Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
70401	Evaluate the Limit	limit as x approaches 0 of sin(1/(x^2))	$lim_{x \to 0} \sin (\frac{1}{x^{2}})$
70402	Evaluate the Limit	limit as x approaches a of (x-a)/( square root of x- square root of a)	$lim_{x \to a} \frac{x - a}{\sqrt{x} - \sqrt{a}}$
70403	Evaluate the Limit	limit as x approaches 0 of x^3(x^4+2x^3)^-1	$lim_{x \to 0} x^{3} {(x^{4} + 2 x^{3})}^{- 1}$
70404	Find the Derivative - d/dx	1/(sec(x)^2)	$\frac{1}{\sec^{2} (x)}$
70405	Find dy/dx	y=xe^y	$y = x e^{y}$
70406	Find the Derivative - d/dx	((x^2+1)^(3/2))/x	$\frac{{(x^{2} + 1)}^{\frac{3}{2}}}{x}$
70407	Find the Derivative - d/dx	y=(1+1/x)^3	$y = {(1 + \frac{1}{x})}^{3}$
70408	Find dy/dx	x^2+y^2-2x=1	$x^{2} + y^{2} - 2 x = 1$
70409	Find dy/dx	3(x^2+y^2)^2=25(x^2-y^2)	$3 {(x^{2} + y^{2})}^{2} = 25 (x^{2} - y^{2})$
70410	Find the Derivative - d/dx	y=(x^2+x-2)/(x^3+6)	$y = \frac{x^{2} + x - 2}{x^{3} + 6}$
70411	Find the Maximum/Minimum Value	F(x)=8x^3-5x^2-3x	$F (x) = 8 x^{3} - 5 x^{2} - 3 x$
70412	Find the Derivative - d/dx	1/3e^(3x)	$\frac{1}{3} e^{3 x}$
70413	Determine if Continuous	f(x)=(-x^2+1)/(x^2+1)	$f (x) = \frac{- x^{2} + 1}{x^{2} + 1}$
70414	Find dy/dx	y=x^2-5x	$y = x^{2} - 5 x$
70415	Find the Fourth Derivative	f(x)=x^4-4x^3+x^5	$f (x) = x^{4} - 4 x^{3} + x^{5}$
70416	Find the Tangent Line at (2,-16)	f(x)=-2x^3 at (2,-16)	$f (x) = - 2 x^{3}$ at $(2, - 16)$
70417	Integrate Using Partial Fractions	integral from 0 to 1 of (x-4)/(x^2-5x+6) with respect to x	$\int_{0}^{1} \frac{x - 4}{x^{2} - 5 x + 6} d x$
70418	Find the Derivative - d/dx	x/(\|x\|)	$\frac{x}{\| x \|}$
70419	Evaluate the Integral	integral of (3+ square root of x+x)/x with respect to x	$\int \frac{3 + \sqrt{x} + x}{x} d x$
70420	Find dy/dx	5x^3+xy^2=5x^3y^3	$5 x^{3} + x y^{2} = 5 x^{3} y^{3}$
70421	Find the Center and Radius	16+x^2+y^2-8x-6y=0	$16 + x^{2} + y^{2} - 8 x - 6 y = 0$
70422	Find the Second Derivative	f(x)=x^2+e^x-cos(x)	$f (x) = x^{2} + e^{x} - \cos (x)$
70423	Evaluate the Integral	integral from 0 to 4 of (1+3x-x^2) with respect to x	$\int_{0}^{4} (1 + 3 x - x^{2}) d x$
70424	Evaluate Using L'Hospital's Rule	limit as x approaches 0 from the right of x^(1/x)	$lim_{x \to 0^{+}} x^{\frac{1}{x}}$
70425	Find the Derivative - d/dx	-(4x)/(3y)	$- \frac{4 x}{3 y}$
70426	Find the Center and Radius	(x+2)^2-(y-6)^2=45	${(x + 2)}^{2} - {(y - 6)}^{2} = 45$
70427	Find dy/dx	y=(x^2+8x+3)/( square root of x)	$y = \frac{x^{2} + 8 x + 3}{\sqrt{x}}$
70428	Evaluate the Integral	integral of (b+4)(2b^2+4) with respect to b	$\int (b + 4) (2 b^{2} + 4) d b$
70429	Find the Maximum/Minimum Value	f(x)=5/4sin(x)+1	$f (x) = \frac{5}{4} \sin (x) + 1$
70430	Find the Derivative - d/dx	3sin(x)+8e^x	$3 \sin (x) + 8 e^{x}$
70431	Find the Tangent Line at (-1,-1)	f(x)=x^3 at (-1,-1)	$f (x) = x^{3}$ at $(- 1, - 1)$
70432	Evaluate the Integral	integral of (x^3)/( cube root of x^4-81) with respect to x	$\int \frac{x^{3}}{\sqrt[3]{x^{4} - 81}} d x$
70433	Find Where Increasing/Decreasing	f(x)=2(2)^x-5	$f (x) = 2 {(2)}^{x} - 5$
70434	Find the Maximum/Minimum Value	f(x)=(x^3)/3-x^2-3x+1	$f (x) = \frac{x^{3}}{3} - x^{2} - 3 x + 1$
70435	Find dy/dx	y=x^(x^x)	$y = x^{x^{x}}$
70436	Find the Tangent Line at (-2,8)	f(x)=-x^3 at (-2,8)	$f (x) = - x^{3}$ at $(- 2, 8)$
70437	Find the Tangent Line at (0,2)	y=x^4+2e^x , (0,2)	$y = x^{4} + 2 e^{x}$ , $(0, 2)$
70438	Integrate By Parts	integral of natural log of (x)^2 with respect to x	$\int \ln ({(x)}^{2}) d x$
70439	Find the Tangent Line at (2,-8)	f(x)=-x^3 at (2,-8)	$f (x) = - x^{3}$ at $(2, - 8)$
70440	Find the Derivative - d/dx	3cot(x)^2	$3 \cot^{2} (x)$
70441	Find the Tangent Line at x=5	f(x) = square root of x^2+39 , x=5	$f (x) = \sqrt{x^{2} + 39}$ , $x = 5$
70442	Evaluate Using L'Hospital's Rule	limit as x approaches 1 from the right of x^(1/(1-x))	$lim_{x \to 1^{+}} x^{\frac{1}{1 - x}}$
70443	Evaluate the Limit	limit as x approaches infinity of x(e^(1/x)-1)	$lim_{x \to \infty} x (e^{\frac{1}{x}} - 1)$
70444	Find the Derivative - d/dx	4x^6-3x^4+2x^3+e^2	$4 x^{6} - 3 x^{4} + 2 x^{3} + e^{2}$
70445	Integrate Using Trig Substitution	integral of sin(x)^3 with respect to x	$\int \sin^{3} (x) d x$
70446	Find the Derivative - d/dx	d/(dx)(3x)	$\frac{d}{d x} (3 x)$
70447	Find the Derivative - d/dx	y=9/((3x^2+8)^2)	$y = \frac{9}{{(3 x^{2} + 8)}^{2}}$
70448	Find the Derivative - d/dx	(2x+3)	$(2 x + 3)$
70449	Find the Derivative - d/dx	1/( cube root of x^2-1)	$\frac{1}{\sqrt[3]{x^{2} - 1}}$
70450	Solve the Differential Equation	(dy)/(dx)=(y^3)/(x^2)	$\frac{d y}{d x} = \frac{y^{3}}{x^{2}}$
70451	Find dy/dx	2x^3y+3xy^3=5	$2 x^{3} y + 3 x y^{3} = 5$
70452	Evaluate the Limit	limit as x approaches 0 of (cos(x)-cos(5x))/(xtan(2x))	$lim_{x \to 0} \frac{\cos (x) - \cos (5 x)}{x \tan (2 x)}$
70453	Evaluate the Integral	integral from 1 to infinity of (e^(-1/x))/(x^2) with respect to x	$\int_{1}^{\infty} \frac{e^{- \frac{1}{x}}}{x^{2}} d x$
70454	Find the Derivative - d/dx	log base x of 2	$\log_{x} (2)$
70455	Evaluate the Derivative at a=1/9	f(x)=4/( square root of x) , a=1/9	$f (x) = \frac{4}{\sqrt{x}}$ , $a = \frac{1}{9}$
70456	Evaluate the Limit	limit as x approaches 0 of (sin(7x)+tan(3x)-sin(5x))/(tan(9x)-tan(3x)-sin(x))	$lim_{x \to 0} \frac{\sin (7 x) + \tan (3 x) - \sin (5 x)}{\tan (9 x) - \tan (3 x) - \sin (x)}$
70457	Evaluate the Limit	limit as x approaches 3 of (5x^2-16x+3)/(x^2-6x+9)	$lim_{x \to 3} \frac{5 x^{2} - 16 x + 3}{x^{2} - 6 x + 9}$
70458	Find dy/dx	x^2-xy^2=2	$x^{2} - x y^{2} = 2$
70459	Find Where Increasing/Decreasing	y=-\|x-2\|	$y = - \| x - 2 \|$
70460	Find the Integral	(dx)/( square root of x)	$\frac{d x}{\sqrt{x}}$
70461	Find dy/dx	e^ysin(x)=x+xy	$e^{y} \sin (x) = x + x y$
70462	Find the Derivative - d/dx	x^2+e^x	$x^{2} + e^{x}$
70463	Find the Area Under the Curve	y=4/( square root of x)	$y = \frac{4}{\sqrt{x}}$
70464	Find dy/dx	xy=3	$x y = 3$
70465	Find the Derivative - d/dx	-3cot(x)-sec(x)	$- 3 \cot (x) - \sec (x)$
70466	Find the Derivative - d/dx	5x^2+4sin(x)	$5 x^{2} + 4 \sin (x)$
70467	Evaluate the Limit	limit as x approaches negative infinity of (x^2+x-2)/(x^2+4x+3)	$lim_{x \to - \infty} \frac{x^{2} + x - 2}{x^{2} + 4 x + 3}$
70468	Find the Derivative - d/dx	5^( square root of x)	$5^{\sqrt{x}}$
70469	Find the Derivative - d/dx	y=4^(x^2)	$y = 4^{x^{2}}$
70470	Find the Tangent Line at (9,0)	y = natural log of x^2-9x+1 , (9,0)	$y = \ln (x^{2} - 9 x + 1)$ , $(9, 0)$
70471	Evaluate the Limit	limit as x approaches 2 of (x^2+2x-8)/( square root of x^2+5-(x+1))	$lim_{x \to 2} \frac{x^{2} + 2 x - 8}{\sqrt{x^{2} + 5} - (x + 1)}$
70472	Evaluate the Limit	limit as h approaches 0 of (cos(pi/2+h)-cos(pi/2))/h	$lim_{h \to 0} \frac{\cos (\frac{π}{2} + h) - \cos (\frac{π}{2})}{h}$
70473	Find the Slope	f(x)=-2/3x+4	$f (x) = - \frac{2}{3} x + 4$
70474	Evaluate the Limit	limit as x approaches infinity of ((x-2)(3x^2+3))/((6x+4)^3)	$lim_{x \to \infty} \frac{(x - 2) (3 x^{2} + 3)}{{(6 x + 4)}^{3}}$
70475	Find dy/dx	x^2y=1+y^2x	$x^{2} y = 1 + y^{2} x$
70476	Find the Derivative - d/dx	y=(3x^3+1)(-4x^2-3)^4	$y = (3 x^{3} + 1) {(- 4 x^{2} - 3)}^{4}$
70477	Find Where Increasing/Decreasing	x^(1/3)(x+4)	$x^{\frac{1}{3}} (x + 4)$
70478	Find the Derivative - d/dx	arcsec(x^2)	$arcsec (x^{2})$
70479	Evaluate the Limit	limit as x approaches infinity of (x+3x^2)/(4x-1)	$lim_{x \to \infty} \frac{x + 3 x^{2}}{4 x - 1}$
70480	Find the Second Derivative	x square root of 9-x	$x \sqrt{9 - x}$
70481	Find the Derivative - d/dx	y=(x^2+17)(x^3-3x+1)	$y = (x^{2} + 17) (x^{3} - 3 x + 1)$
70482	Find the Derivative - d/dx	y = square root of (1-cx)/(1+cx)	$y = \sqrt{\frac{1 - c x}{1 + c x}}$
70483	Find the Second Derivative	e^(rx)	$e^{r x}$
70484	Find the Derivative - d/dx	cube root of 8	$\sqrt[3]{8}$
70485	Evaluate the Integral	integral from 1 to 4 of (2x-3 square root of x) with respect to x	$\int_{1}^{4} (2 x - 3 \sqrt{x}) d x$
70486	Evaluate the Integral	integral of x^2arctan(x) with respect to x	$\int x^{2} \arctan (x) d x$
70487	Find dy/dx	y=3x+2	$y = 3 x + 2$
70488	Find the Maximum/Minimum Value	f(x)=x^5 natural log of x	$f (x) = x^{5} \ln (x)$
70489	Find the Derivative - d/dx	3 cube root of x^2	$3 \sqrt[3]{x^{2}}$
70490	Find dy/dx	x^3-y^5+3x^2-6y=1	$x^{3} - y^{5} + 3 x^{2} - 6 y = 1$
70491	Integrate Using u-Substitution	integral of x^2 natural log of x with respect to x	$\int x^{2} \ln (x) d x$
70492	Find the Derivative - d/dx	y = square root of square root of 4x+3	$y = \sqrt{\sqrt{4 x + 3}}$
70493	Find dx/dy	y=ax^2+bx+c	$y = a x^{2} + b x + c$
70494	Find dy/dx	x^3+2xy-y^2=11	$x^{3} + 2 x y - y^{2} = 11$
70495	Evaluate the Limit	limit as x approaches pi/2 of cot(x)	$lim_{x \to \frac{π}{2}} \cot (x)$
70496	Find Where Increasing/Decreasing	y=(x^3)/16-3x	$y = \frac{x^{3}}{16} - 3 x$
70497	Find dy/dx	x^2y+y^2x=0	$x^{2} y + y^{2} x = 0$
70498	Integrate Using u-Substitution	integral of xsin(x^2) with respect to x	$\int x \sin (x^{2}) d x$
70499	Find the Derivative - d/dx	1/((x^2-3x)^2)	$\frac{1}{{(x^{2} - 3 x)}^{2}}$
70500	Integrate By Parts	integral of natural log of x+1 with respect to x	$\int \ln (x + 1) d x$