Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
31701	Evaluate the Limit	( limit as x approaches 1 of x-3)/(x^2+2x-4)	$\frac{lim_{x \to 1} x - 3}{x^{2} + 2 x - 4}$
31702	Evaluate the Limit	limit as x approaches 10 of (x-4)^3	$lim_{x \to 10} {(x - 4)}^{3}$
31703	Evaluate the Limit	( limit as x approaches 10 of \|10-x\|)/(10-x)	$\frac{lim_{x \to 10} \| 10 - x \|}{10 - x}$
31704	Evaluate the Limit	( limit as x approaches 10 of square root of 3x-5)/(x-10)	$\frac{lim_{x \to 10} \sqrt{3 x - 5}}{x - 10}$
31705	Find the Derivative - d/d@VAR	f(x) = square root of x^2-2x+1	$f (x) = \sqrt{x^{2} - 2 x + 1}$
31706	Evaluate the Limit	( limit as x approaches 10 of x^2-8x-20)/(x^2-11x+10)	$\frac{lim_{x \to 10} x^{2} - 8 x - 20}{x^{2} - 11 x + 10}$
31707	Evaluate the Limit	( limit as x approaches -10 of x^3+1000)/(x+10)	$\frac{lim_{x \to - 10} x^{3} + 1000}{x + 10}$
31708	Evaluate the Limit	( limit as x approaches -10 of 100-x^2)/(10x^2+x^3)	$\frac{lim_{x \to - 10} 100 - x^{2}}{10 x^{2} + x^{3}}$
31709	Evaluate the Limit	( limit as x approaches 10 of 2)/(x+9)	$\frac{lim_{x \to 10} 2}{x + 9}$
31710	Evaluate the Limit	( limit as x approaches -10 from the left of 7x-70)/(\|x+10\|)	$\frac{lim_{x \to - 10} 7 x - 70}{\| x + 10 \|}$
31711	Evaluate the Limit	( limit as x approaches 5 of 2/(x-1)-2)/(x-2)	$\frac{lim_{x \to 5} \frac{2}{x - 1} - 2}{x - 2}$
31712	Evaluate the Limit	( limit as x approaches 5 of 1/x-1/5)/(x-5)	$\frac{lim_{x \to 5} \frac{1}{x} - \frac{1}{5}}{x - 5}$
31713	Evaluate the Limit	( limit as x approaches 5 of x^2-2x-15)/(x-5)	$\frac{lim_{x \to 5} x^{2} - 2 x - 15}{x - 5}$
31714	Evaluate the Limit	( limit as x approaches 5 of x^2-4x-5)/((x-5)^3)	$\frac{lim_{x \to 5} x^{2} - 4 x - 5}{{(x - 5)}^{3}}$
31715	Evaluate the Limit	( limit as x approaches 5 of x^3-25x)/(x-5)	$\frac{lim_{x \to 5} x^{3} - 25 x}{x - 5}$
31716	Evaluate the Limit	( limit as x approaches 5 of 3x^2-13x+4)/(2x^2-8x)	$\frac{lim_{x \to 5} 3 x^{2} - 13 x + 4}{2 x^{2} - 8 x}$
31717	Evaluate the Limit	( limit as x approaches 5 of x-5)/(( square root of x)- square root of 10-x)	$\frac{lim_{x \to 5} x - 5}{(\sqrt{x}) - \sqrt{10 - x}}$
31718	Evaluate the Limit	( limit as x approaches 5 of x-5)/(x^2-14x+45)	$\frac{lim_{x \to 5} x - 5}{x^{2} - 14 x + 45}$
31719	Evaluate the Limit	( limit as x approaches 5 of x-5)/( square root of x+4-3)	$\frac{lim_{x \to 5} x - 5}{\sqrt{x + 4} - 3}$
31720	Evaluate the Limit	( limit as x approaches 5 of (x^2-24)^(4-1))/(x-5)	$\frac{lim_{x \to 5} {(x^{2} - 24)}^{4 - 1}}{x - 5}$
31721	Evaluate the Limit	( limit as x approaches 5 of \|5-x\|)/(x-5)	$\frac{lim_{x \to 5} \| 5 - x \|}{x - 5}$
31722	Evaluate the Limit	( limit as x approaches 5 of square root of 17- square root of 3x+2)/(6- square root of 5x+11)	$\frac{lim_{x \to 5} \sqrt{17} - \sqrt{3 x + 2}}{6 - \sqrt{5 x + 11}}$
31723	Evaluate the Limit	( limit as x approaches 5 of square root of 3x-1-4)/(x-5)	$\frac{lim_{x \to 5} \sqrt{3 x - 1} - 4}{x - 5}$
31724	Find the Derivative - d/d@VAR	f(x)=t square root of 4-t^2	$f (x) = t \sqrt{4 - t^{2}}$
31725	Evaluate the Limit	( limit as x approaches 5 of square root of x-1-2)/(x^2-25)	$\frac{lim_{x \to 5} \sqrt{x - 1} - 2}{x^{2} - 25}$
31726	Evaluate the Limit	( limit as x approaches 5 of x^2+25)/(x+5)	$\frac{lim_{x \to 5} x^{2} + 25}{x + 5}$
31727	Evaluate the Limit	( limit as x approaches 5 of x^2+2x-35)/(x^2-10x+25)	$\frac{lim_{x \to 5} x^{2} + 2 x - 35}{x^{2} - 10 x + 25}$
31728	Find the Derivative - d/d@VAR	p(t)=3/2t^4-8t^2+3t	$p (t) = \frac{3}{2} t^{4} - 8 t^{2} + 3 t$
31729	Evaluate the Limit	limit as theta approaches 0 of (sin(7)theta)/theta	$lim_{θ \to 0} \frac{\sin (7) θ}{θ}$
31730	Evaluate the Limit	( limit as x approaches 4 from the right of \|x-4\|)/(-8+2x)	$\frac{lim_{x \to 4} \| x - 4 \|}{- 8 + 2 x}$
31731	Find the Derivative - d/d@VAR	f(x)=84x^(2/3)	$f (x) = 84 x^{\frac{2}{3}}$
31732	Evaluate the Limit	( limit as x approaches 4 of (3x^2)-9)/(\|x-2\|)	$\frac{lim_{x \to 4} (3 x^{2}) - 9}{\| x - 2 \|}$
31733	Evaluate the Limit	( limit as x approaches 4 of square root of 2x+1-3)/(4-x)	$\frac{lim_{x \to 4} \sqrt{2 x + 1} - 3}{4 - x}$
31734	Evaluate the Limit	( limit as x approaches 4 of (x)-1)/(x^2-1)	$\frac{lim_{x \to 4} (x) - 1}{x^{2} - 1}$
31735	Evaluate the Limit	( limit as x approaches 5 of x^2-6x+5)/(x-5)*5	$\frac{lim_{x \to 5} x^{2} - 6 x + 5}{x - 5} \cdot 5$
31736	Find the Derivative - d/dt	t^3-12t^2+36t	$t^{3} - 12 t^{2} + 36 t$
31737	Evaluate the Limit	( limit as x approaches 5 of x^3-25x)/(x^2-5x)	$\frac{lim_{x \to 5} x^{3} - 25 x}{x^{2} - 5 x}$
31738	Evaluate the Limit	( limit as x approaches 5 of x^4-625)/(x^3-125)	$\frac{lim_{x \to 5} x^{4} - 625}{x^{3} - 125}$
31739	Evaluate the Limit	( limit as x approaches 5 of 2x^2+15x+25)/(5-4x-x^2)	$\frac{lim_{x \to 5} 2 x^{2} + 15 x + 25}{5 - 4 x - x^{2}}$
31740	Evaluate the Limit	( limit as x approaches 5 of 2x^2-11x+5)/(x-5)	$\frac{lim_{x \to 5} 2 x^{2} - 11 x + 5}{x - 5}$
31741	Evaluate the Limit	( limit as x approaches 5 of -3)/((x-5)^3)	$\frac{lim_{x \to 5} - 3}{{(x - 5)}^{3}}$
31742	Evaluate the Limit	( limit as x approaches 5 of 3x^2-14x-5)/(2x^2-13x+15)	$\frac{lim_{x \to 5} 3 x^{2} - 14 x - 5}{2 x^{2} - 13 x + 15}$
31743	Evaluate the Limit	( limit as x approaches -5 of 3x)/(2x+10)	$\frac{lim_{x \to - 5} 3 x}{2 x + 10}$
31744	Evaluate the Limit	( limit as x approaches 5 of 5x(5-x))/(3x-15)	$\frac{lim_{x \to 5} 5 x (5 - x)}{3 x - 15}$
31745	Evaluate the Limit	( limit as x approaches 5 of x)/(x-5)	$\frac{lim_{x \to 5} x}{x - 5}$
31746	Evaluate the Limit	( limit as x approaches 5 of x+4)/(x-5)	$\frac{lim_{x \to 5} x + 4}{x - 5}$
31747	Evaluate the Limit	( limit as x approaches 5 of x-5)/(x^2+4x-5)	$\frac{lim_{x \to 5} x - 5}{x^{2} + 4 x - 5}$
31748	Evaluate the Limit	( limit as x approaches -4 of (x^2+13x)+36)/(x^2-16)	$\frac{lim_{x \to - 4} (x^{2} + 13 x) + 36}{x^{2} - 16}$
31749	Evaluate the Limit	( limit as x approaches 4 of x^2+2x-24)/(x^2+6x+28)	$\frac{lim_{x \to 4} x^{2} + 2 x - 24}{x^{2} + 6 x + 28}$
31750	Evaluate the Limit	( limit as x approaches 4 of x^2+3x-28)/(x-4)	$\frac{lim_{x \to 4} x^{2} + 3 x - 28}{x - 4}$
31751	Evaluate the Limit	( limit as x approaches 4 from the left of x^2-10x+24)/(x^2-8x+16)	$\frac{lim_{x \to 4} x^{2} - 10 x + 24}{x^{2} - 8 x + 16}$
31752	Evaluate the Limit	( limit as x approaches 4 of x^2-16)/( cube root of x- cube root of 4)	$\frac{lim_{x \to 4} x^{2} - 16}{\sqrt[3]{x} - \sqrt[3]{4}}$
31753	Find the Derivative - d/dx	(x^2)/(x-9)	$\frac{x^{2}}{x - 9}$
31754	Evaluate the Limit	( limit as x approaches 4 of -7x^2-4)/(x^3-5x+4)	$\frac{lim_{x \to 4} - 7 x^{2} - 4}{x^{3} - 5 x + 4}$
31755	Evaluate the Limit	limit as x approaches -4 of (x+3)^1998	$lim_{x \to - 4} {(x + 3)}^{1998}$
31756	Evaluate the Limit	( limit as x approaches 4 of (x+2)^2-9x)/(x-4)	$\frac{lim_{x \to 4} {(x + 2)}^{2} - 9 x}{x - 4}$
31757	Evaluate the Limit	limit as x approaches 1 of 3x-2	$lim_{x \to 1} 3 x - 2$
31758	Find the Derivative - d/dx	(6x-8)^(1/2)	${(6 x - 8)}^{\frac{1}{2}}$
31759	Evaluate the Limit	( limit as x approaches 4 of square root of x^2+9-5)/(x+4)	$\frac{lim_{x \to 4} \sqrt{x^{2} + 9} - 5}{x + 4}$
31760	Evaluate the Limit	( limit as x approaches 4 of square root of x^2-3x-2)/(5- square root of x^2+9)	$\frac{lim_{x \to 4} \sqrt{x^{2} - 3 x} - 2}{5 - \sqrt{x^{2} + 9}}$
31761	Find the Derivative - d/dx	-x/(5y)	$- \frac{x}{5 y}$
31762	Evaluate the Limit	( limit as x approaches -4 of x^2-16)/(x-4)	$\frac{lim_{x \to - 4} x^{2} - 16}{x - 4}$
31763	Find the Derivative - d/dx	3x^2-1	$3 x^{2} - 1$
31764	Evaluate the Limit	( limit as x approaches 4 of x^2-7x-12)/(2x^2-32)	$\frac{lim_{x \to 4} x^{2} - 7 x - 12}{2 x^{2} - 32}$
31765	Evaluate the Limit	( limit as x approaches 4 of 0)/(2+ square root of x)	$\frac{lim_{x \to 4} 0}{2 + \sqrt{x}}$
31766	Find the Derivative - d/dx	4-x	$4 - x$
31767	Evaluate the Limit	( limit as x approaches 4 of 2x)/(x-4)-8/(x-4)	$\frac{lim_{x \to 4} 2 x}{x - 4} - \frac{8}{x - 4}$
31768	Evaluate the Limit	( limit as x approaches 4 of 3x^2-9)/(\|x-2\|)	$\frac{lim_{x \to 4} 3 x^{2} - 9}{\| x - 2 \|}$
31769	Evaluate the Limit	( limit as x approaches -4 of -3x+4)/(-x+4)	$\frac{lim_{x \to - 4} - 3 x + 4}{- x + 4}$
31770	Evaluate the Limit	( limit as x approaches 4 of 4-x)/(5- square root of x^2-9)	$\frac{lim_{x \to 4} 4 - x}{5 - \sqrt{x^{2} - 9}}$
31771	Evaluate the Limit	( limit as x approaches 4 of square root of x+5)/(x-4)- square root of 3	$\frac{lim_{x \to 4} \sqrt{x + 5}}{x - 4} - \sqrt{3}$
31772	Evaluate the Limit	( limit as x approaches 4 of 4x-x^2)/(2+ square root of x)	$\frac{lim_{x \to 4} 4 x - x^{2}}{2 + \sqrt{x}}$
31773	Evaluate the Limit	( limit as x approaches -4 of (5x)+20)/(x^2-16)	$\frac{lim_{x \to - 4} (5 x) + 20}{x^{2} - 16}$
31774	Evaluate the Limit	( limit as x approaches 4 of 6x-24)/(x^2-16)	$\frac{lim_{x \to 4} 6 x - 24}{x^{2} - 16}$
31775	Solve for ?	2sin(theta)- square root of 3=0	$2 \sin (θ) - \sqrt{3} = 0$
31776	Evaluate the Limit	( limit as x approaches 3 of x^2-2x-3)/(3-x)	$\frac{lim_{x \to 3} x^{2} - 2 x - 3}{3 - x}$
31777	Evaluate the Limit	( limit as x approaches 3 of x^2-2x-6)/(x-3)	$\frac{lim_{x \to 3} x^{2} - 2 x - 6}{x - 3}$
31778	Evaluate the Limit	( limit as x approaches 3 of x^2-36)/(x-6)	$\frac{lim_{x \to 3} x^{2} - 36}{x - 6}$
31779	Evaluate the Limit	( limit as x approaches -3 of x-3)/(8x^2-5x+4)	$\frac{lim_{x \to - 3} x - 3}{8 x^{2} - 5 x + 4}$
31780	Evaluate the Limit	( limit as x approaches -3 of (-3.001)^3-9*-3.010)/((-3.010)+3)	$\frac{lim_{x \to - 3} {(- 3.001)}^{3} - 9 \cdot - 3.01}{(- 3.01) + 3}$
31781	Evaluate the Limit	( limit as x approaches -3 of (-3.100)^3-9*-3.100)/((-3.100)+3)	$\frac{lim_{x \to - 3} {(- 3.1)}^{3} - 9 \cdot - 3.1}{(- 3.1) + 3}$
31782	Evaluate the Limit	( limit as x approaches 3 of x^4-81)/(x-3)	$\frac{lim_{x \to 3} x^{4} - 81}{x - 3}$
31783	Evaluate the Limit	( limit as x approaches 3 of 2x-5)/(x+3)	$\frac{lim_{x \to 3} 2 x - 5}{x + 3}$
31784	Evaluate the Limit	( limit as x approaches 3 of 3x+2)/(2x+5)	$\frac{lim_{x \to 3} 3 x + 2}{2 x + 5}$
31785	Evaluate the Limit	( limit as x approaches 3 of 4x-12)/(x-3)	$\frac{lim_{x \to 3} 4 x - 12}{x - 3}$
31786	Evaluate the Limit	limit as x approaches 3 of (5-4x)^2	$lim_{x \to 3} {(5 - 4 x)}^{2}$
31787	Evaluate the Limit	( limit as x approaches 3 of x^3-3x^2+4x-12)/(x^4-3x^3+x-3)	$\frac{lim_{x \to 3} x^{3} - 3 x^{2} + 4 x - 12}{x^{4} - 3 x^{3} + x - 3}$
31788	Evaluate the Limit	( limit as x approaches 2 of square root of x- square root of 2)/(( square root of x- square root of 2)( square root of x+ square root of 2))	$\frac{lim_{x \to 2} \sqrt{x} - \sqrt{2}}{(\sqrt{x} - \sqrt{2}) (\sqrt{x} + \sqrt{2})}$
31789	Evaluate the Limit	( limit as x approaches 2 of x-2)/( square root of 2- square root of x)	$\frac{lim_{x \to 2} x - 2}{\sqrt{2} - \sqrt{x}}$
31790	Evaluate the Limit	( limit as x approaches 2 of x-2)/( square root of 4x+1-3)	$\frac{lim_{x \to 2} x - 2}{\sqrt{4 x + 1} - 3}$
31791	Evaluate the Limit	( limit as x approaches 2 of x-2)/(x^2+4x+3)	$\frac{lim_{x \to 2} x - 2}{x^{2} + 4 x + 3}$
31792	Evaluate the Limit	( limit as x approaches 2 of x-2)/(x^2-3x+2)	$\frac{lim_{x \to 2} x - 2}{x^{2} - 3 x + 2}$
31793	Evaluate the Limit	( limit as x approaches 3 of 2^x-8)/(5x-15)	$\frac{lim_{x \to 3} 2^{x} - 8}{5 x - 15}$
31794	Evaluate the Limit	( limit as x approaches 3 of e^x)/(x-3)	$\frac{lim_{x \to 3} e^{x}}{x - 3}$
31795	Evaluate the Limit	( limit as x approaches 3 of square root of 10- square root of 3x+1)/(4- square root of 5x+1)	$\frac{lim_{x \to 3} \sqrt{10} - \sqrt{3 x + 1}}{4 - \sqrt{5 x + 1}}$
31796	Evaluate the Limit	( limit as x approaches 3 of square root of 2x-3- square root of 3)/( square root of 3- square root of x)	$\frac{lim_{x \to 3} \sqrt{2 x - 3} - \sqrt{3}}{\sqrt{3} - \sqrt{x}}$
31797	Evaluate the Limit	( limit as x approaches 3 of square root of x+1-2)/(x^3-4x-15)	$\frac{lim_{x \to 3} \sqrt{x + 1} - 2}{x^{3} - 4 x - 15}$
31798	Evaluate the Limit	( limit as x approaches 3 of ( square root of x+6)-x)/(x^3-3x^2)	$\frac{lim_{x \to 3} (\sqrt{x + 6}) - x}{x^{3} - 3 x^{2}}$
31799	Evaluate the Limit	( limit as x approaches -3 of x^2)/(x^2-9)+x-6	$\frac{lim_{x \to - 3} x^{2}}{x^{2} - 9} + x - 6$
31800	Evaluate the Limit	( limit as x approaches -3 of x^2+11x+24)/(x^2-2x-15)	$\frac{lim_{x \to - 3} x^{2} + 11 x + 24}{x^{2} - 2 x - 15}$