Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
2601	Evaluate the Limit	limit as x approaches 0 of sin(pi/x)	$lim_{x \to 0} \sin (\frac{π}{x})$
2602	Evaluate the Limit	limit as x approaches 1 of (\|x-1\|)/(x-1)	$lim_{x \to 1} \frac{\| x - 1 \|}{x - 1}$
2603	Evaluate the Limit	limit as x approaches 0 of (sin(3x))/(2x)	$lim_{x \to 0} \frac{\sin (3 x)}{2 x}$
2604	Evaluate the Limit	limit as x approaches 0 of (tan(2x))/x	$lim_{x \to 0} \frac{\tan (2 x)}{x}$
2605	Evaluate the Limit	limit as x approaches infinity of 5e^x	$lim_{x \to \infty} 5 e^{x}$
2606	Evaluate the Limit	limit as x approaches 0 of (sin(2x))/(sin(3x))	$lim_{x \to 0} \frac{\sin (2 x)}{\sin (3 x)}$
2607	Evaluate the Limit	limit as x approaches 169 of ( square root of x-13)/(x-169)	$lim_{x \to 169} \frac{\sqrt{x} - 13}{x - 169}$
2608	Evaluate the Limit	limit as x approaches 4 of (x-4)/(x^2-16)	$lim_{x \to 4} \frac{x - 4}{x^{2} - 16}$
2609	Evaluate the Limit	limit as x approaches 5 of (x^2-5x)/(x^2-4x-5)	$lim_{x \to 5} \frac{x^{2} - 5 x}{x^{2} - 4 x - 5}$
2610	Evaluate the Limit	( limit as x approaches 8 of sin(x))/x	$\frac{lim_{x \to 8} \sin (x)}{x}$
2611	Evaluate the Limit	( limit as x approaches 64 of square root of x-8)/(x-64)	$\frac{lim_{x \to 64} \sqrt{x} - 8}{x - 64}$
2612	Evaluate the Limit	( limit as x approaches -6 of x^2-36)/(x+6)	$\frac{lim_{x \to - 6} x^{2} - 36}{x + 6}$
2613	Evaluate the Limit	( limit as x approaches 7 of x^2-49)/(x-7)	$\frac{lim_{x \to 7} x^{2} - 49}{x - 7}$
2614	Evaluate the Limit	( limit as x approaches 3 of x^2-x-6)/(x-3)	$\frac{lim_{x \to 3} x^{2} - x - 6}{x - 3}$
2615	Evaluate the Limit	( limit as x approaches 4 of 4x-x^2)/(2- square root of x)	$\frac{lim_{x \to 4} 4 x - x^{2}}{2 - \sqrt{x}}$
2616	Find the Derivative - d/dx	y=5x-x^2	$y = 5 x - x^{2}$
2617	Evaluate the Limit	( limit as x approaches 3 of x-3)/(x^2-9)	$\frac{lim_{x \to 3} x - 3}{x^{2} - 9}$
2618	Evaluate the Limit	( limit as x approaches 1 of x^2+3x-4)/(x^2-1)	$\frac{lim_{x \to 1} x^{2} + 3 x - 4}{x^{2} - 1}$
2619	Evaluate the Limit	( limit as x approaches 1 of x^2+7x-8)/(x^2-1)	$\frac{lim_{x \to 1} x^{2} + 7 x - 8}{x^{2} - 1}$
2620	Evaluate the Limit	( limit as x approaches 1 of 2-x)/((x-1)^2)	$\frac{lim_{x \to 1} 2 - x}{{(x - 1)}^{2}}$
2621	Evaluate the Limit	( limit as x approaches 10 of x^2-100)/(x-10)	$\frac{lim_{x \to 10} x^{2} - 100}{x - 10}$
2622	Evaluate the Limit	( limit as x approaches 2 of (1/x)-(1/2))/(x-2)	$\frac{lim_{x \to 2} (\frac{1}{x}) - (\frac{1}{2})}{x - 2}$
2623	Evaluate the Limit	limit as h approaches 0 of (1/((x+h)^2)-1/(x^2))/h	$lim_{h \to 0} \frac{\frac{1}{{(x + h)}^{2}} - \frac{1}{x^{2}}}{h}$
2624	Evaluate the Limit	limit as x approaches 3 of (x^3-27)/(x-3)	$lim_{x \to 3} \frac{x^{3} - 27}{x - 3}$
2625	Find the Derivative - d/dx	seventh root of x	$\sqrt[7]{x}$
2626	Multiply	(d^2)/(dr^2)*(pir^2)	$\frac{d^{2}}{d r^{2}} \cdot (π r^{2})$
2627	Find the Antiderivative	f(x)=5x^2-5x	$f (x) = 5 x^{2} - 5 x$
2628	Find the Antiderivative	f(x)=x^4	$f (x) = x^{4}$
2629	Find the Antiderivative	sin(3x)	$\sin (3 x)$
2630	Find the Antiderivative	f(x) = square root of x	$f (x) = \sqrt{x}$
2631	Find the Antiderivative	f(x)=x^3	$f (x) = x^{3}$
2632	Find the Antiderivative	f(x)=sec(x)^2	$f (x) = \sec^{2} (x)$
2633	Find the Antiderivative	4x^2	$4 x^{2}$
2634	Find the Antiderivative	3/x	$\frac{3}{x}$
2635	Find the Antiderivative	x^-1	$x^{- 1}$
2636	Simplify/Condense	natural log of 3- natural log of 1	$\ln (3) - \ln (1)$
2637	Expand the Logarithmic Expression	natural log of x(x+1)(x+2)	$\ln (x (x + 1) (x + 2))$
2638	Find the Local Maxima and Minima	f(x)=sin(x)^2+cos(x)	$f (x) = \sin^{2} (x) + \cos (x)$
2639	Find the Derivative - d/d@VAR	f(x)=4x^3	$f (x) = 4 x^{3}$
2640	Find the Derivative - d/d@VAR	F(X)=4e^X	$F (X) = 4 e^{X}$
2641	Find the Derivative - d/d@VAR	f(x)=(x^3-3x^2+4)/(x^2)	$f (x) = \frac{x^{3} - 3 x^{2} + 4}{x^{2}}$
2642	Find the Derivative - d/d@VAR	f(x) = natural log of x^3	$f (x) = \ln (x^{3})$
2643	Find the Derivative - d/d@VAR	f(x) = natural log of x^5	$f (x) = \ln (x^{5})$
2644	Find the Derivative - d/d@VAR	f(x)=2x^2+3x-2	$f (x) = 2 x^{2} + 3 x - 2$
2645	Find the Derivative - d/d@VAR	f(x)=sec(x)	$f (x) = \sec (x)$
2646	Find the Derivative - d/d@VAR	f(x)=1/(x^5)	$f (x) = \frac{1}{x^{5}}$
2647	Find dy/dx	x^3+y^3-6xy=0	$x^{3} + y^{3} - 6 x y = 0$
2648	Evaluate the Summation	sum from k=1 to 12 of k^2	$\sum_{k = 1}^{12} k^{2}$
2649	Find the Local Maxima and Minima	y=x^3-6x^2-135x	$y = x^{3} - 6 x^{2} - 135 x$
2650	Find the Local Maxima and Minima	y=x/(x^2+25)	$y = \frac{x}{x^{2} + 25}$
2651	Find the Local Maxima and Minima	f(x)=x^3-27x	$f (x) = x^{3} - 27 x$
2652	Find the Local Maxima and Minima	f(x)=x^2-4x+5	$f (x) = x^{2} - 4 x + 5$
2653	Find the Local Maxima and Minima	f(x)=x^3-6x^2+1	$f (x) = x^{3} - 6 x^{2} + 1$
2654	Find the Local Maxima and Minima	f(x)=x^4-4x^3+10	$f (x) = x^{4} - 4 x^{3} + 10$
2655	Find the Local Maxima and Minima	f(x)=x^4-32x^2+256	$f (x) = x^{4} - 32 x^{2} + 256$
2656	Find the Local Maxima and Minima	f(x)=x^4-50x^2+625	$f (x) = x^{4} - 50 x^{2} + 625$
2657	Find the Local Maxima and Minima	f(x)=3x^4-6x^2+7	$f (x) = 3 x^{4} - 6 x^{2} + 7$
2658	Evaluate the Limit	limit as x approaches 4 of 1/(x-4)	$lim_{x \to 4} \frac{1}{x - 4}$
2659	Evaluate the Limit	limit as x approaches 0 of x/(x^2-x)	$lim_{x \to 0} \frac{x}{x^{2} - x}$
2660	Evaluate the Limit	limit as x approaches -3 of (x^2-9)/(2x^2+7x+3)	$lim_{x \to - 3} \frac{x^{2} - 9}{2 x^{2} + 7 x + 3}$
2661	Evaluate the Limit	limit as x approaches 9 of (x^2-9x)/(x^2-8x-9)	$lim_{x \to 9} \frac{x^{2} - 9 x}{x^{2} - 8 x - 9}$
2662	Evaluate the Limit	limit as x approaches 3 of tan((pix)/4)	$lim_{x \to 3} \tan (\frac{π x}{4})$
2663	Evaluate the Limit	limit as x approaches 3 of natural log of x^2-9	$lim_{x \to 3} \ln (x^{2} - 9)$
2664	Evaluate the Limit	limit as x approaches 3 of 7	$lim_{x \to 3} 7$
2665	Evaluate the Limit	limit as x approaches 0 of ( square root of x+9-3)/x	$lim_{x \to 0} \frac{\sqrt{x + 9} - 3}{x}$
2666	Evaluate the Limit	limit as t approaches infinity of ( square root of t+t^2)/(7t-t^2)	$lim_{t \to \infty} \frac{\sqrt{t} + t^{2}}{7 t - t^{2}}$
2667	Evaluate the Limit	limit as x approaches 1 of (x-1)/(x^3-1)	$lim_{x \to 1} \frac{x - 1}{x^{3} - 1}$
2668	Evaluate the Limit	limit as x approaches 16 of (x-16)/( square root of x-4)	$lim_{x \to 16} \frac{x - 16}{\sqrt{x} - 4}$
2669	Evaluate the Limit	limit as x approaches 5 of f(x)	$lim_{x \to 5} f (x)$
2670	Evaluate the Limit	limit as x approaches pi of 4sin(x+sin(x))	$lim_{x \to π} 4 \sin (x + \sin (x))$
2671	Evaluate the Limit	limit as x approaches -3 of (x^2+6x+9)/(x^4-81)	$lim_{x \to - 3} \frac{x^{2} + 6 x + 9}{x^{4} - 81}$
2672	Find dy/dx	x^2-8xy+y^2=8	$x^{2} - 8 x y + y^{2} = 8$
2673	Evaluate the Limit	limit as t approaches infinity of ( square root of t+t^2)/(8t-t^2)	$lim_{t \to \infty} \frac{\sqrt{t} + t^{2}}{8 t - t^{2}}$
2674	Evaluate the Limit	limit as x approaches 3 of (x^2-3x)/(x^2-2x-3)	$lim_{x \to 3} \frac{x^{2} - 3 x}{x^{2} - 2 x - 3}$
2675	Evaluate the Limit	limit as x approaches 1 of ( square root of x+3-2)/(x-1)	$lim_{x \to 1} \frac{\sqrt{x + 3} - 2}{x - 1}$
2676	Evaluate the Limit	limit as x approaches 36 of (6- square root of x)/(36x-x^2)	$lim_{x \to 36} \frac{6 - \sqrt{x}}{36 x - x^{2}}$
2677	Evaluate the Limit	limit as x approaches 9 of (9-x)/(3- square root of x)	$lim_{x \to 9} \frac{9 - x}{3 - \sqrt{x}}$
2678	Evaluate the Limit	limit as x approaches infinity of (sin(x))/x	$lim_{x \to \infty} \frac{\sin (x)}{x}$
2679	Evaluate the Limit	limit as x approaches pi of tan(x)	$lim_{x \to π} \tan (x)$
2680	Determine if Continuous	f(x)=tan((pix)/2)	$f (x) = \tan (\frac{π x}{2})$
2681	Determine if Continuous	f(x)=(x^2-16)/(x-4)	$f (x) = \frac{x^{2} - 16}{x - 4}$
2682	Graph	y=3x^3-36x-2	$y = 3 x^{3} - 36 x - 2$
2683	Graph	y=x^3-6x^2-96x	$y = x^{3} - 6 x^{2} - 96 x$
2684	Find the Antiderivative	e^(3x)	$e^{3 x}$
2685	Graph	f(x)=(x^2-8)/(x+3)	$f (x) = \frac{x^{2} - 8}{x + 3}$
2686	Graph	f(x) = natural log of x^4+27	$f (x) = \ln (x^{4} + 27)$
2687	Graph	e^(-x^2)	$e^{- x^{2}}$
2688	Evaluate	2cos(0)	$2 \cos (0)$
2689	Evaluate	180(14)-0.30*14^3	$180 (14) - 0.3 \cdot 14^{3}$
2690	Evaluate	sec(-pi/4)^2	$\sec^{2} (- \frac{π}{4})$
2691	Evaluate	-6/((18^4)/6)	$\frac{- 6}{\frac{18^{4}}{6}}$
2692	Find the Derivative - d/d@VAR	f(theta)=cos(theta^2)	$f (θ) = \cos (θ^{2})$
2693	Find the Critical Points	f(x)=2x^3-3x^2-36x	$f (x) = 2 x^{3} - 3 x^{2} - 36 x$
2694	Find the Critical Points	f(x)=3x^4-4x^3	$f (x) = 3 x^{4} - 4 x^{3}$
2695	Find the Critical Points	f(x)=e^(1-20x+5x^2)	$f (x) = e^{1 - 20 x + 5 x^{2}}$
2696	Find the Critical Points	f(x)=x^3+6x^2-15x	$f (x) = x^{3} + 6 x^{2} - 15 x$
2697	Find the Critical Points	xe^x	$x e^{x}$
2698	Find the Critical Points	12x^2-176x+484	$12 x^{2} - 176 x + 484$
2699	Evaluate	cos(arcsin(5/13))	$\cos (\arcsin (\frac{5}{13}))$
2700	Evaluate	sin(4)	$\sin (4)$