Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
4601	Find the Tangent Line at the Point	y=8 square root of x , (16,32)	$y = 8 \sqrt{x}$ , $(16, 32)$
4602	Find f(g(x))	f(x)=2x-6 , g(x)=x^2+9	$f (x) = 2 x - 6$ , $g (x) = x^{2} + 9$
4603	Evaluate the Limit	( limit as x approaches 0 of tan(2x))/(sin(5x))	$\frac{lim_{x \to 0} \tan (2 x)}{\sin (5 x)}$
4604	Evaluate the Limit	( limit as x approaches 0 of tan(3x))/x	$\frac{lim_{x \to 0} \tan (3 x)}{x}$
4605	Evaluate the Limit	( limit as x approaches 0 of tan(4x))/x	$\frac{lim_{x \to 0} \tan (4 x)}{x}$
4606	Evaluate the Limit	( limit as x approaches 0 of tan(5x))/x	$\frac{lim_{x \to 0} \tan (5 x)}{x}$
4607	Evaluate the Limit	( limit as x approaches 0 of sin(x))/(tan(x))	$\frac{lim_{x \to 0} \sin (x)}{\tan (x)}$
4608	Evaluate the Limit	( limit as x approaches 0 of sin(5x))/(3x)	$\frac{lim_{x \to 0} \sin (5 x)}{3 x}$
4609	Evaluate the Limit	( limit as x approaches 0 of sin(3x)sin(5x))/(x^2)	$\frac{lim_{x \to 0} \sin (3 x) \sin (5 x)}{x^{2}}$
4610	Evaluate the Limit	( limit as x approaches 1 of (10x-5)^2-25)/(5x-5)	$\frac{lim_{x \to 1} {(10 x - 5)}^{2} - 25}{5 x - 5}$
4611	Evaluate the Limit	( limit as x approaches 0 of cos(x-1))/(sin(x))	$\frac{lim_{x \to 0} \cos (x - 1)}{\sin (x)}$
4612	Find the Tangent Line at (2π,0)	y=sin(sin(x)) , (2pi,0)	$\frac{lim_{x \to 0} 1 - \sqrt{\cos (x)}}{x^{2}}$
4613	Evaluate the Limit	( limit as x approaches 0 of sin(3x)^2)/(x^2)	$\frac{lim_{x \to 0} \sin^{2} (3 x)}{x^{2}}$
4614	Evaluate the Limit	limit as n approaches 8 of (1+1/n)^n	$lim_{n \to 8} {(1 + \frac{1}{n})}^{n}$
4615	Evaluate the Limit	( limit as t approaches 0 of square root of 1+t- square root of 1-t)/t	$\frac{lim_{t \to 0} \sqrt{1 + t} - \sqrt{1 - t}}{t}$
4616	Evaluate the Limit	( limit as t approaches 0 of tan(6t))/(sin(2t))	$\frac{lim_{t \to 0} \tan (6 t)}{\sin (2 t)}$
4617	Evaluate the Limit	( limit as x approaches pi/2 of -2)/(cos(x))	$\frac{lim_{x \to \frac{π}{2}} - 2}{\cos (x)}$
4618	Find the Tangent Line at the Point	x^2+xy+y^2=3 , (1,1)	$x^{2} + x y + y^{2} = 3$ , $(1, 1)$
4619	Find the Tangent Line at the Point	y=x^3-2x , (2,4)	$y = x^{3} - 2 x$ , $(2, 4)$
4620	Find the Tangent Line at the Point	2x^2+y^2=41 , (-4,3)	$2 x^{2} + y^{2} = 41$ , $(- 4, 3)$
4621	Find the Tangent Line at the Point	2x^2+y^2=54 , (5,2)	$2 x^{2} + y^{2} = 54$ , $(5, 2)$
4622	Find the Area Between the Curves	y=x , y=2 square root of x	$y = x$ , $y = 2 \sqrt{x}$
4623	Find the Area Between the Curves	y=x^2 , y=4	$y = x^{2}$ , $y = 4$
4624	Find the Area Between the Curves	y=x^2+5x-4 , y=x+3	$y = x^{2} + 5 x - 4$ , $y = x + 3$
4625	Find the Area Between the Curves	y=6-x^2 , y=x+4	$y = 6 - x^{2}$ , $y = x + 4$
4626	Find the Area Between the Curves	y=7-x^2 , y=x+1	$y = 7 - x^{2}$ , $y = x + 1$
4627	Evaluate the Limit	limit as x approaches -2 of (x^2-3x-10)/(x+2)	$lim_{x \to - 2} \frac{x^{2} - 3 x - 10}{x + 2}$
4628	Evaluate the Limit	limit as x approaches -2 of (x^2-x-6)/(x+2)	$lim_{x \to - 2} \frac{x^{2} - x - 6}{x + 2}$
4629	Evaluate the Limit	limit as x approaches -2 of (x^3-4x)/(x+2)	$lim_{x \to - 2} \frac{x^{3} - 4 x}{x + 2}$
4630	Evaluate the Limit	limit as x approaches 2 of 7	$lim_{x \to 2} 7$
4631	Evaluate the Limit	limit as x approaches 2 of 6	$lim_{x \to 2} 6$
4632	Evaluate the Limit	limit as x approaches -2 of x	$lim_{x \to - 2} x$
4633	Evaluate the Limit	limit as x approaches 2 of x(x-4)	$lim_{x \to 2} x (x - 4)$
4634	Evaluate the Limit	limit as x approaches pi of 6sin(x+sin(x))	$lim_{x \to π} 6 \sin (x + \sin (x))$
4635	Evaluate the Limit	limit as x approaches 2 of x^2-4	$lim_{x \to 2} x^{2} - 4$
4636	Evaluate the Limit	limit as x approaches 1 of ((x^2-1)^3)/(x^3-1)	$lim_{x \to 1} \frac{{(x^{2} - 1)}^{3}}{x^{3} - 1}$
4637	Evaluate the Limit	limit as x approaches 1 of 1/(1-x)-2/(1-x^2)	$lim_{x \to 1} \frac{1}{1 - x} - \frac{2}{1 - x^{2}}$
4638	Evaluate the Limit	limit as x approaches 2 of (x^2-4x+4)/(x^2+x-6)	$lim_{x \to 2} \frac{x^{2} - 4 x + 4}{x^{2} + x - 6}$
4639	Evaluate the Limit	limit as x approaches -1 of F(x)	$lim_{x \to - 1} F (x)$
4640	Evaluate the Limit	limit as x approaches 1 of x-1	$lim_{x \to 1} x - 1$
4641	Evaluate the Limit	limit as x approaches infinity of square root of x^2+9	$lim_{x \to \infty} \sqrt{x^{2} + 9}$
4642	Evaluate the Limit	limit as x approaches 0 of cos(x+sin(x))	$lim_{x \to 0} \cos (x + \sin (x))$
4643	Evaluate the Limit	limit as x approaches 0 of csc(x)	$lim_{x \to 0} \csc (x)$
4644	Evaluate the Limit	limit as x approaches 0 of x^2cos(1/x)	$lim_{x \to 0} x^{2} \cos (\frac{1}{x})$
4645	Evaluate the Limit	limit as x approaches 0 of x^2+1	$lim_{x \to 0} x^{2} + 1$
4646	Evaluate the Limit	limit as x approaches pi of xsec(x)	$lim_{x \to π} x \sec (x)$
4647	Evaluate the Limit	limit as h approaches 0 of ( square root of 14h+1-1)/h	$lim_{h \to 0} \frac{\sqrt{14 h + 1} - 1}{h}$
4648	Evaluate the Limit	limit as x approaches 0 of -5/2*(10x-20)	$lim_{x \to 0} - \frac{5}{2} \cdot (10 x - 20)$
4649	Evaluate the Limit	limit as x approaches 0 of (cos(x)tan(x))/x	$lim_{x \to 0} \frac{\cos (x) \tan (x)}{x}$
4650	Evaluate the Limit	limit as x approaches 0 of (cos(2x))/x	$lim_{x \to 0} \frac{\cos (2 x)}{x}$
4651	Evaluate the Limit	limit as x approaches 0 of (tan(7x))/(sin(5x))	$lim_{x \to 0} \frac{\tan (7 x)}{\sin (5 x)}$
4652	Evaluate the Limit	limit as x approaches 0 of (x(x^2-1))/(x^2)	$lim_{x \to 0} \frac{x (x^{2} - 1)}{x^{2}}$
4653	Evaluate the Limit	limit as x approaches 4 of (x^3-64)/(x-4)	$lim_{x \to 4} \frac{x^{3} - 64}{x - 4}$
4654	Evaluate the Limit	limit as x approaches 0 of (sin(3x))/(5x)	$lim_{x \to 0} \frac{\sin (3 x)}{5 x}$
4655	Evaluate the Limit	limit as h approaches 0 of ((3+h)^3-27)/h	$lim_{h \to 0} \frac{{(3 + h)}^{3} - 27}{h}$
4656	Evaluate the Limit	limit as x approaches 0 of 1/(sin(x))-1/x	$lim_{x \to 0} \frac{1}{\sin (x)} - \frac{1}{x}$
4657	Evaluate the Limit	limit as x approaches -7 of (7-\|x\|)/(7+x)	$lim_{x \to - 7} \frac{7 - \| x \|}{7 + x}$
4658	Evaluate the Limit	limit as x approaches 0 of (sin(4x))/(sin(2x))	$lim_{x \to 0} \frac{\sin (4 x)}{\sin (2 x)}$
4659	Evaluate the Limit	limit as x approaches 0 of pi	$lim_{x \to 0} π$
4660	Evaluate the Limit	limit as x approaches 0 of 4sin(x-1)	$lim_{x \to 0} 4 \sin (x - 1)$
4661	Evaluate the Limit	limit as x approaches 16 of (x^2+3x-304)/(x^2-256)	$lim_{x \to 16} \frac{x^{2} + 3 x - 304}{x^{2} - 256}$
4662	Evaluate the Limit	limit as x approaches 0 of (cos(x)-1)/x	$lim_{x \to 0} \frac{\cos (x) - 1}{x}$
4663	Evaluate the Limit	limit as x approaches 0 of (1+3x)^(1/x)	$lim_{x \to 0} {(1 + 3 x)}^{\frac{1}{x}}$
4664	Evaluate the Limit	limit as x approaches 2 of (x^2-2x)/(x^2-x-2)	$lim_{x \to 2} \frac{x^{2} - 2 x}{x^{2} - x - 2}$
4665	Evaluate the Limit	limit as x approaches 0 of (1/(x+7)-1/7)/x	$lim_{x \to 0} \frac{\frac{1}{x + 7} - \frac{1}{7}}{x}$
4666	Evaluate the Limit	limit as h approaches 0 of ((3+h)^-1-3^-1)/h	$lim_{h \to 0} \frac{{(3 + h)}^{- 1} - 3^{- 1}}{h}$
4667	Evaluate the Limit	( limit as x approaches 81 of square root of x-9)/(x-81)	$\frac{lim_{x \to 81} \sqrt{x} - 9}{x - 81}$
4668	Evaluate the Limit	( limit as x approaches 8 of 1)/x	$\frac{lim_{x \to 8} 1}{x}$
4669	Evaluate the Limit	( limit as x approaches 4 of x^2-7x+12)/(x-4)	$\frac{lim_{x \to 4} x^{2} - 7 x + 12}{x - 4}$
4670	Evaluate the Limit	( limit as x approaches 4 of 2- square root of x)/(4x-x^2)	$\frac{lim_{x \to 4} 2 - \sqrt{x}}{4 x - x^{2}}$
4671	Evaluate the Limit	( limit as x approaches 4 of x^2+4x-32)/(x^2-16)	$\frac{lim_{x \to 4} x^{2} + 4 x - 32}{x^{2} - 16}$
4672	Evaluate the Limit	( limit as x approaches -1 of x^2+3x+2)/(x^2+1)	$\frac{lim_{x \to - 1} x^{2} + 3 x + 2}{x^{2} + 1}$
4673	Evaluate the Limit	( limit as x approaches 1 of x^3-x)/(x-1)	$\frac{lim_{x \to 1} x^{3} - x}{x - 1}$
4674	Evaluate the Limit	( limit as x approaches 1 of x^3-1)/(x^4-1)	$\frac{lim_{x \to 1} x^{3} - 1}{x^{4} - 1}$
4675	Evaluate the Limit	( limit as x approaches 1 of x^2-x)/(x^2-1)	$\frac{lim_{x \to 1} x^{2} - x}{x^{2} - 1}$
4676	Evaluate the Limit	( limit as x approaches 1 of x-2)/(x^2+x-6)	$\frac{lim_{x \to 1} x - 2}{x^{2} + x - 6}$
4677	Evaluate the Limit	( limit as x approaches -1 of 2x+1)/(x^2-3x+4)	$\frac{lim_{x \to - 1} 2 x + 1}{x^{2} - 3 x + 4}$
4678	Evaluate the Limit	( limit as x approaches 2 of x^2+2x-8)/(x^2-4)	$\frac{lim_{x \to 2} x^{2} + 2 x - 8}{x^{2} - 4}$
4679	Evaluate the Limit	( limit as x approaches 2 of x^2+3x-10)/(x^2-4)	$\frac{lim_{x \to 2} x^{2} + 3 x - 10}{x^{2} - 4}$
4680	Evaluate the Limit	( limit as x approaches 2 of x^2+x-6)/(2-x)	$\frac{lim_{x \to 2} x^{2} + x - 6}{2 - x}$
4681	Evaluate the Limit	( limit as x approaches 2 of x^2+x-6)/(x^2-4)	$\frac{lim_{x \to 2} x^{2} + x - 6}{x^{2} - 4}$
4682	Evaluate the Limit	( limit as x approaches 2 of x^2-4x+4)/(x^2+x-6)	$\frac{lim_{x \to 2} x^{2} - 4 x + 4}{x^{2} + x - 6}$
4683	Evaluate the Limit	( limit as x approaches 2 of x^2-7x+10)/(x-2)	$\frac{lim_{x \to 2} x^{2} - 7 x + 10}{x - 2}$
4684	Evaluate the Limit	( limit as x approaches 2 of x^4-16)/(x-2)	$\frac{lim_{x \to 2} x^{4} - 16}{x - 2}$
4685	Evaluate the Limit	limit as t approaches 0 of 7/(t square root of 1+t)-7/t	$lim_{t \to 0} \frac{7}{t \sqrt{1 + t}} - \frac{7}{t}$
4686	Evaluate the Limit	limit as x approaches -4 of (4-\|x\|)/(4+x)	$lim_{x \to - 4} \frac{4 - \| x \|}{4 + x}$
4687	Evaluate the Limit	limit as x approaches 5 of ( square root of x+5-3)/(x-4)	$lim_{x \to 5} \frac{\sqrt{x + 5} - 3}{x - 4}$
4688	Evaluate the Limit	limit as x approaches 1 of sin(pix)	$lim_{x \to 1} \sin (π x)$
4689	Evaluate the Limit	limit as x approaches pi/2 of -2/(cos(x))	$lim_{x \to \frac{π}{2}} - \frac{2}{\cos (x)}$
4690	Evaluate the Limit	limit as x approaches pi/2 of xsec(x)^2	$lim_{x \to \frac{π}{2}} x \sec^{2} (x)$
4691	Evaluate the Limit	limit as h approaches 0 of h(2+5/h)	$lim_{h \to 0} h (2 + \frac{5}{h})$
4692	Evaluate the Limit	limit as x approaches negative infinity of x^6+2x^9	$lim_{x \to - \infty} x^{6} + 2 x^{9}$
4693	Evaluate the Limit	limit as h approaches 0 of ((4+h)^2-16)/h	$lim_{h \to 0} \frac{{(4 + h)}^{2} - 16}{h}$
4694	Evaluate the Limit	limit as x approaches 0 of (sin(4x))/x	$lim_{x \to 0} \frac{\sin (4 x)}{x}$
4695	Evaluate the Limit	limit as h approaches 0 of (2xh+h^2)/h	$lim_{h \to 0} \frac{2 x h + h^{2}}{h}$
4696	Evaluate the Limit	limit as h approaches 0 of (4(x+h-3)^2-4(x-3)^2)/h	$lim_{h \to 0} \frac{4 {(x + h - 3)}^{2} - 4 {(x - 3)}^{2}}{h}$
4697	Evaluate the Limit	limit as x approaches 1 of (1-x)/(1- square root of x)	$lim_{x \to 1} \frac{1 - x}{1 - \sqrt{x}}$
4698	Find the Derivative - d/dx	0	$0$
4699	Find the Roots (Zeros)	f(x) = square root of 9-x^2	$f (x) = \sqrt{9 - x^{2}}$
4700	Find dy/dx	y=(x+9)(x^2-9)	$y = (x + 9) (x^{2} - 9)$