3)/x	$lim_{x \to 1} \frac{\sqrt{2 x + 1} - \sqrt{3}}{x}$
30733	Evaluate the Limit	limit as x approaches 1 of ( square root of 2x-1-1)/(x-1)	$lim_{x \to 1} \frac{\sqrt{2 x - 1 - 1}}{x - 1}$
30734	Evaluate the Limit	limit as x approaches 1 of ((x-1)^5)/(x^5-1)	$lim_{x \to 1} \frac{{(x - 1)}^{5}}{x^{5} - 1}$
30735	Evaluate the Limit	limit as x approaches -1 of (-0.99^2-7-0.99)/(-0.99^2-6-0.99-7)	$lim_{x \to - 1} \frac{- {0.99}^{2} - 7 \cdot - 0.99}{- {0.99}^{2} - 6 \cdot - 0.99 - 7}$
30736	Evaluate the Limit	limit as x approaches 1 of (( log base 4 of x)/( log base 2 of x))(1)	$lim_{x \to 1} (\frac{\log_{4} (x)}{\log_{2} (x)}) (1)$
30737	Evaluate the Limit	limit as x approaches 1 of (\|x^2-1\|)/(x-1)	$lim_{x \to 1} \frac{\| x^{2} - 1 \|}{x - 1}$
30738	Evaluate the Limit	limit as x approaches 0 of (5+6x+sin(x))/(6cos(x))	$lim_{x \to 0} \frac{5 + 6 x + \sin (x)}{6 \cos (x)}$
30739	Find the Derivative - d/d@VAR	f(x)=e^x(3+5x)^2	$f (x) = e^{x} {(3 + 5 x)}^{2}$
30740	Evaluate the Limit	limit as x approaches -1 of (-1.01^2-7-1.01)/(-1.01^2-6-1.01-7)	$lim_{x \to - 1} \frac{- {1.01}^{2} - 7 \cdot - 1.01}{- {1.01}^{2} - 6 \cdot - 1.01 - 7}$
30741	Evaluate the Limit	limit as x approaches -1 of (-1.010^3-(1.010))/(-1.010+1)	$lim_{x \to - 1} \frac{- {1.01}^{3} - (1.01)}{- 1.01 + 1}$
30742	Evaluate the Limit	limit as x approaches -1 of (-1.100^3-1.100)/(-1.100+1)	$lim_{x \to - 1} \frac{- {1.1}^{3} - 1.1}{- 1.1 + 1}$
30743	Evaluate the Limit	limit as x approaches -1 of -(x^2-1)/(x-1)	$lim_{x \to - 1} - \frac{x^{2} - 1}{x - 1}$
30744	Evaluate the Limit	limit as x approaches -1 of (x^2-1)/(-(x-1))	$lim_{x \to - 1} \frac{x^{2} - 1}{- (x - 1)}$
30745	Evaluate the Limit	limit as x approaches 1 of -(x^2-x-2)/(x^2-1)	$lim_{x \to 1} - \frac{x^{2} - x - 2}{x^{2} - 1}$
30746	Evaluate the Limit	limit as x approaches 1 of (x^3+2x-3)/(x-1)	$lim_{x \to 1} \frac{x^{3} + 2 x - 3}{x - 1}$
30747	Evaluate the Limit	limit as x approaches 1 of (x^4+2x^3+2x^2-10x+5)/(x^2-1)	$lim_{x \to 1} \frac{x^{4} + 2 x^{3} + 2 x^{2} - 10 x + 5}{x^{2} - 1}$
30748	Evaluate the Limit	limit as x approaches 1 of (x^6-1)/(x^9-1)	$lim_{x \to 1} \frac{x^{6} - 1}{x^{9} - 1}$
30749	Evaluate the Limit	limit as x approaches 1 of (1-x+ natural log of x)/(1+cos(pix))	$lim_{x \to 1} \frac{1 - x + \ln (x)}{1 + \cos (π x)}$
30750	Evaluate the Limit	limit as x approaches 1 of (2x^2+3x-5)/(x^3-1)	$lim_{x \to 1} \frac{2 x^{2} + 3 x - 5}{x^{3} - 1}$
30751	Evaluate the Limit	limit as x approaches 1 of (3-2x^2)/(x-1)	$lim_{x \to 1} \frac{3 - 2 x^{2}}{x - 1}$
30752	Evaluate the Limit	limit as x approaches -1 of ( natural log of x+1- natural log of 2)/(x-1)	$lim_{x \to - 1} \frac{\ln (x + 1) - \ln (2)}{x - 1}$
30753	Evaluate the Limit	limit as x approaches 1 of (x-1)/(x^2+6x-7)	$lim_{x \to 1} \frac{x - 1}{x^{2} + 6 x - 7}$
30754	Evaluate the Limit	limit as x approaches 1 of (1+3x)/((1+4x^2+3x^4)^3)	$lim_{x \to 1} \frac{1 + 3 x}{{(1 + 4 x^{2} + 3 x^{4})}^{3}}$
30755	Evaluate the Limit	limit as x approaches -1 of (x+3)/(x+1)*arctan(x)	$lim_{x \to - 1} \frac{x + 3}{x + 1} \cdot \arctan (x)$
30756	Evaluate the Limit	limit as x approaches 1 of (x-1)/(x-1- natural log of x)	$lim_{x \to 1} \frac{x - 1}{x - 1 - \ln (x)}$
30757	Evaluate the Limit	limit as x approaches 1 of (x-6)/(x^2-6x)	$lim_{x \to 1} \frac{x - 6}{x^{2} - 6 x}$
30758	Evaluate the Limit	limit as x approaches 1 of 1-2x^2	$lim_{x \to 1} 1 - 2 x^{2}$
30759	Evaluate the Limit	limit as x approaches 1 of 2-5/((x-1)^2)	$lim_{x \to 1} 2 - \frac{5}{{(x - 1)}^{2}}$
30760	Evaluate the Limit	limit as x approaches -1 of 2x^4-2x^3-2x^2-2	$lim_{x \to - 1} 2 x^{4} - 2 x^{3} - 2 x^{2} - 2$
30761	Evaluate the Limit	limit as x approaches 1 of 2+x	$lim_{x \to 1} 2 + x$
30762	Evaluate the Limit	limit as x approaches 1 of 2-x	$lim_{x \to 1} 2 - x$
30763	Evaluate the Limit	limit as x approaches 1 of 2x-5	$lim_{x \to 1} 2 x - 5$
30764	Evaluate the Limit	limit as x approaches -1 of (3t-1)(5t^2+2)	$lim_{x \to - 1} (3 t - 1) (5 t^{2} + 2)$
30765	Evaluate the Limit	limit as x approaches 1 of 4x^2-7x+5	$lim_{x \to 1} 4 x^{2} - 7 x + 5$
30766	Evaluate the Limit	limit as x approaches 1 of 5(x-1)	$lim_{x \to 1} 5 (x - 1)$
30767	Evaluate the Limit	limit as x approaches 1 of 5x^5-9x^2+8	$lim_{x \to 1} 5 x^{5} - 9 x^{2} + 8$
30768	Evaluate the Limit	limit as x approaches -1 of 5x-2	$lim_{x \to - 1} 5 x - 2$
30769	Evaluate the Limit	limit as x approaches -1 of 5x-3	$lim_{x \to - 1} 5 x - 3$
30770	Evaluate the Limit	limit as x approaches 1 from the left of 7x-2	$lim_{x \to 1} 7 x - 2$
30771	Evaluate the Limit	limit as x approaches 1 from the left of f(x)+g(x)	$lim_{x \to 1} f (x) + g (x)$
30772	Evaluate the Limit	limit as x approaches 1 of f(x)-gx	$lim_{x \to 1} f (x) - g x$
30773	Evaluate the Limit	limit as x approaches 1 of natural log of 3x+e^x	$lim_{x \to 1} \ln (3 x + e^{x})$
30774	Evaluate the Limit	limit as x approaches 1 of x+1/x	$lim_{x \to 1} x + \frac{1}{x}$
30775	Evaluate the Limit	limit as x approaches 1 of (x-1)tan((pix)/2)	$lim_{x \to 1} (x - 1) \tan (\frac{π x}{2})$
30776	Evaluate the Limit	limit as x approaches 1 of -(x-17)(x-1)	$lim_{x \to 1} - (x - 17) (x - 1)$
30777	Find the Derivative - d/d@VAR	f(x)=6x+4	$f (x) = 6 x + 4$
30778	Evaluate the Limit	limit as x approaches 1 of (f(x))/(g(x)-hx)	$lim_{x \to 1} \frac{f (x)}{g (x) - h x}$
30779	Evaluate the Limit	limit as x approaches 1 of 4f(8)	$lim_{x \to 1} 4 f (8)$
30780	Evaluate the Limit	limit as x approaches 1 of ((2/x)-2)/(x-1)	$lim_{x \to 1} \frac{(\frac{2}{x}) - 2}{x - 1}$
30781	Evaluate the Limit	limit as x approaches 1 of (x/(x-1))-(1/(x-1))	$lim_{x \to 1} (\frac{x}{x - 1}) - (\frac{1}{x - 1})$
30782	Evaluate the Limit	limit as x approaches 1 from the left of x^(1/(1-x))	$lim_{x \to 1} x^{\frac{1}{1 - x}}$
30783	Evaluate the Limit	limit as x approaches -1 of -x^2+7x-4	$lim_{x \to - 1} - x^{2} + 7 x - 4$
30784	Evaluate the Limit	limit as x approaches 1 of -x^2+8x-4	$lim_{x \to 1} - x^{2} + 8 x - 4$
30785	Evaluate the Limit	limit as x approaches -1 of -x^2+9x-1	$lim_{x \to - 1} - x^{2} + 9 x - 1$
30786	Find the Derivative - d/d@VAR	s(t)=3t^3-t^2+7t-6	$s (t) = 3 t^{3} - t^{2} + 7 t - 6$
30787	Evaluate the Limit	limit as x approaches 1 of x^4	$lim_{x \to 1} x^{4}$
30788	Evaluate the Limit	limit as x approaches 1 of (x^4-3x)(x^2+5x+3)	$lim_{x \to 1} (x^{4} - 3 x) (x^{2} + 5 x + 3)$
30789	Find the Derivative - d/dc	c	$c$
30790	Evaluate the Limit	limit as x approaches 1 of (x^2-1)/(3x^2-x-2)	$lim_{x \to 1} \frac{x^{2} - 1}{3 x^{2} - x - 2}$
30791	Find the Derivative - d/dx	(12x^2-24x+24)e^x	$(12 x^{2} - 24 x + 24) e^{x}$
30792	Find the Derivative - d/du	u^(1/2)	$u^{\frac{1}{2}}$
30793	Evaluate the Limit	limit as x approaches 0 of (6x-6)/(x^3-9x+3)	$lim_{x \to 0} \frac{6 x - 6}{x^{3} - 9 x + 3}$
30794	Evaluate the Limit	limit as x approaches 0 of (9x)/(4- square root of 3x+16)	$lim_{x \to 0} \frac{9 x}{4 - \sqrt{3 x + 16}}$
30795	Evaluate the Limit	limit as x approaches 0 of (sin(4x))/(sin(3x))	$lim_{x \to 0} \frac{\sin (4 x)}{\sin (3 x)}$
30796	Evaluate the Limit	limit as x approaches 0 from the right of ( natural log of (x)^2)/(e^(1/x))	$lim_{x \to 0} \frac{\ln ({(x)}^{2})}{e^{\frac{1}{x}}}$
30797	Evaluate the Limit	limit as x approaches 0 from the right of 1/(3x)	$lim_{x \to 0} \frac{1}{3 x}$
30798	Evaluate the Limit	limit as x approaches 1 of ((2x-x+1)/(3x-2))^2	$lim_{x \to 1} {(\frac{2 x - x + 1}{3 x - 2})}^{2}$
30799	Evaluate the Limit	limit as x approaches 1 of (x^17-1)/(x-1)	$lim_{x \to 1} \frac{x^{17} - 1}{x - 1}$
30800	Evaluate the Limit	limit as y approaches -9 of 6y^4-7y^3+12y+25	$lim_{y \to - 9} 6 y^{4} - 7 y^{3} + 12 y + 25$