Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
601	Evaluate the Limit	( limit as x approaches 4 of square root of x+5-3)/(x-4)	$\frac{lim_{x \to 4} \sqrt{x + 5} - 3}{x - 4}$
602	Evaluate the Limit	( limit as x approaches 3 of x^2-9)/(x-3)	$\frac{lim_{x \to 3} x^{2} - 9}{x - 3}$
603	Evaluate the Limit	( limit as x approaches 2 of x^2+x-6)/(x-2)	$\frac{lim_{x \to 2} x^{2} + x - 6}{x - 2}$
604	Evaluate the Limit	limit as x approaches 0 of (sin(2x))/x	$lim_{x \to 0} \frac{\sin (2 x)}{x}$
605	Evaluate the Limit	limit as x approaches 25 of ( square root of x-5)/(x-25)	$lim_{x \to 25} \frac{\sqrt{x} - 5}{x - 25}$
606	Evaluate the Limit	limit as x approaches 1 of 1/(x-1)	$lim_{x \to 1} \frac{1}{x - 1}$
607	Graph	2 natural log of x	$2 \ln (x)$
608	Find the Derivative - d/dx	-2xsin(x^2)	$- 2 x \sin (x^{2})$
609	Find the Derivative - d/dx	(x^2+4x+3)/( square root of x)	$\frac{x^{2} + 4 x + 3}{\sqrt{x}}$
610	Find the Derivative - d/dx	x^8	$x^{8}$
611	Find the Derivative - d/dx	y = square root of x+6	$y = \sqrt{x + 6}$
612	Find the Derivative - d/dx	x/( natural log of x)	$\frac{x}{\ln (x)}$
613	Find the Derivative - d/dx	(x+1)^2	${(x + 1)}^{2}$
614	Find the Derivative - d/dx	fourth root of x^3	$\sqrt[4]{x^{3}}$
615	Find the Derivative - d/dx	2x^4	$2 x^{4}$
616	Find the Derivative - d/dx	y=((x+3)x)/(x+1)	$y = \frac{(x + 3) x}{x + 1}$
617	Find the Derivative - d/dd	(dy)/(dx)	$\frac{d y}{d x}$
618	Find the Derivative - d/dy	(1/(y^2)-9/(y^4))(y+3y^3)	$(\frac{1}{y^{2}} - \frac{9}{y^{4}}) (y + 3 y^{3})$
619	Find the Derivative - d/dZ	y=sec(x)tan(x)	$y = \sec (x) \tan (x)$
620	Find the Derivative - d/dx	-x^3	$- x^{3}$
621	Find the Derivative - d/dx	natural log of e^x	$\ln (e^{x})$
622	Find the Derivative - d/dx	(e^x)/(1+x)	$\frac{e^{x}}{1 + x}$
623	Find the Derivative - d/dx	6/x	$\frac{6}{x}$
624	Find the Integral	-cos(x)	$- \cos (x)$
625	Find the Derivative - d/dx	(x^2)/3	$\frac{x^{2}}{3}$
626	Find the Derivative - d/dx	f(x)=csc(x)	$f (x) = \csc (x)$
627	Find the Derivative - d/dx	cos(xy)	$\cos (x y)$
628	Find the Derivative - d/dx	e^xsin(x)	$e^{x} \sin (x)$
629	Find dy/dx	x^2+y^2=1	$x^{2} + y^{2} = 1$
630	Find the Derivative - d/dx	2x^2-7x+5	$2 x^{2} - 7 x + 5$
631	Find the Derivative - d/dx	7x^2	$7 x^{2}$
632	Find the Derivative - d/dx	3x+2 square root of x+32/(x^2)	$3 x + 2 \sqrt{x} + \frac{32}{x^{2}}$
633	Evaluate the Integral	integral of x^2cos(3x) with respect to x	$\int x^{2} \cos (3 x) d x$
634	Find the 2nd Derivative	y = square root of x+3	$y = \sqrt{x + 3}$
635	Find the 2nd Derivative	f(x)=sec(x)	$f (x) = \sec (x)$
636	Evaluate the Integral	integral from -5 to 5 of square root of 25-x^2 with respect to x	$\int_{- 5}^{5} \sqrt{25 - x^{2}} d x$
637	Evaluate the Integral	integral of 1/(x( natural log of x)^2) with respect to x	$\int \frac{1}{x \ln^{2} (x)} d x$
638	Evaluate the Integral	integral of e^x square root of 1+e^x with respect to x	$\int e^{x} \sqrt{1 + e^{x}} d x$
639	Evaluate the Integral	integral from 0 to 1 of (x^2+4)e^(-x) with respect to x	$\int_{0}^{1} (x^{2} + 4) e^{- x} d x$
640	Evaluate the Integral	integral of 1/t with respect to t	$\int \frac{1}{t} d t$
641	Evaluate the Integral	integral of z^3e^z with respect to z	$\int z^{3} e^{z} d z$
642	Evaluate the Integral	integral of sin( square root of x) with respect to x	$\int \sin (\sqrt{x}) d x$
643	Evaluate the Integral	integral from 0 to 2 of square root of 4-x^2 with respect to x	$\int_{0}^{2} \sqrt{4 - x^{2}} d x$
644	Evaluate the Integral	integral from 0 to pi of cos(x)^2 with respect to x	$\int_{0}^{π} \cos^{2} (x) d x$
645	Evaluate the Integral	integral from 25 to 3 of 6( natural log of y)/( square root of y) with respect to y	$\int_{25}^{36} \frac{\ln (y)}{\sqrt{y}} d y$
646	Evaluate the Integral	integral of (12x+5)^2 with respect to x	$\int {(12 x + 5)}^{2} d x$
647	Evaluate the Integral	integral of arctan(4t) with respect to t	$\int \arctan (4 t) d t$
648	Evaluate the Integral	integral from 0 to 1 of (r^3)/( square root of 16+r^2) with respect to r	$\int_{0}^{1} \frac{r^{3}}{\sqrt{16 + r^{2}}} d r$
649	Evaluate the Integral	integral of cos(x)e^(sin(x)) with respect to x	$\int \cos (x) e^{\sin (x)} d x$
650	Evaluate the Integral	2 integral of x with respect to x	$2 \int x d x$
651	Evaluate the Integral	integral from -3 to 3 of square root of 9-x^2 with respect to x	$\int_{- 3}^{3} \sqrt{9 - x^{2}} d x$
652	Evaluate the Integral	integral of 3/x with respect to x	$\int \frac{3}{x} d x$
653	Evaluate the Integral	integral from 0 to 1 of 4x^5-5x^4 with respect to x	$\int_{0}^{1} 4 x^{5} - 5 x^{4} d x$
654	Evaluate the Limit	limit as x approaches -24 of ( square root of x^2+49-25)/(x+24)	$lim_{x \to - 24} \frac{\sqrt{x^{2} + 49} - 25}{x + 24}$
655	Evaluate the Integral	integral from 0 to 45 of 1/( square root of t+4) with respect to t	$\int_{0}^{45} \frac{1}{\sqrt{t + 4}} d t$
656	Find the Absolute Max and Min over the Interval	f(x)=5x^2-3x-1 , [-1,3]	$f (x) = 5 x^{2} - 3 x - 1$ , $[- 1, 3]$
657	Find dy/dx	9x^2+y^2=9	$9 x^{2} + y^{2} = 9$
658	Find dy/dx	x^2+y^2=16	$x^{2} + y^{2} = 16$
659	Find the Derivative - d/dx	sin(x)^4	$\sin^{4} (x)$
660	Find the Derivative - d/d@VAR	f(x)=x^2+1	$f (x) = x^{2} + 1$
661	Find the Derivative - d/d@VAR	f(x)=x^3+x^2	$f (x) = x^{3} + x^{2}$
662	Find the Derivative - d/dx	fifth root of 6x	$\sqrt[5]{6 x}$
663	Find the Derivative - d/dx	y=3x^2	$y = 3 x^{2}$
664	Find the Derivative - d/dx	y=4x-x^2	$y = 4 x - x^{2}$
665	Find the Derivative - d/dx	square root of x^2+3	$\sqrt{x^{2} + 3}$
666	Find the Derivative - d/dx	y=8/(3x^2)	$y = \frac{8}{3 x^{2}}$
667	Find the Derivative - d/dx	e^(sin(x))	$e^{\sin (x)}$
668	Find the Derivative - d/dx	e^(x^5)	$e^{x^{5}}$
669	Find the Derivative - d/dx	(6x+1)^2	${(6 x + 1)}^{2}$
670	Find the Derivative - d/dx	8e^x	$8 e^{x}$
671	Find the Derivative - d/dx	e^(1-20x+5x^2)	$e^{1 - 20 x + 5 x^{2}}$
672	Simplify	e^infinity	$e^{\infty}$
673	Find the Derivative - d/dt	d/(dt)(at^2+bt+c)	$\frac{d}{d t} (a t^{2} + b t + c)$
674	Find the Derivative - d/dx	x(x^2+1)	$x (x^{2} + 1)$
675	Find the Derivative - d/dx	(2x)/(x^2+1)	$\frac{2 x}{x^{2} + 1}$
676	Find the Derivative - d/dx	x+2/x	$x + \frac{2}{x}$
677	Find the Derivative - d/dx	x(x^2-5/x)	$x (x^{2} - \frac{5}{x})$
678	Find the Derivative - d/dx	x/3	$\frac{x}{3}$
679	Find the Derivative - d/dx	square root of 1-6x	$\sqrt{1 - 6 x}$
680	Find the Derivative - d/dx	x(x-4)^3	$x {(x - 4)}^{3}$
681	Find the Derivative - d/dx	x/(x+2)	$\frac{x}{x + 2}$
682	Find the Derivative - d/dx	x/(x^2+2)	$\frac{x}{x^{2} + 2}$
683	Find the Derivative - d/dx	x/(x^2+9)	$\frac{x}{x^{2} + 9}$
684	Find the Derivative - d/dx	x^8e^x	$x^{8} e^{x}$
685	Find the Derivative - d/dx	2tan(x)	$2 \tan (x)$
686	Find the Derivative - d/dx	e^6	$e^{6}$
687	Find the Derivative - d/dx	tan((pix)/2)	$\tan (\frac{π x}{2})$
688	Find the Derivative - d/dx	natural log of 5	$\ln (5)$
689	Find the Derivative - d/dx	y=1/(x^5)	$y = \frac{1}{x^{5}}$
690	Simplify	1/8	$\frac{1}{8}$
691	Simplify	(x+8)(24/x+12)	$(x + 8) (\frac{24}{x} + 12)$
692	Solve for v	v = square root of 3^2+(-1)^2	$v = \sqrt{3^{2} + {(- 1)}^{2}}$
693	Graph	natural log of sin(x)	$\ln (\sin (x))$
694	Evaluate the Limit	( limit as x approaches 0 of tan(x))/x	$\frac{lim_{x \to 0} \tan (x)}{x}$
695	Evaluate the Limit	limit as x approaches 0 of cos(1/x)	$lim_{x \to 0} \cos (\frac{1}{x})$
696	Evaluate the Limit	( limit as x approaches -3 of x^2-9)/(x+3)	$\frac{lim_{x \to - 3} x^{2} - 9}{x + 3}$
697	Evaluate the Limit	( limit as x approaches 4 of square root of x-2)/(x-4)	$\frac{lim_{x \to 4} \sqrt{x} - 2}{x - 4}$
698	Evaluate the Limit	limit as x approaches infinity of e^x	$lim_{x \to \infty} e^{x}$
699	Find the Antiderivative	3x	$3 x$
700	Find the Antiderivative	e^(2x)	$e^{2 x}$