Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
6001	Evaluate the Limit	limit as x approaches 0 of (cos(a+x)-cos(a-x))/x	$lim_{x \to 0} \frac{\cos (a + x) - \cos (a - x)}{x}$
6002	Evaluate the Limit	limit as x approaches 0 of (cos(x)-1+1/2x^2)/(x^4)	$lim_{x \to 0} \frac{\cos (x) - 1 + \frac{1}{2} x^{2}}{x^{4}}$
6003	Evaluate the Limit	limit as x approaches 0 of (arcsin(x))/x	$lim_{x \to 0} \frac{\arcsin (x)}{x}$
6004	Evaluate the Limit	limit as x approaches 0 of (cos(x))/(x^2)	$lim_{x \to 0} \frac{\cos (x)}{x^{2}}$
6005	Evaluate the Limit	limit as x approaches 0 of (6x)/(x^4)	$lim_{x \to 0} \frac{6 x}{x^{4}}$
6006	Evaluate the Limit	limit as x approaches 0 of (csc(2x))/x	$lim_{x \to 0} \frac{\csc (2 x)}{x}$
6007	Evaluate the Limit	limit as x approaches 0 of e^(sin(x))	$lim_{x \to 0} e^{\sin (x)}$
6008	Evaluate the Limit	limit as x approaches 0 of (cos(x-1))/(sin(x))	$lim_{x \to 0} \frac{\cos (x - 1)}{\sin (x)}$
6009	Evaluate the Limit	limit as x approaches 0 of sec(x)^2	$lim_{x \to 0} \sec^{2} (x)$
6010	Evaluate the Limit	limit as x approaches 0 of 4/(x^2)	$lim_{x \to 0} \frac{4}{x^{2}}$
6011	Evaluate the Limit	limit as x approaches 0 of (2x)/(tan(3x))	$lim_{x \to 0} \frac{2 x}{\tan (3 x)}$
6012	Evaluate the Limit	limit as x approaches negative infinity of ( square root of 4x^2+3x)+2x	$lim_{x \to - \infty} (\sqrt{4 x^{2} + 3 x}) + 2 x$
6013	Evaluate the Limit	limit as x approaches 0 of x*sin(1/x)	$lim_{x \to 0} x \cdot \sin (\frac{1}{x})$
6014	Evaluate the Limit	limit as x approaches 0 of xcot(3x)	$lim_{x \to 0} x \cot (3 x)$
6015	Evaluate the Limit	limit as x approaches 0 of x^3cot(x)	$lim_{x \to 0} x^{3} \cot (x)$
6016	Evaluate the Limit	limit as x approaches 0 of 2x+9	$lim_{x \to 0} 2 x + 9$
6017	Evaluate the Limit	limit as x approaches 0 of (3x)/(cos(x))	$lim_{x \to 0} \frac{3 x}{\cos (x)}$
6018	Evaluate the Limit	limit as x approaches negative infinity of (cos(pix))/x	$lim_{x \to - \infty} \frac{\cos (π x)}{x}$
6019	Evaluate the Limit	limit as x approaches 1 of x^(6/(x-1))	$lim_{x \to 1} x^{\frac{6}{x - 1}}$
6020	Evaluate the Limit	limit as x approaches 1 of e^x	$lim_{x \to 1} e^{x}$
6021	Evaluate the Limit	limit as x approaches infinity of arctan(x)	$lim_{x \to \infty} \arctan (x)$
6022	Evaluate the Limit	limit as x approaches 1 of ( natural log of x)/(x^2-1)	$lim_{x \to 1} \frac{\ln (x)}{x^{2} - 1}$
6023	Evaluate the Limit	limit as x approaches 1 of square root of x-1	$lim_{x \to 1} \sqrt{x - 1}$
6024	Evaluate the Limit	limit as x approaches 1 of square root of 3+f(x)	$lim_{x \to 1} \sqrt{3 + f (x)}$
6025	Evaluate the Limit	limit as x approaches 10 of (x-10)/( square root of x- square root of 20-x)	$lim_{x \to 10} \frac{x - 10}{\sqrt{x} - \sqrt{20 - x}}$
6026	Evaluate the Limit	limit as x approaches 1 of sin(x)	$lim_{x \to 1} \sin (x)$
6027	Evaluate the Limit	limit as x approaches infinity of (4x^2+7x-5)/(5x^2-6x+4)	$lim_{x \to \infty} \frac{4 x^{2} + 7 x - 5}{5 x^{2} - 6 x + 4}$
6028	Evaluate the Limit	limit as x approaches -1 of x^4-2x+3	$lim_{x \to - 1} x^{4} - 2 x + 3$
6029	Evaluate the Limit	limit as x approaches -1 of 2x^2+6x-1	$lim_{x \to - 1} 2 x^{2} + 6 x - 1$
6030	Evaluate the Limit	limit as x approaches 1 of 3x^2-6x+1	$lim_{x \to 1} 3 x^{2} - 6 x + 1$
6031	Evaluate the Limit	limit as x approaches 1 of (x^3-1)/(x^4-1)	$lim_{x \to 1} \frac{x^{3} - 1}{x^{4} - 1}$
6032	Evaluate the Limit	limit as x approaches 1 of -1/((x-1)^2)	$lim_{x \to 1} - \frac{1}{{(x - 1)}^{2}}$
6033	Evaluate the Limit	limit as x approaches 1 of (x^2+7x-8)/(x^2-1)	$lim_{x \to 1} \frac{x^{2} + 7 x - 8}{x^{2} - 1}$
6034	Evaluate the Limit	limit as x approaches 1 of ((2x-1)^2-1)/(x-1)	$lim_{x \to 1} \frac{{(2 x - 1)}^{2} - 1}{x - 1}$
6035	Evaluate the Limit	limit as x approaches 10 of (x^2+3x-130)/(x^2-100)	$lim_{x \to 10} \frac{x^{2} + 3 x - 130}{x^{2} - 100}$
6036	Evaluate the Limit	limit as x approaches infinity of 4cos(x)	$lim_{x \to \infty} 4 \cos (x)$
6037	Evaluate the Limit	limit as x approaches 2 of x/(x-2)	$lim_{x \to 2} \frac{x}{x - 2}$
6038	Evaluate the Limit	limit as x approaches 2 of square root of (2x^2+1)/(3x-2)	$lim_{x \to 2} \sqrt{\frac{2 x^{2} + 1}{3 x - 2}}$
6039	Evaluate the Limit	limit as x approaches 2 of x/( square root of x^2-4)	$lim_{x \to 2} \frac{x}{\sqrt{x^{2} - 4}}$
6040	Evaluate the Limit	limit as h approaches 0 of ((-8+h)^2-64)/h	$lim_{h \to 0} \frac{{(- 8 + h)}^{2} - 64}{h}$
6041	Evaluate the Limit	limit as x approaches 2 of x-2	$lim_{x \to 2} x - 2$
6042	Evaluate the Limit	limit as x approaches 2 of (x^2-7x+10)/(x-2)	$lim_{x \to 2} \frac{x^{2} - 7 x + 10}{x - 2}$
6043	Evaluate the Limit	limit as x approaches 2 of (x^4-16)/(x^3-8)	$lim_{x \to 2} \frac{x^{4} - 16}{x^{3} - 8}$
6044	Evaluate the Limit	limit as x approaches 2 of (x^2+x-6)/(\|x-2\|)	$lim_{x \to 2} \frac{x^{2} + x - 6}{\| x - 2 \|}$
6045	Evaluate the Limit	limit as x approaches 2 of 1/(x^2-4)	$lim_{x \to 2} \frac{1}{x^{2} - 4}$
6046	Evaluate the Limit	limit as x approaches 2 of (x^2+3x-10)/(x^2-4)	$lim_{x \to 2} \frac{x^{2} + 3 x - 10}{x^{2} - 4}$
6047	Find the Derivative - d/dd	(d^2y)/(dx^2)	$\frac{d^{2} y}{d x^{2}}$
6048	Evaluate the Limit	limit as h approaches 0 of ((9+h)^3-729)/h	$lim_{h \to 0} \frac{{(9 + h)}^{3} - 729}{h}$
6049	Evaluate the Limit	limit as x approaches 0 of (sin(x))/(x^2+3x)	$lim_{x \to 0} \frac{\sin (x)}{x^{2} + 3 x}$
6050	Evaluate the Limit	limit as h approaches 0 of ( square root of 9+h-3)/h	$lim_{h \to 0} \frac{(\sqrt{9 + h} - 3)}{h}$
6051	Find the Derivative - d/d@VAR	f(x)=7x^3	$f (x) = 7 x^{3}$
6052	Evaluate the Limit	limit as x approaches 0 of xsin(1/x)	$lim_{x \to 0} x \sin (\frac{1}{x})$
6053	Evaluate the Limit	limit as x approaches 2 of (3x^2-12)/(x-2)	$lim_{x \to 2} \frac{3 x^{2} - 12}{x - 2}$
6054	Evaluate the Limit	limit as x approaches 2 of x^2-4x+5	$lim_{x \to 2} x^{2} - 4 x + 5$
6055	Evaluate the Limit	limit as t approaches 25 of (25-t)/(5- square root of t)	$lim_{t \to 25} \frac{25 - t}{5 - \sqrt{t}}$
6056	Evaluate the Limit	limit as x approaches 2 of 5x-3	$lim_{x \to 2} 5 x - 3$
6057	Find the Area Between the Curves	y=3x-4 , y=x	$y = 3 x - 4$ , $y = x$
6058	Find the Area Between the Curves	y=2x+15 , y=x^2	$y = 2 x + 15$ , $y = x^{2}$
6059	Find the Area Between the Curves	y=4x-x^2 , y=-x	$y = 4 x - x^{2}$ , $y = - x$
6060	Find the Area Between the Curves	y=2x+3 , y=x^2	$y = 2 x + 3$ , $y = x^{2}$
6061	Find the Area Between the Curves	y=2x+8 , y=x^2	$y = 2 x + 8$ , $y = x^{2}$
6062	Find the Area Between the Curves	y=2x , y=0 , x=3	$y = 2 x$ , $y = 0$ , $x = 3$
6063	Find the Area Between the Curves	y=16-x^2 , y=0 , x=-2 , x=3	$y = 16 - x^{2}$ , $y = 0$ , $x = - 2$ , $x = 3$
6064	Find the Area Between the Curves	y=16-x^2 , y=0 , x=-3 , x=2	$y = 16 - x^{2}$ , $y = 0$ , $x = - 3$ , $x = 2$
6065	Find the Area Between the Curves	y=6x-x^2 , y=-5x	$y = 6 x - x^{2}$ , $y = - 5 x$
6066	Find the Area Between the Curves	y=8x+9 , y=x^2	$y = 8 x + 9$ , $y = x^{2}$
6067	Find the Area Between the Curves	y=sin(x) , y=cos(x)	$y = \sin (x)$ , $y = \cos (x)$
6068	Find the Area Between the Curves	y=x^2+6x-4 , y=x+2	$y = x^{2} + 6 x - 4$ , $y = x + 2$
6069	Find the Area Between the Curves	y=1-x^2 , y=0	$y = 1 - x^{2}$ , $y = 0$
6070	Find the Area Between the Curves	y=x^2 , y=2x-x^2	$y = x^{2}$ , $y = 2 x - x^{2}$
6071	Find the Area Between the Curves	y=x^2 , y=2x	$y = x^{2}$ , $y = 2 x$
6072	Find the Area Between the Curves	y=x^(12/11) , y=10x^(1/11)	$y = x^{\frac{12}{11}}$ , $y = 10 x^{\frac{1}{11}}$
6073	Find the Tangent Line at the Point	2x^2+y^2=41 , (4,3)	$2 x^{2} + y^{2} = 41$ , $(4, 3)$
6074	Find the Tangent Line at the Point	2(x^2+y^2)^2=25(x^2-y^2) , (3,1)	$2 {(x^{2} + y^{2})}^{2} = 25 (x^{2} - y^{2})$ , $(3, 1)$
6075	Find the Tangent Line at the Point	2x^2+y^2=34 , (3,4)	$2 x^{2} + y^{2} = 34$ , $(3, 4)$
6076	Find the Tangent Line at the Point	y^4+x^3=y^2+10x , (0,1)	$y^{4} + x^{3} = y^{2} + 10 x$ , $(0, 1)$
6077	Find the Tangent Line at the Point	tan(xy)=x-1 , (1,0)	$\tan (x y) = x - 1$ , $(1, 0)$
6078	Find the Tangent Line at the Point	y=18/(x^2+2) , (1,6)	$y = \frac{18}{x^{2} + 2}$ , $(1, 6)$
6079	Find the Tangent Line at the Point	y = square root of x , (9,3)	$y = \sqrt{x}$ , $(9, 3)$
6080	Find the Tangent Line at the Point	y=x^2+2 , (2,6)	$y = x^{2} + 2$ , $(2, 6)$
6081	Find the Tangent Line at the Point	(x^2+4)y=8 , (2,1)	$(x^{2} + 4) y = 8$ , $(2, 1)$
6082	Find the Tangent Line at the Point	x^3+y^3-9xy=0 , (2,4)	$x^{3} + y^{3} - 9 x y = 0$ , $(2, 4)$
6083	Find the Tangent Line at the Point	y^2-x^3=9 , (3,-6)	$y^{2} - x^{3} = 9$ , $(3, - 6)$
6084	Find the Tangent Line at the Point	x^2+xy-y^2=-1 , (1,2)	$x^{2} + x y - y^{2} = - 1$ , $(1, 2)$
6085	Find the Tangent Line at the Point	x^2+xy-y^2=-9 , (3,6)	$x^{2} + x y - y^{2} = - 9$ , $(3, 6)$
6086	Find the Tangent Line at the Point	e^(x^2+y^2)=xe^(5y)-y^2e^((5x)/2) , (2,1)	$e^{x^{2} + y^{2}} = x e^{5 y} - y^{2} e^{\frac{5 x}{2}}$ , $(2, 1)$
6087	Find the Tangent Line at the Point	x^(2/3)+y^(2/3)=4 , (-3 square root of 3,1)	$x^{\frac{2}{3}} + y^{\frac{2}{3}} = 4$ , $(- 3 \sqrt{3}, 1)$
6088	Evaluate the Limit	( limit as x approaches pi/2 of 1-sin(x))/(cos(x))	$\frac{lim_{x \to \frac{π}{2}} 1 - \sin (x)}{\cos (x)}$
6089	Evaluate the Limit	( limit as x approaches pi/2 of sin(x))/x	$\frac{lim_{x \to \frac{π}{2}} \sin (x)}{x}$
6090	Evaluate the Limit	( limit as u approaches 2 of square root of 4u+1-3)/(u-2)	$\frac{lim_{u \to 2} \sqrt{4 u + 1} - 3}{u - 2}$
6091	Evaluate the Limit	( limit as t approaches 0 of tan(6t))/(sin(3t))	$\frac{lim_{t \to 0} \tan (6 t)}{\sin (3 t)}$
6092	Evaluate the Limit	( limit as t approaches 0 of sin(3t))/(2t)	$\frac{lim_{t \to 0} \sin (3 t)}{2 t}$
6093	Evaluate the Limit	( limit as h approaches 1 of h^3-1)/(h-1)	$\frac{lim_{h \to 1} h^{3} - 1}{h - 1}$
6094	Evaluate the Limit	( limit as h approaches 7 of h^3-343)/(h-7)	$\frac{lim_{h \to 7} h^{3} - 343}{h - 7}$
6095	Evaluate the Limit	( limit as x approaches 0 of e^(2x)-e^(-2x)-4x)/(x-sin(x))	$\frac{lim_{x \to 0} e^{2 x} - e^{- 2 x} - 4 x}{x - \sin (x)}$
6096	Evaluate the Limit	( limit as x approaches 0 of e^(2x)-1)/x	$\frac{lim_{x \to 0} e^{2 x} - 1}{x}$
6097	Evaluate the Limit	( limit as x approaches 0 of e^(3x)-1)/x	$\frac{lim_{x \to 0} e^{3 x} - 1}{x}$
6098	Find dy/dx	xy=2	$x y = 2$
6099	Evaluate the Limit	limit as x approaches 1 of (2-x)/((x-1)^2)	$lim_{x \to 1} \frac{(2 - x)}{{(x - 1)}^{2}}$
6100	Evaluate the Limit	( limit as x approaches 0 of (1+x)^2-1)/x	$\frac{lim_{x \to 0} {(1 + x)}^{2} - 1}{x}$