Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
63801	Evaluate the Limit	limit as x approaches 2 from the right of 14/(8-4x)	$lim_{x \to 2} \frac{14}{8 - 4 x}$
63802	Evaluate the Limit	limit as x approaches -1 of x^2+3x-4	$lim_{x \to - 1} x^{2} + 3 x - 4$
63803	Solve for x	x^2e^x+2xe^x-8e^x=0	$x^{2} e^{x} + 2 x e^{x} - 8 e^{x} = 0$
63804	Find the Antiderivative	0	$0$
63805	Find the Antiderivative	-1/x	$- \frac{1}{x}$
63806	Evaluate the Limit	limit as x approaches 0 from the left of (\|x\|)/x	$lim_{x \to 0} \frac{\| x \|}{x}$
63807	Evaluate the Limit	limit as x approaches 0 of (e^(2x)-1)/x	$lim_{x \to 0} \frac{e^{2 x} - 1}{x}$
63808	Find the Antiderivative	1/2x^2	$\frac{1}{2} x^{2}$
63809	Find the Antiderivative	square root of 1-x^2	$\sqrt{1 - x^{2}}$
63810	Find the Antiderivative	4 square root of x	$4 \sqrt{x}$
63811	Find the Antiderivative	4/(x^3)	$\frac{4}{x^{3}}$
63812	Find the Antiderivative	1/y	$\frac{1}{y}$
63813	Find the Antiderivative	1/(y^2)	$\frac{1}{y^{2}}$
63814	Find the Antiderivative	5x^3	$5 x^{3}$
63815	Find the Foci	25x^2-4y^2=400	$25 x^{2} - 4 y^{2} = 400$
63816	Solve for x	square root of x-5+ square root of x-14=3 square root of 3	$\sqrt{x - 5} + \sqrt{x - 14} = 3 \sqrt{3}$
63817	Solve for x	x- square root of x=12	$x - \sqrt{x} = 12$
63818	Evaluate the Limit	limit as x approaches 4 from the left of 1/(x-4)	$lim_{x \to 4} \frac{1}{x - 4}$
63819	Find dy/dx	x^(2/5)+y^(2/5)=1	$x^{\frac{2}{5}} + y^{\frac{2}{5}} = 1$
63820	Evaluate the Limit	limit as x approaches infinity of (x-4)/x	$lim_{x \to \infty} \frac{x - 4}{x}$
63821	Find the Domain and Range	x^2-9y^2=200	$x^{2} - 9 y^{2} = 200$
63822	Find the Derivative - d/d@VAR	f(x)=x^3-3x	$f (x) = x^{3} - 3 x$
63823	Find the Derivative - d/d@VAR	f(x)=arctan(x)	$f (x) = \arctan (x)$
63824	Evaluate the Summation	sum from n=1 to 5 of 3n-3	$\sum_{n = 1}^{5} 3 n - 3$
63825	Find the Derivative - d/d@VAR	f(t)=tsin(pit)	$f (t) = t \sin (π t)$
63826	Find the Derivative - d/d@VAR	f(t)=(6-t)(6+t^3)^-1	$f (t) = (6 - t) {(6 + t^{3})}^{- 1}$
63827	Find the Derivative - d/d@VAR	f(x)=e^(sin(x))	$f (x) = e^{\sin (x)}$
63828	Find the Integral	integral of 1/( square root of x) with respect to x	$\int \frac{1}{\sqrt{x}} d x$
63829	Find the Integral	integral of arcsin(x) with respect to x	$\int \arcsin (x) d x$
63830	Verify the Identity	csc(x)^3*tan(x)^2=(csc(x))(1+tan(x)^2)	$\csc^{3} (x) \cdot \tan^{2} (x) = (\csc (x)) (1 + \tan^{2} (x))$
63831	Find the Integral	integral from 0 to 1 of (3x^2-x^2+2x-4)/( square root of x^2-3x+2) with respect to x	$\int_{0}^{1} \frac{3 x^{2} - x^{2} + 2 x - 4}{\sqrt{x^{2} - 3 x + 2}} d x$
63832	Find the Derivative - d/d@VAR	f(x)=(cos(x))/(1-sin(x))	$f (x) = \frac{\cos (x)}{1 - \sin (x)}$
63833	Find the Derivative - d/d@VAR	f(x)=e^(9x)	$f (x) = e^{9 x}$
63834	Find the Sample Standard Deviation	10 , 10 , 10.5 , 11 , 11.25 , 12 , 12.25	$10$ , $10$ , $10.5$ , $11$ , $11.25$ , $12$ , $12.25$
63835	Evaluate the Summation	sum from k=1 to 3 of 2*3^k	$\sum_{k = 1}^{3} 2 \cdot 3^{k}$
63836	Find the Derivative - d/d@VAR	g(x)=x^2(1-2x)	$g (x) = x^{2} (1 - 2 x)$
63837	Find the Derivative - d/d@VAR	g(t)=cos(1/t)e^(5t^2)	$g (t) = \cos (\frac{1}{t}) e^{5 t^{2}}$
63838	Find the Derivative - d/d@VAR	f(x)=9x^2	$f (x) = 9 x^{2}$
63839	Evaluate the Summation	sum from n=6 to 97 of 152+3n	$\sum_{n = 6}^{97} 152 + 3 n$
63840	Find the Derivative - d/d@VAR	f(t)=te^tcot(t)	$f (t) = t e^{t} \cot (t)$
63841	Find the Derivative - d/d@VAR	f(x)=xe^(2x)	$f (x) = x e^{2 x}$
63842	Find the Integral	integral of sec(x)^2 with respect to x	$\int \sec^{2} (x) d x$
63843	Evaluate the Summation	sum from n=1 to 4 of 3n+1	$\sum_{n = 1}^{4} 3 n + 1$
63844	Evaluate the Summation	sum from 1 to 32 of (i-8)^2	$\sum_{1}^{32} {(i - 8)}^{2}$
63845	Evaluate the Summation	sum from i=2 to 5 of 2i^2-1	$\sum_{i = 2}^{5} 2 i^{2} - 1$
63846	Find the Derivative - d/d@VAR	f(x)=(x^-2+x^-3)(x^5-2x^2)	$f (x) = (x^{- 2} + x^{- 3}) (x^{5} - 2 x^{2})$
63847	Find the Derivative - d/d@VAR	f(x)=(6x^3-12x)^(4/3)	$f (x) = {(6 x^{3} - 12 x)}^{\frac{4}{3}}$
63848	Find the Derivative - d/d@VAR	f(x)=tan(x)^2	$f (x) = \tan^{2} (x)$
63849	Find the Derivative - d/d@VAR	f(x)=2^90	$f (x) = 2^{90}$
63850	Find the Integral	integral of (( natural log of x)^6)/x with respect to x	$\int \frac{\ln^{6} (x)}{x} d x$
63851	Find the Integral	square root of 1+x^2	$\sqrt{1 + x^{2}}$
63852	Evaluate the Summation	sum from i=1 to 5 of 5*2^(2i-1)	$\sum_{i = 1}^{5} 5 \cdot 2^{2 i - 1}$
63853	Evaluate the Summation	sum from i=1 to 13 of 2i+2	$\sum_{i = 1}^{13} 2 i + 2$
63854	Find dy/dx	xy+x=12	$x y + x = 12$
63855	Evaluate the Summation	sum from k=1 to 5 of 16(3/2)^(k-1)	$\sum_{k = 1}^{5} 16 {(\frac{3}{2})}^{k - 1}$
63856	Evaluate the Summation	sum from n=18 to 64 of 1/2n	$\sum_{n = 18}^{64} \frac{1}{2} n$
63857	Solve for r	984=800e^(r^5)	$984 = 800 e^{r^{5}}$
63858	Find the Integral	integral of 2x with respect to x	$\int 2 x d x$
63859	Find the Derivative - d/d@VAR	f(x)=1/( cube root of 7x^2)	$f (x) = \frac{1}{\sqrt[3]{7 x^{2}}}$
63860	Find the Derivative - d/d@VAR	f(t)=e^(5t)sin(t)	$f (t) = e^{5 t} \sin (t)$
63861	Find the Derivative - d/d@VAR	f(x)=8x^4	$f (x) = 8 x^{4}$
63862	Find the Derivative - d/d@VAR	f(x)=6/( square root of x)	$f (x) = \frac{6}{\sqrt{x}}$
63863	Find the Second Derivative	2x^(3/2)	$2 x^{\frac{3}{2}}$
63864	Find the Second Derivative	f(x)=5x^(3/2)	$f (x) = 5 x^{\frac{3}{2}}$
63865	Evaluate the Summation	sum from n=1 to 7 of 5-2n	$\sum_{n = 1}^{7} 5 - 2 n$
63866	Evaluate the Summation	sum from n=1 to 30 of 20+5(n-1)	$\sum_{n = 1}^{30} 20 + 5 (n - 1)$
63867	Find dy/dx	x^2+y^2=7	$x^{2} + y^{2} = 7$
63868	Find dy/dx	y=2 square root of x	$y = 2 \sqrt{x}$
63869	Simplify	y>=-2x-8	$y \geq - 2 x - 8$
63870	Find the Derivative - d/d@VAR	g(x)=x^(2/3)	$g (x) = x^{\frac{2}{3}}$
63871	Find the Derivative - d/d@VAR	f(x)=x^3-6x^2	$f (x) = x^{3} - 6 x^{2}$
63872	Find the Derivative - d/d@VAR	F(x)=(3x+1)^2	$F (x) = {(3 x + 1)}^{2}$
63873	Find the Derivative - d/d@VAR	f(x)=arcsec(7x)	$f (x) = arcsec (7 x)$
63874	Evaluate the Summation	sum from i=0 to 8 of 7*2^i	$\sum_{i = 0}^{8} 7 \cdot 2^{i}$
63875	Evaluate the Summation	sum from i=1 to 8 of 3^i	$\sum_{i = 1}^{8} 3^{i}$
63876	Find dy/dx	y=4x^3	$y = 4 x^{3}$
63877	Evaluate the Summation	sum from n=0 to 4 of 1+3n	$\sum_{n = 0}^{4} 1 + 3 n$
63878	Evaluate the Summation	sum from n=1 to 48 of 5+2(n-1)	$\sum_{n = 1}^{48} 5 + 2 (n - 1)$
63879	Find the Directrix	x=y^2+14y-2	$x = y^{2} + 14 y - 2$
63880	Find the Integral	integral of square root of 1+x^2 with respect to x	$\int \sqrt{1 + x^{2}} d x$
63881	Find the Second Derivative	5x^4-6x^2+7	$5 x^{4} - 6 x^{2} + 7$
63882	Find the Second Derivative	integral from 0 to 1 of (3x^3-x^2+2x-4)/( square root of x^2-3x+2) with respect to x	$\int_{0}^{1} \frac{3 x^{3} - x^{2} + 2 x - 4}{\sqrt{x^{2} - 3 x + 2}} d x$
63883	Find the Derivative - d/d@VAR	f(x)=(2x-6)^4(x^2+x+1)^5	$f (x) = {(2 x - 6)}^{4} {(x^{2} + x + 1)}^{5}$
63884	Find the Derivative - d/d@VAR	f(t)=(2t)/(2+ square root of t)	$f (t) = \frac{2 t}{2 + \sqrt{t}}$
63885	Find the Derivative - d/d@VAR	f(x)=3e^xcos(x)	$f (x) = 3 e^{x} \cos (x)$
63886	Find the Derivative - d/d@VAR	f(x)=2x^2+3x+2	$f (x) = 2 x^{2} + 3 x + 2$
63887	Find the Derivative - d/d@VAR	f(x)=(5x^3+4)(3x^7-5)	$f (x) = (5 x^{3} + 4) (3 x^{7} - 5)$
63888	Find the Derivative - d/d@VAR	f(x)=sin(x^3)	$f (x) = \sin (x^{3})$
63889	Find the Derivative - d/dy	1/(8y^2)	$\frac{1}{8 y^{2}}$
63890	Find the Derivative - d/d@VAR	f(x)=x^2-4x+5	$f (x) = x^{2} - 4 x + 5$
63891	Find the Derivative - d/d@VAR	h(z)=(7-z^2)(z^3-z+5)	$h (z) = (7 - z^{2}) (z^{3} - z + 5)$
63892	Evaluate the Summation	sum from n=1 to 104 of 6	$\sum_{n = 1}^{104} 6$
63893	Evaluate the Summation	sum from k=1 to 5 of 5(2)^(k-1)	$\sum_{k = 1}^{5} 5 {(2)}^{k - 1}$
63894	Evaluate the Summation	sum from k=1 to 19 of 4-3k	$\sum_{k = 1}^{19} 4 - 3 k$
63895	Find dy/dx	x^3+y^3=24xy	$x^{3} + y^{3} = 24 x y$
63896	Find dy/dx	y=x^5	$y = x^{5}$
63897	Find the Integral	integral of (3x^3-x^2+2x-4)/( square root of x^2-3x+2) with respect to x	$\int \frac{3 x^{3} - x^{2} + 2 x - 4}{\sqrt{x^{2} - 3 x + 2}} d x$
63898	Find the Integral	square root of y	$\sqrt{y}$
63899	Find the Derivative - d/d@VAR	F(x)=x^(sin(x))	$F (x) = x^{\sin (x)}$
63900	Find the Derivative - d/d@VAR	f(x) = natural log of x^2	$f (x) = \ln (x^{2})$