Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
81501	Evaluate from the Left	limit as x approaches 2 of 1+3x	$lim_{x \to 2} 1 + 3 x$
81502	Find dy/dx	2x^2+x^3-x-4y^3-3y^2=0	$2 x^{2} + x^{3} - x - 4 y^{3} - 3 y^{2} = 0$
81503	Evaluate the Integral	integral from -3 to 3 of \|x-2x-3\| with respect to x	$\int_{- 3}^{3} \| x - 2 x - 3 \| d x$
81504	Find the Derivative - d/dx	-3x^(-5/3)	$- 3 x^{- \frac{5}{3}}$
81505	Integrate Using u-Substitution	integral of x(5x^2+4)^3 with respect to x	$\int x {(5 x^{2} + 4)}^{3} d x$
81506	Find the Antiderivative	1/(x(x+3))	$\frac{1}{x (x + 3)}$
81507	Find the Antiderivative	-1/((6x+1)^2)	$- \frac{1}{{(6 x + 1)}^{2}}$
81508	Evaluate the Limit	limit as x approaches -2 of 2x-4=-8	$lim_{x \to - 2} 2 x - 4 = - 8$
81509	Evaluate the Limit	limit as t approaches 10 of (2(t-10)^2)/t	$lim_{t \to 10} \frac{2 {(t - 10)}^{2}}{t}$
81510	Find the Derivative - d/dx	d/(dx)(e^xsin(x)+e^xcos(x))	$\frac{d}{d x} (e^{x} \sin (x) + e^{x} \cos (x))$
81511	Evaluate the Integral	integral of sin(3x)+e^(2x+1) with respect to x	$\int \sin (3 x) + e^{2 x + 1} d x$
81512	Evaluate Using L'Hospital's Rule	limit as x approaches 1 of (4 natural log of 3x-2)/(2-2x^2)	$lim_{x \to 1} \frac{4 \ln (3 x - 2)}{2 - 2 x^{2}}$
81513	Find the Percentage Rate of Change	g(t)=240(0.75)^t	$g (t) = 240 {(0.75)}^{t}$
81514	Evaluate the Limit	limit as x approaches 0 of square root of 7+2e^(2x)	$lim_{x \to 0} \sqrt{7 + 2 e^{2 x}}$
81515	Find the Antiderivative	natural log of x-1	$\ln (x - 1)$
81516	Evaluate the Integral	integral of (3x(7^(x^2)))/(7^(x^2)-5) with respect to x	$\int \frac{3 x (7^{x^{2}})}{7^{x^{2}} - 5} d x$
81517	Find the Antiderivative	-1/(x square root of 1-( natural log of x)^2)	$\frac{- 1}{x \sqrt{1 - \ln^{2} (x)}}$
81518	Find dy/dx	-xy^2+x+4-y^3=0	$- x y^{2} + x + 4 - y^{3} = 0$
81519	Find the Derivative - d/dx	( square root of x)/(1+x+x^3)	$\frac{\sqrt{x}}{1 + x + x^{3}}$
81520	Evaluate the Integral	integral of (2^x+3^x) with respect to x	$\int (2^{x} + 3^{x}) d x$
81521	Find the Maximum/Minimum Value	y=-7cos((2x)/3-4)+3	$y = - 7 \cos (\frac{2 x}{3} - 4) + 3$
81522	Evaluate the Limit	limit as x approaches infinity of 1/( square root of x) integral from 1 to x of 1/( square root of t) with respect to t	$lim_{x \to \infty} \frac{1}{\sqrt{x}} \int_{1}^{x} \frac{1}{\sqrt{t}} d t$
81523	Find the Derivative - d/dx	y=1/(e^(2x))	$y = \frac{1}{e^{2 x}}$
81524	Evaluate the Integral	integral of 6/(2x+3x^2) with respect to x	$\int \frac{6}{2 x + 3 x^{2}} d x$
81525	Find the Percentage Rate of Change	y=10(1+0.4)^t	$y = 10 {(1 + 0.4)}^{t}$
81526	Evaluate the Integral	integral of [3x^3(x^5+4/(x^4))] with respect to x	$\int [3 x^{3} (x^{5} + \frac{4}{x^{4}})] d x$
81527	Find the Antiderivative	(x^2)/(x+2)	$\frac{x^{2}}{x + 2}$
81528	Evaluate the Limit	limit as x approaches infinity of (1+1/(x^2))^x	$lim_{x \to \infty} {(1 + \frac{1}{x^{2}})}^{x}$
81529	Find the Integral	x/(1+x)	$\frac{x}{1 + x}$
81530	Evaluate the Limit	limit as x approaches infinity of log of 5^(1/x)	$lim_{x \to \infty} \log (5^{\frac{1}{x}})$
81531	Integrate Using u-Substitution	integral of cos(8x) with respect to x , u=8x	$\int \cos (8 x) d x$ , $u = 8 x$
81532	Evaluate the Limit	limit as x approaches 1 of (x^2-4)/4	$lim_{x \to 1} \frac{x^{2} - 4}{4}$
81533	Find the Derivative - d/dx	x^2-pi^2	$x^{2} - π^{2}$
81534	Find the Antiderivative	x^e+e^x	$x^{e} + e^{x}$
81535	Evaluate the Integral	integral from 1 to e of (x^2+1)/x with respect to x	$\int_{1}^{e} \frac{x^{2} + 1}{x} d x$
81536	Evaluate the Limit	limit as x approaches infinity of 3x^-5+4x^-2+5	$lim_{x \to \infty} 3 x^{- 5} + 4 x^{- 2} + 5$
81537	Find the Derivative - d/dx	d/(dx)(arctan(x)+2 square root of x)	$\frac{d}{d x} (\arctan (x) + 2 \sqrt{x})$
81538	Find the Maximum/Minimum Value	y=x^4+2x^2+8x+3	$y = x^{4} + 2 x^{2} + 8 x + 3$
81539	Evaluate the Limit	limit as x approaches 3 of (x-3)/(\|x^3-3x^2\|)	$lim_{x \to 3} \frac{x - 3}{\| x^{3} - 3 x^{2} \|}$
81540	Find the Integral	(5/8x^4-3x^2+2x^-1)dx	$(\frac{5}{8} x^{4} - 3 x^{2} + 2 x^{- 1}) d x$
81541	Integrate By Parts	integral of e^(-x^2) with respect to x	$\int e^{- x^{2}} d x$
81542	Evaluate the Integral	integral from square root of pi/2 to square root of pi of 3theta^3cos(theta^2) with respect to theta	$\int_{\sqrt{\frac{π}{2}}}^{\sqrt{π}} 3 θ^{3} \cos (θ^{2}) d θ$
81543	Find the Maximum/Minimum Value	V(w)=(60-4w)w^2	$V (w) = (60 - 4 w) w^{2}$
81544	Find the Antiderivative	(x+1)/(x-1)	$\frac{x + 1}{x - 1}$
81545	Find the Maximum/Minimum Value	y=x^3+x^2-5	$y = x^{3} + x^{2} - 5$
81546	Evaluate Using Summation Formulas	sum from k=1 to n of k	$\sum_{k = 1}^{n} k$
81547	Evaluate the Limit	limit as x approaches 2 of (4-x^2)tan(x)(pix)/4	$lim_{x \to 2} (4 - x^{2}) \tan (x) \frac{π x}{4}$
81548	Evaluate the Integral	integral of (2+tan(theta)^2) with respect to theta	$\int (2 + \tan^{2} (θ)) d θ$
81549	Find dy/dx	-3y^3-5-y^2-x^3=y	$- 3 y^{3} - 5 - y^{2} - x^{3} = y$
81550	Find the Derivative - d/dx	(-sin(-2x))	$(- \sin (- 2 x))$
81551	Find the Derivative - d/dx	y=4 square root of x^5	$y = 4 \sqrt{x^{5}}$
81552	Evaluate the Integral	integral of (2 sixth root of x^4-18) with respect to x	$\int (2 \sqrt[6]{x^{4}} - 18) d x$
81553	Find dy/dx	-y^3=4+x^2	$- y^{3} = 4 + x^{2}$
81554	Find the Derivative Using Chain Rule - d/dx	integral from -2 to 2 of 2x square root of x^2+4dx with respect to x dx	$\int_{- 2}^{2} 2 x \sqrt{x^{2} + 4 d x} d x$ $d x$
81555	Find the Derivative - d/dx	3x^3-4/(x^2)	$3 x^{3} - \frac{4}{x^{2}}$
81556	Evaluate the Limit	limit as x approaches infinity of x^(1/(x^2))	$lim_{x \to \infty} x^{\frac{1}{x^{2}}}$
81557	Find dy/dx	-xy+3-y=2x^3	$- x y + 3 - y = 2 x^{3}$
81558	Evaluate the Integral	integral from 1 to e of ((x^2-1)/x) with respect to x	$\int_{1}^{e} (\frac{x^{2} - 1}{x}) d x$
81559	Evaluate the Limit	limit as x approaches 0 of (tan(x)-sin(x))/(sin(x)^3)	$lim_{x \to 0} \frac{\tan (x) - \sin (x)}{\sin^{3} (x)}$
81560	Find dy/dx	-4-x^2=xy^2+y^3	$- 4 - x^{2} = x y^{2} + y^{3}$
81561	Evaluate the Integral	integral of 1/(25-4x^2) with respect to x	$\int \frac{1}{25 - 4 x^{2}} d x$
81562	Find the Integral	x/( square root of 1+x^2)	$\frac{x}{\sqrt{1 + x^{2}}}$
81563	Find the Antiderivative	f(x)=(x^3+x)/(x^2+1)	$f (x) = \frac{x^{3} + x}{x^{2} + 1}$
81564	Find dy/dx	-y+2x^2-x=-5y^3	$- y + 2 x^{2} - x = - 5 y^{3}$
81565	Find the Derivative - d/dx	(2x)/( square root of 3x-1)	$\frac{2 x}{\sqrt{3 x - 1}}$
81566	Evaluate the Integral	integral of -1/2e^(-2x) with respect to x	$\int - \frac{1}{2} e^{- 2 x} d x$
81567	Evaluate from the Left	limit as x approaches 0 of (x-1)/(x+1)	$lim_{x \to 0} \frac{x - 1}{x + 1}$
81568	Evaluate the Integral	integral from 0 to 1 of x^2e^(-x^3) with respect to x	$\int_{0}^{1} x^{2} e^{- x^{3}} d x$
81569	Evaluate the Integral	integral of (1+x^2)^2*6x with respect to x	$\int {(1 + x^{2})}^{2} \cdot 6 x d x$
81570	Evaluate the Integral	8/pi integral from 0 to infinity of 1/(1+x^2) with respect to x	$\frac{8}{π} \int_{0}^{\infty} \frac{1}{1 + x^{2}} d x$
81571	Find dy/dx	-5=3y^3+x-xy^2	$- 5 = 3 y^{3} + x - x y^{2}$
81572	Evaluate the Integral	integral of 2x^2-6x+4/x-3 with respect to x	$\int 2 x^{2} - 6 x + \frac{4}{x} - 3 d x$
81573	Evaluate the Integral	integral from 1/2 to 3/2 of (-2x+4) with respect to x	$\int_{\frac{1}{2}}^{\frac{3}{2}} (- 2 x + 4) d x$
81574	Find the Derivative - d/dy	natural log of x+ square root of x^2+y^2	$\ln (x + \sqrt{x^{2} + y^{2}})$
81575	Find dy/dx	-2y-5x^3+2x^2-3=-y^3	$- 2 y - 5 x^{3} + 2 x^{2} - 3 = - y^{3}$
81576	Find the Antiderivative	e^x*sin(x)	$e^{x} \cdot \sin (x)$
81577	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of square root of (x+2020)(x+2021)-x	$lim_{x \to \infty} \sqrt{(x + 2020) (x + 2021)} - x$
81578	Find dy/dx	y = square root of 2^x+2e^x	$y = \sqrt{2^{x} + 2 e^{x}}$
81579	Evaluate the Integral	integral of (6x)/( square root of 100-x^4) with respect to x	$\int \frac{6 x}{\sqrt{100 - x^{4}}} d x$
81580	Find dy/dx	3y^3+1+x=x^3y	$3 y^{3} + 1 + x = x^{3} y$
81581	Find the Antiderivative	3x^2*sin(x^3+2003)	$3 x^{2} \cdot \sin (x^{3} + 2003)$
81582	Evaluate the Limit	limit as x approaches -1 of (1/(x+3)+3/(x-5))/(x+1)	$lim_{x \to - 1} \frac{\frac{1}{x + 3} + \frac{3}{x - 5}}{x + 1}$
81583	Evaluate the Integral	integral from 1 to 4 of (3-\|x-3\|) with respect to x	$\int_{1}^{4} (3 - \| x - 3 \|) d x$
81584	Find dx/dy	y=((3x-1)/(x^2+3))^2	$y = {(\frac{3 x - 1}{x^{2} + 3})}^{2}$
81585	Find the Domain and Range	f(x)=3x+1,x<1; 5-x,x>=1	$f (x) = {\begin{cases} 3 x + 1, x < 1 \\ 5 - x, x \geq 1 \end{cases}$
81586	Find dy/dx	y-y^2+x+x^2=-2y^3	$y - y^{2} + x + x^{2} = - 2 y^{3}$
81587	Find dy/dx	y=(e^(2x))/(e^x+1)	$y = \frac{e^{2 x}}{e^{x} + 1}$
81588	Find the Second Derivative	e^(-x)+2xe^(-x)+x^2e^(-x)	$e^{- x} + 2 x e^{- x} + x^{2} e^{- x}$
81589	Evaluate the Limit	limit as x approaches -5 from the right of ((x+5)^2)/(x^2+5x)	$lim_{x \to {(- 5)}^{+}} \frac{{(x + 5)}^{2}}{x^{2} + 5 x}$
81590	Evaluate the Integral	integral of (sin(x)^2)(cos(x)^2) with respect to x	$\int (\sin^{2} (x)) (\cos^{2} (x)) d x$
81591	Find the Center and Radius	9x^2+9y^2-25	$9 x^{2} + 9 y^{2} - 25$
81592	Evaluate the Integral	integral of (2x^3-4x+3x) with respect to x	$\int (2 x^{3} - 4 x + 3 x) d x$
81593	Find dy/dx	-xy+3=y	$- x y + 3 = y$
81594	Find dy/dx	-3y-x=4y^3+2y^2+3x^3	$- 3 y - x = 4 y^{3} + 2 y^{2} + 3 x^{3}$
81595	Find the Antiderivative	f(x)=sin(3x+pi/6)	$f (x) = \sin (3 x + \frac{π}{6})$
81596	Find dy/dx	-x^3y-2y^2+4x=0	$- x^{3} y - 2 y^{2} + 4 x = 0$
81597	Find the Antiderivative	natural log of 2	$\ln (2)$
81598	Evaluate the Limit	limit as x approaches 2 from the left of (2+\|x\|)/(2+x)	$lim_{x \to 2^{-}} \frac{2 + \| x \|}{2 + x}$
81599	Evaluate the Integral	integral of x^2(x-2)^(3/2) with respect to x	$\int x^{2} {(x - 2)}^{\frac{3}{2}} d x$
81600	Find Where Increasing/Decreasing	f(x)=2* log base 1/4 of x	$f (x) = 2 \cdot \log_{\frac{1}{4}} (x)$