Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
701	Evaluate the Limit	limit as x approaches 3 of (\|x-3\|)/(x-3)	$lim_{x \to 3} \frac{\| x - 3 \|}{x - 3}$
702	Evaluate the Limit	limit as x approaches 2 of (x^2-4)/(x-2)	$lim_{x \to 2} \frac{x^{2} - 4}{x - 2}$
703	Evaluate the Limit	limit as x approaches -2 of (x+2)/(x^3+8)	$lim_{x \to - 2} \frac{x + 2}{x^{3} + 8}$
704	Evaluate the Limit	limit as x approaches 2 of (x^3-8)/(x-2)	$lim_{x \to 2} \frac{x^{3} - 8}{x - 2}$
705	Find the Derivative - d/dx	(e^x)/(x^2)	$\frac{e^{x}}{x^{2}}$
706	Evaluate	e^(-0)	$e^{- 0}$
707	Find the Absolute Max and Min over the Interval	f(x)=3x^2-1 , [1,3]	$f (x) = 3 x^{2} - 1$ , $[1, 3]$
708	Find the Inflection Points	f(x)=1/2x^4+2x^3	$f (x) = \frac{1}{2} x^{4} + 2 x^{3}$
709	Solve the Function Operation	f(x)=5x^2-2x , g(x)=8x+3 , f(g(k))	$f (x) = 5 x^{2} - 2 x$ , $g (x) = 8 x + 3$ , $f (g (k))$
710	Evaluate the Limit	limit as x approaches 1 of (x^2-1)/(x-1)	$lim_{x \to 1} \frac{x^{2} - 1}{x - 1}$
711	Find the Derivative of the Integral	integral of 2x with respect to x	$\int 2 x d x$
712	Evaluate the Integral	integral of x^2e^(3x) with respect to x	$\int x^{2} e^{3 x} d x$
713	Evaluate the Integral	integral of 10x with respect to x	$\int 10 x d x$
714	Evaluate the Integral	integral from 1 to 9 of square root of x with respect to x	$\int_{1}^{9} \sqrt{x} d x$
715	Evaluate the Integral	integral from 0 to 2 of 2x^2 with respect to x	$\int_{0}^{2} 2 x^{2} d x$
716	Find the Derivative - d/dx	( square root of x-9)/( square root of x+9)	$\frac{\sqrt{x} - 9}{\sqrt{x} + 9}$
717	Evaluate the Integral	integral of 2x^2 natural log of x with respect to x	$\int 2 x^{2} \ln (x) d x$
718	Evaluate the Integral	integral of log of x with respect to x	$\int \log (x) d x$
719	Evaluate the Integral	integral of xsin(x^2) with respect to x	$\int x \sin (x^{2}) d x$
720	Evaluate the Integral	integral of x square root of x+2 with respect to x	$\int x \sqrt{x + 2} d x$
721	Evaluate the Integral	integral of 9x^3 with respect to x	$\int 9 x^{3} d x$
722	Evaluate the Integral	integral of 9x with respect to x	$\int 9 x d x$
723	Evaluate the Integral	integral of square root of 8x+1 with respect to x	$\int \sqrt{8 x + 1} d x$
724	Evaluate the Integral	integral of sin(x^2) with respect to x	$\int \sin (x^{2}) d x$
725	Evaluate the Integral	integral of sec(x)^2tan(x) with respect to x	$\int \sec^{2} (x) \tan (x) d x$
726	Evaluate the Integral	integral of xsin(2x) with respect to x	$\int x \sin (2 x) d x$
727	Evaluate the Integral	integral of e^(2x)x^2 with respect to x	$\int e^{2 x} x^{2} d x$
728	Evaluate the Integral	integral of ( natural log of t)^2 with respect to t	$\int \ln^{2} (t) d t$
729	Find the 2nd Derivative	f(x) = natural log of x	$f (x) = \ln (x)$
730	Find the 2nd Derivative	tan(x)	$\tan (x)$
731	Evaluate the Integral	integral of (x+1)^2 with respect to x	$\int {(x + 1)}^{2} d x$
732	Evaluate the Integral	integral of sin(4x) with respect to x	$\int \sin (4 x) d x$
733	Find the Derivative - d/dx	y=x^x	$y = x^{x}$
734	Find the Derivative - d/dx	(x-2)^2	${(x - 2)}^{2}$
735	Find the Derivative - d/dx	x+1/x	$x + \frac{1}{x}$
736	Find the 2nd Derivative	1/x	$\frac{1}{x}$
737	Find the Derivative - d/dx	y=( square root of x)^x	$y = {(\sqrt{x})}^{x}$
738	Find the Derivative - d/dx	(x^2+1)^2	${(x^{2} + 1)}^{2}$
739	Find the Antiderivative	f(x)=3x^2	$f (x) = 3 x^{2}$
740	Find the Antiderivative	x^(1/2)	$x^{\frac{1}{2}}$
741	Evaluate the Limit	limit as x approaches 4 of (\|x-4\|)/(x-4)	$lim_{x \to 4} \frac{\| x - 4 \|}{x - 4}$
742	Evaluate the Limit	limit as x approaches -12 of ( square root of x^2+25-13)/(x+12)	$lim_{x \to - 12} \frac{\sqrt{x^{2} + 25} - 13}{x + 12}$
743	Evaluate the Limit	limit as x approaches -1 of f(x)	$lim_{x \to - 1} f (x)$
744	Evaluate the Limit	( limit as x approaches 0 of square root of x+4-2)/x	$\frac{lim_{x \to 0} \sqrt{x + 4} - 2}{x}$
745	Graph	( natural log of x)/(x^2)	$\frac{\ln (x)}{x^{2}}$
746	Graph	natural log of x^3	$\ln (x^{3})$
747	Find the Derivative - d/dx	square root of x+5/( square root of x)	$\sqrt{x} + \frac{5}{\sqrt{x}}$
748	Find the Derivative - d/dx	(x^4)/4	$\frac{x^{4}}{4}$
749	Find the Derivative - d/dx	5e^xcos(x)	$5 e^{x} \cos (x)$
750	Find the Derivative - d/dx	x^(sin(x))	$x^{\sin (x)}$
751	Find the Derivative - d/dx	y=((x+6)x)/(x+1)	$y = \frac{(x + 6) x}{x + 1}$
752	Find the Derivative - d/dx	e^(x^4)	$e^{x^{4}}$
753	Find the Derivative - d/dx	tan(x^4+1)^2	$\tan^{2} (x^{4} + 1)$
754	Find the Derivative - d/dx	y = square root of x+12	$y = \sqrt{x + 12}$
755	Find the Derivative - d/dx	x^(cos(x))	$x^{\cos (x)}$
756	Find the Derivative - d/dx	x^3+2x	$x^{3} + 2 x$
757	Find the Derivative - d/dx	2x^2-x	$2 x^{2} - x$
758	Find the Derivative - d/dx	-20e^(1-4x)+20	$- 20 e^{1 - 4 x} + 20$
759	Find the Derivative - d/dx	y=((x+7)x)/(x+1)	$y = \frac{(x + 7) x}{x + 1}$
760	Find the Derivative - d/dx	y=tan(x)	$y = \tan (x)$
761	Find the Derivative - d/dx	3xy	$3 x y$
762	Find the Derivative - d/dx	e^(-(5-3x)^2)	$e^{- {(5 - 3 x)}^{2}}$
763	Find the Derivative - d/dt	-1/((2+t)^2)	$- \frac{1}{{(2 + t)}^{2}}$
764	Find the Derivative - d/dx	( square root of x)/(x^3+1)	$\frac{\sqrt{x}}{x^{3} + 1}$
765	Find the Derivative - d/dx	(x^3+x+1)/x	$\frac{x^{3} + x + 1}{x}$
766	Find the Derivative - d/dx	1+cos(x)	$1 + \cos (x)$
767	Find the Derivative - d/dx	2e^xcos(x)	$2 e^{x} \cos (x)$
768	Find the Derivative - d/dx	y = natural log of 5x	$y = \ln (5 x)$
769	Find the Derivative Using Quotient Rule - d/dx	x/(x^2+1)	$\frac{x}{x^{2} + 1}$
770	Find the Derivative - d/dx	1+cos(x)^2	$1 + \cos^{2} (x)$
771	Find the Derivative - d/dx	( natural log of x)^4	$\ln^{4} (x)$
772	Find the Derivative - d/dx	3/(x^3)	$\frac{3}{x^{3}}$
773	Find the Derivative - d/dx	(x^2+1)(x^2-1)	$(x^{2} + 1) (x^{2} - 1)$
774	Find the Derivative - d/dx	x^2+x-2	$x^{2} + x - 2$
775	Find the Derivative - d/dx	sin(x^3)	$\sin (x^{3})$
776	Find the Derivative - d/dx	x^3sin(x)	$x^{3} \sin (x)$
777	Find the Antiderivative	e^(-x)	$e^{- x}$
778	Find the Derivative - d/dx	f(x)=xe^x	$f (x) = x e^{x}$
779	Find the Derivative - d/dx	f(x)=3 square root of x	$f (x) = 3 \sqrt{x}$
780	Find the Integral	cos(5x)	$\cos (5 x)$
781	Find dy/dx	x^2+y^2=4	$x^{2} + y^{2} = 4$
782	Find dy/dx	x^2+y^2=9	$x^{2} + y^{2} = 9$
783	Find dy/dx	tan(x-y)=y/(1+x^2)	$\tan (x - y) = \frac{y}{1 + x^{2}}$
784	Find the Derivative - d/dx	x(x^2+5)^(1/3)	$x {(x^{2} + 5)}^{\frac{1}{3}}$
785	Find the Derivative - d/dx	square root of 1+x^2	$\sqrt{1 + x^{2}}$
786	Find the Derivative - d/dx	2/x-2/(x^3)+1/(x^4)	$\frac{2}{x} - \frac{2}{x^{3}} + \frac{1}{x^{4}}$
787	Find the Derivative - d/dx	1/(2 square root of x)	$\frac{1}{2 \sqrt{x}}$
788	Find the Derivative - d/dx	square root of x+9/( square root of x)	$\sqrt{x} + \frac{9}{\sqrt{x}}$
789	Find the Derivative - d/dx	tan(3x)	$\tan (3 x)$
790	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of x natural log of x	$lim_{x \to 0} x \ln (x)$
791	Evaluate the Integral	integral from 1 to 4 of square root of x with respect to x	$\int_{1}^{4} \sqrt{x} d x$
792	Evaluate the Integral	integral of 9x^2+2x-9 with respect to x	$\int 9 x^{2} + 2 x - 9 d x$
793	Evaluate the Integral	integral of (x^2)/(1+x^2) with respect to x	$\int \frac{x^{2}}{1 + x^{2}} d x$
794	Evaluate the Integral	integral of 6x with respect to x	$\int 6 x d x$
795	Evaluate the Integral	integral of (2x+6)^5 with respect to x	$\int {(2 x + 6)}^{5} d x$
796	Evaluate the Integral	integral of (x^2-9)^3(2x) with respect to x	$\int {(x^{2} - 9)}^{3} (2 x) d x$
797	Find the 2nd Derivative	f(x)=5/(x^2+5)	$f (x) = \frac{5}{x^{2} + 5}$
798	Find the 2nd Derivative	y = square root of x+2	$y = \sqrt{x + 2}$
799	Evaluate the Integral	integral from 0 to 2 of x^2 with respect to x	$\int_{0}^{2} x^{2} d x$
800	Evaluate the Integral	integral of e^(-3t) with respect to t	$\int e^{- 3 t} d t$