Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
51701	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of (xsin(x))/( square root of x)	$lim_{x \to \infty} \frac{x \sin (x)}{\sqrt{x}}$
51702	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of (2x^2+4x-7)/(x^3+3x^2-5)	$lim_{x \to \infty} \frac{2 x^{2} + 4 x - 7}{x^{3} + 3 x^{2} - 5}$
51703	Evaluate Using L'Hospital's Rule	limit as theta approaches 0 of (cos(theta)^2-1)/theta	$lim_{θ \to 0} \frac{\cos^{2} (θ) - 1}{θ}$
51704	Evaluate Using L'Hospital's Rule	limit as t approaches 0 of (e^t-1)/(t^3)	$lim_{t \to 0} \frac{e^{t} - 1}{t^{3}}$
51705	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (arcsin(4x))/x	$lim_{x \to 0} \frac{\arcsin (4 x)}{x}$
51706	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (sin(3x))/(sin(7x))	$lim_{x \to 0} \frac{\sin (3 x)}{\sin (7 x)}$
51707	Evaluate Using L'Hospital's Rule	limit as h approaches 0 of ((3+h)^4-81)/h	$lim_{h \to 0} \frac{{(3 + h)}^{4} - 81}{h}$
51708	Evaluate Using L'Hospital's Rule	limit as x approaches 3 of (9-x^2)/(cos(pi/2x))	$lim_{x \to 3} \frac{(9 - x^{2})}{\cos (\frac{π}{2} x)}$
51709	Evaluate Using L'Hospital's Rule	limit as x approaches negative infinity of (3x)/( square root of 16x^2-9x)	$lim_{x \to - \infty} \frac{3 x}{\sqrt{16 x^{2} - 9 x}}$
51710	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of square root of x natural log of 10x	$lim_{x \to 0} \sqrt{x} \ln (10 x)$
51711	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of ( natural log of x)/(x^4)	$lim_{x \to \infty} \frac{\ln (x)}{x^{4}}$
51712	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of natural log of y = limit as x approaches 0 of ( natural log of e^x+x)/x = limit as x approaches 0 of 7	$lim_{x \to 0} \ln (y) = lim_{x \to 0} \frac{\ln (e^{x} + x)}{x} = lim_{x \to 0} 7$
51713	Evaluate Using L'Hospital's Rule	limit as x approaches 1 of (4sin(pix))/(cos(pix)+x)	$lim_{x \to 1} \frac{4 \sin (π x)}{\cos (π x) + x}$
51714	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (e^x-1)/(sin(15x))	$lim_{x \to 0} \frac{e^{x} - 1}{\sin (15 x)}$
51715	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (1-cos(6x))/(7x^2)	$lim_{x \to 0} \frac{1 - \cos (6 x)}{7 x^{2}}$
51716	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of 11xe^(1/x)-11x	$lim_{x \to \infty} 11 x e^{\frac{1}{x}} - 11 x$
51717	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (sin(6x))/(sin(2x))	$lim_{x \to 0} \frac{\sin (6 x)}{\sin (2 x)}$
51718	Evaluate Using L'Hospital's Rule	limit as t approaches infinity of (e^(3t)+t^2)/(2e^(3t)-t)	$lim_{t \to \infty} \frac{e^{3 t} + t^{2}}{2 e^{3 t} - t}$
51719	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (tan(x)-x)/(sin(x))	$lim_{x \to 0} \frac{\tan (x) - x}{\sin (x)}$
51720	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of (9-e^x)/(9+4e^x)	$lim_{x \to \infty} \frac{9 - e^{x}}{9 + 4 e^{x}}$
51721	Evaluate Using L'Hospital's Rule	limit as x approaches 4 of arctan((x^2-16)/(5x^2-20x))	$lim_{x \to 4} \arctan (\frac{x^{2} - 16}{5 x^{2} - 20 x})$
51722	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of (5x^3-4x)/(7x^3+5)	$lim_{x \to \infty} \frac{5 x^{3} - 4 x}{7 x^{3} + 5}$
51723	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (1-cos(3x))/(2x^2)	$lim_{x \to 0} \frac{1 - \cos (3 x)}{2 x^{2}}$
51724	Evaluate Using L'Hospital's Rule	limit as x approaches pi/4 of (4-4tan(x))/(sin(x)-cos(x))	$lim_{x \to \frac{π}{4}} \frac{4 - 4 \tan (x)}{\sin (x) - \cos (x)}$
51725	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (1+ax)^(b/x)	$lim_{x \to 0} {(1 + a x)}^{\frac{b}{x}}$
51726	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of ( cube root of 8+x-2)/x	$lim_{x \to 0} \frac{\sqrt[3]{8 + x} - 2}{x}$
51727	Evaluate Using L'Hospital's Rule	limit as x approaches 1 of (x-1)/( natural log of x-sin(pix))	$lim_{x \to 1} \frac{x - 1}{\ln (x) - \sin (π x)}$
51728	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (sin(x)-x)/(x^3)	$lim_{x \to 0} \frac{\sin (x) - x}{x^{3}}$
51729	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (tan(5x))/(sin(4x))	$lim_{x \to 0} \frac{\tan (5 x)}{\sin (4 x)}$
51730	Evaluate Using L'Hospital's Rule	limit as t approaches 0 of (tan(8t))/(sin(4t))	$lim_{t \to 0} \frac{\tan (8 t)}{\sin (4 t)}$
51731	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (sin(2x))/(tan(7x))	$lim_{x \to 0} \frac{\sin (2 x)}{\tan (7 x)}$
51732	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (sin(4x))/(sin(7x))	$lim_{x \to 0} \frac{\sin (4 x)}{\sin (7 x)}$
51733	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of 12xe^(1/x)-12x	$lim_{x \to \infty} 12 x e^{\frac{1}{x}} - 12 x$
51734	Evaluate Using L'Hospital's Rule	limit as t approaches 0 of (tan(15t))/(sin(3t))	$lim_{t \to 0} \frac{\tan (15 t)}{\sin (3 t)}$
51735	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of arcsec(x/2)	$lim_{x \to \infty} arcsec (\frac{x}{2})$
51736	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of xsin(11/x)	$lim_{x \to \infty} x \sin (\frac{11}{x})$
51737	Evaluate Using L'Hospital's Rule	limit as x approaches 1 of ( natural log of x)/(9x-x^2-8)	$lim_{x \to 1} \frac{\ln (x)}{9 x - x^{2} - 8}$
51738	Evaluate Using L'Hospital's Rule	limit as x approaches 0 from the right of (3(e^x-1-x))/(10x^3)	$lim_{x \to 0} \frac{3 (e^{x} - 1 - x)}{10 x^{3}}$
51739	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of ((sin(x))^3)/(sin(x^3))	$lim_{x \to 0} \frac{\sin^{3} (x)}{\sin (x^{3})}$
51740	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of sin(x)cos(1/(x^3))	$lim_{x \to 0} \sin (x) \cos (\frac{1}{x^{3}})$
51741	Evaluate the Function	f(x)=( natural log of x)^5 at x=4	$lim_{x \to 0} \frac{\ln (\sin (x))}{\ln (\tan (x))}$
51742	Evaluate Using L'Hospital's Rule	limit as t approaches 0 of (tan(9t))/(sin(3t))	$lim_{t \to 0} \frac{\tan (9 t)}{\sin (3 t)}$
51743	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (sin(x))/(sin(pix))	$lim_{x \to 0} \frac{\sin (x)}{\sin (π x)}$
51744	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of x^3sin(1/(2x^3))	$lim_{x \to \infty} x^{3} \sin (\frac{1}{2 x^{3}})$
51745	Evaluate Using L'Hospital's Rule	limit as x approaches negative infinity of x natural log of 1-1/x	$lim_{x \to - \infty} x \ln (1 - \frac{1}{x})$
51746	Evaluate Using L'Hospital's Rule	limit as n approaches infinity of ((-1)^n)/(9 square root of n)	$lim_{n \to \infty} \frac{{(- 1)}^{n}}{9 \sqrt{n}}$
51747	Evaluate Using L'Hospital's Rule	limit as x approaches 1 of (7x)/(x-1)-7/( natural log of x)	$lim_{x \to 1} \frac{7 x}{x - 1} - \frac{7}{\ln (x)}$
51748	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (sin(4x))/(tan(5x))	$lim_{x \to 0} \frac{\sin (4 x)}{\tan (5 x)}$
51749	Evaluate Using L'Hospital's Rule	limit as x approaches -3 of (x^2-9)/(6-x-x^2)	$lim_{x \to - 3} \frac{x^{2} - 9}{6 - x - x^{2}}$
51750	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of 1/x-cot(x)	$lim_{x \to 0} \frac{1}{x} - \cot (x)$
51751	Evaluate Using L'Hospital's Rule	limit as x approaches negative infinity of 9x^2e^x	$lim_{x \to - \infty} 9 x^{2} e^{x}$
51752	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of square root of x^2+ax- square root of x^2+bx	$lim_{x \to \infty} \sqrt{x^{2} + a x} - \sqrt{x^{2} + b x}$
51753	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of x/(cos(2x))	$lim_{x \to 0} \frac{x}{\cos (2 x)}$
51754	Evaluate Using L'Hospital's Rule	limit as h approaches 0 of (sin(x+h)-sin(x))/h	$lim_{h \to 0} \frac{\sin (x + h) - \sin (x)}{h}$
51755	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (sin(2x))/(tan(5x))	$lim_{x \to 0} \frac{\sin (2 x)}{\tan (5 x)}$
51756	Evaluate Using L'Hospital's Rule	limit as x approaches negative infinity of 3x^2e^x	$lim_{x \to - \infty} 3 x^{2} e^{x}$
51757	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of (4x)/( natural log of x^2+1)	$lim_{x \to \infty} \frac{4 x}{\ln (x^{2} + 1)}$
51758	Evaluate Using L'Hospital's Rule	limit as x approaches 1 of (x^(7a)-7ax+7a-1)/((x-1)^2)	$lim_{x \to 1} \frac{(x^{7 a} - 7 a x + 7 a - 1)}{{(x - 1)}^{2}}$
51759	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of (x^2-3x+7)/( square root of 4x^4-3x^3+2x^2)	$lim_{x \to \infty} \frac{x^{2} - 3 x + 7}{\sqrt{4 x^{4} - 3 x^{3} + 2 x^{2}}}$
51760	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (e^(7x)-1-7x)/(x^2)	$lim_{x \to 0} \frac{(e^{7 x} - 1 - 7 x)}{x^{2}}$
51761	Convert to Set Notation	3x-2(x-1)>=5x-4(2+x)	$3 x - 2 (x - 1) \geq 5 x - 4 (2 + x)$
51762	Evaluate Using Scientific Notation	(110^-14)/(4.910^-10)	$\frac{(1 \cdot 10^{- 14})}{(4.9 \cdot 10^{- 10})}$
51763	Evaluate Using Scientific Notation	(1.010^-14)/(1.810^-5)	$\frac{1 \cdot 10^{- 14}}{1.8 \cdot 10^{- 5}}$
51764	Evaluate Using L'Hospital's Rule	limit as x approaches pi/2 of (2tan(x))/(sec(x)^2)	$lim_{x \to \frac{π}{2}} \frac{2 \tan (x)}{\sec^{2} (x)}$
51765	Write as a Function of P	Q=30-P	$Q = 30 - P$
51766	Write as a Function of Q	TR=90Q-3Q^2	$T R = 90 Q - 3 Q^{2}$
51767	Write as a Function of t	Q(t)=Q_0(1-e^(-t/a))	$Q (t) = Q_{0} (1 - e^{- \frac{t}{a}})$
51768	Write as a Function of w	w=4/(t^3)	$w = \frac{4}{t^{3}}$
51769	Write as a Function of p	p=-0.17(x)+374	$p = - 0.17 (x) + 374$
51770	Write as a Function of t	h=-16t^2+64t+80	$h = - 16 t^{2} + 64 t + 80$
51771	Write as a Function of Q	Q(t)=Q_0(1-e^(-t/a))	$Q (t) = Q_{0} (1 - e^{- \frac{t}{a}})$
51772	Write as a Function of s	s(t)=-16t^2+v_0t+s_0	$s (t) = - 16 t^{2} + v_{0} t + s_{0}$
51773	Write as a Function of c	c=8x+100000/x	$c = 8 x + \frac{100000}{x}$
51774	Write as a Function of t	(dy)/(dt)=1-2y	$\frac{d y}{d t} = 1 - 2 y$
51775	Write as a Function of r	r^2cos(2theta)=1	$r^{2} \cos (2 θ) = 1$
51776	Write as a Function of T	TR=90Q-3Q^2	$T R = 90 Q - 3 Q^{2}$
51777	Write as a Function of y	(dy)/(dt)=1-2y	$\frac{d y}{d t} = 1 - 2 y$
51778	Write as a Function of y	(dy)/(dx)=3y	$\frac{d y}{d x} = 3 y$
51779	Write as a Function of y	x+(y-1)^2=0	$x + {(y - 1)}^{2} = 0$
51780	Write as a Function of y	y=3/(8x^2)	$y = \frac{3}{8 x^{2}}$
51781	Write as a Function of y	-(x(y+3)(y-3))/((x+2)(x-2))=0	$- \frac{x (y + 3) (y - 3)}{(x + 2) (x - 2)} = 0$
51782	Write as a Function of y	5x+y^3-5xy=1	$5 x + y^{3} - 5 x y = 1$
51783	Write as a Function of y	x=12(y^2-y^3)	$x = 12 (y^{2} - y^{3})$
51784	Write as a Function of y	square root of 3xy=2+x^2y	$\sqrt{3 x y} = 2 + x^{2} y$
51785	Write as a Function of x	x+(y-1)^2=0	$x + {(y - 1)}^{2} = 0$
51786	Write as a Function of x	x+3y=6	$x + 3 y = 6$
51787	Write as a Function of x	5x+y^3-5xy=1	$5 x + y^{3} - 5 x y = 1$
51788	Write as a Function of x	c=8x+100000/x	$c = 8 x + \frac{100000}{x}$
51789	Write as a Function of x	x=12(y^2-y^3)	$x = 12 (y^{2} - y^{3})$
51790	Write as a Function of x	sum from n-1 to 6 of x-3n=-3	$\sum_{n - 1}^{6} x - 3 n = - 3$
51791	Write as a Function of x	square root of 3xy=2+x^2y	$\sqrt{3 x y} = 2 + x^{2} y$
51792	Find Where Increasing/Decreasing Using Derivatives	f(x)=1/2x^4+2/3x^3+10	$f (x) = \frac{1}{2} x^{4} + \frac{2}{3} x^{3} + 10$
51793	Find Where Increasing/Decreasing Using Derivatives	f(t)=6/(81-t^2)	$f (t) = \frac{6}{81 - t^{2}}$
51794	Find Where Increasing/Decreasing Using Derivatives	f(x)=32+(36x^2)/(x^2+191)	$f (x) = 32 + \frac{36 x^{2}}{x^{2} + 191}$
51795	Find Where Increasing/Decreasing Using Derivatives	f(x)=4x^3-36x^2+96x	$f (x) = 4 x^{3} - 36 x^{2} + 96 x$
51796	Find Where Increasing/Decreasing Using Derivatives	F(t)=185-(124t^2)/(t^2+45)	$F (t) = 185 - \frac{124 t^{2}}{t^{2} + 45}$
51797	Find Where Increasing/Decreasing Using Derivatives	f(x)=2.2+5.8x-2.4x^2	$f (x) = 2.2 + 5.8 x - 2.4 x^{2}$
51798	Find Where Increasing/Decreasing Using Derivatives	f(x)=sin(x)+8	$f (x) = \sin (x) + 8$
51799	Find Where Increasing/Decreasing Using Derivatives	f(x)=4-3x+3x^2-x^3	$f (x) = 4 - 3 x + 3 x^{2} - x^{3}$
51800	Find Where Increasing/Decreasing Using Derivatives	f(x)=x^3-7x^2-24x+8	$f (x) = x^{3} - 7 x^{2} - 24 x + 8$