Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
67401	Find the Antiderivative	x^n	$x^{n}$
67402	Find the Slope	f(x)=2x-5	$f (x) = 2 x - 5$
67403	Find dy/dt	y=tan( square root of 3t)	$y = \tan (\sqrt{3 t})$
67404	Find dx/dy	y=1/x	$y = \frac{1}{x}$
67405	Find dy/dx	x^2+xy-y^2=1	$x^{2} + x y - y^{2} = 1$
67406	Find the Derivative - d/dx	(2x)/(x^2+y^2)	$\frac{2 x}{x^{2} + y^{2}}$
67407	Find dy/dx	y = square root of 1-x^2	$y = \sqrt{1 - x^{2}}$
67408	Find the Domain and Range	f(x)=5x-2 if x<1; x-7 if x>=1	$f (x) = {\begin{cases} 5 x - 2 & x < 1 \\ x - 7 & x \geq 1 \end{cases}$
67409	Evaluate the Integral	integral from 1 to 4 of (4x+ square root of x) with respect to x	$\int_{1}^{4} (4 x + \sqrt{x}) d x$
67410	Find Where Increasing/Decreasing	f(x)=(8-x)(x+1)^2	$f (x) = (8 - x) {(x + 1)}^{2}$
67411	Evaluate the Limit	limit as x approaches infinity of (x^2-4)/(2+x-4x^2)	$lim_{x \to \infty} \frac{x^{2} - 4}{2 + x - 4 x^{2}}$
67412	Evaluate the Integral	integral from 2 to 5 of (4-2x) with respect to x	$\int_{2}^{5} (4 - 2 x) d x$
67413	Find the Derivative - d/dx	( square root of x)/(e^x)	$\frac{\sqrt{x}}{e^{x}}$
67414	Find the Linearization at a=π/3	f(x)=sin(x) , a=pi/3	$f (x) = \sin (x)$ , $a = \frac{π}{3}$
67415	Find the Derivative - d/dx	y=e^xcos(x)+sin(x)	$y = e^{x} \cos (x) + \sin (x)$
67416	Find dy/dx	y = cube root of 1+4x	$y = \sqrt[3]{1 + 4 x}$
67417	Find dy/dx	y=arcsin(2x+1)	$y = \arcsin (2 x + 1)$
67418	Find dy/dx	(y-3)^2=4(x-5)	${(y - 3)}^{2} = 4 (x - 5)$
67419	Find dy/dx	x^3+2y^2-xy=2	$x^{3} + 2 y^{2} - x y = 2$
67420	Evaluate the Limit	limit as x approaches negative infinity of ( square root of 4x^2-3x)/(4x+5)	$lim_{x \to - \infty} \frac{\sqrt{4 x^{2} - 3 x}}{4 x + 5}$
67421	Solve the Differential Equation	(dy)/(dx)=5y	$\frac{d y}{d x} = 5 y$
67422	Evaluate the Limit	limit as h approaches 0 of (2h^3-5h^2+h)/(h^4-h^2)	$lim_{h \to 0} \frac{2 h^{3} - 5 h^{2} + h}{h^{4} - h^{2}}$
67423	Find dy/dx	y=x^(cos(x))	$y = x^{\cos (x)}$
67424	Determine if Continuous	f(x)=(x^2-4)/(x-2) if x<2; ax^2-bx+3 if 2<=x<3; 2x-a+b if x>=3	$f (x) = {\begin{cases} \frac{x^{2} - 4}{x - 2} & x < 2 \\ a x^{2} - b x + 3 & 2 \leq x < 3 \\ 2 x - a + b & x \geq 3 \end{cases}$
67425	Integrate By Parts	integral of x^2e^(-x) with respect to x	$\int x^{2} e^{- x} d x$
67426	Find dy/dx	y=x^7	$y = x^{7}$
67427	Evaluate the Integral	integral from 0 to 1 of 1/(x^2-2x+2) with respect to x	$\int_{0}^{1} \frac{1}{x^{2} - 2 x + 2} d x$
67428	Find the Derivative - d/dx	d/(dx)*2x	$\frac{d}{d x} \cdot 2 x$
67429	Find the Maximum/Minimum Value	P(x)=-2(x-3)(x-11)	$P (x) = - 2 (x - 3) (x - 11)$
67430	Evaluate the Limit	limit as x approaches 0 from the left of 1/x-1/(\|x\|)	$lim_{x \to 0^{-}} \frac{1}{x} - \frac{1}{\| x \|}$
67431	Evaluate the Limit	limit as t approaches 2 of ( square root of (t+4)(t-2)^4)/((3t-6)^2)	$lim_{t \to 2} \frac{\sqrt{(t + 4) {(t - 2)}^{4}}}{{(3 t - 6)}^{2}}$
67432	Find dy/dx	y=( natural log of x)/x	$y = \frac{\ln (x)}{x}$
67433	Evaluate the Integral	integral from 0 to 1 of (5x-1)^2*5 with respect to x	$\int_{0}^{1} {(5 x - 1)}^{2} \cdot 5 d x$
67434	Evaluate the Limit	limit as x approaches infinity of (-4x^3+5x)/(2x^3+7)	$lim_{x \to \infty} \frac{- 4 x^{3} + 5 x}{2 x^{3} + 7}$
67435	Find the Derivative - d/dx	1/(x+y)	$\frac{1}{x + y}$
67436	Find dy/dx	y = square root of x^2+4	$y = \sqrt{x^{2} + 4}$
67437	Find dy/dx	x^(2/3)+y^(2/3)=1	$x^{\frac{2}{3}} + y^{\frac{2}{3}} = 1$
67438	Integrate By Parts	integral of x^2e^(-2x) with respect to x	$\int x^{2} e^{- 2 x} d x$
67439	Find the Domain and Range	f(x)=-2x+3 if x<1; 3x-2 if x>=1	$f (x) = {\begin{cases} - 2 x + 3 & x < 1 \\ 3 x - 2 & x \geq 1 \end{cases}$
67440	Find dy/dx	(x^2+4)y=8	$(x^{2} + 4) y = 8$
67441	Evaluate the Limit	limit as x approaches 3 of ( square root of x+6-x)/(x-3)	$lim_{x \to 3} \frac{\sqrt{x + 6} - x}{x - 3}$
67442	Integrate Using u-Substitution	integral of tan(x) with respect to x	$\int \tan (x) d x$
67443	Find the Arc Length	x=(y^4)/8+1/(4y^2) , 1<=y<=2	$x = \frac{y^{4}}{8} + \frac{1}{4 y^{2}}$ , $1 \leq y \leq 2$
67444	Evaluate the Integral	integral of xy with respect to x	$\int x y d x$
67445	Find dy/dx	x^4+x^2y^2+y^3=5	$x^{4} + x^{2} y^{2} + y^{3} = 5$
67446	Find dy/dx	y = square root of 2x+1	$y = \sqrt{2 x + 1}$
67447	Find dy/dx	y = square root of x^2+9	$y = \sqrt{x^{2} + 9}$
67448	Find dy/dx	x=cot(y)	$x = \cot (y)$
67449	Solve the Differential Equation	(dy)/(dx)=-x/y	$\frac{d y}{d x} = - \frac{x}{y}$
67450	Evaluate the Integral	integral from 1 to 4 of (2+x^2)/( square root of x) with respect to x	$\int_{1}^{4} \frac{2 + x^{2}}{\sqrt{x}} d x$
67451	Evaluate the Limit	limit as x approaches infinity of (2x(2x+1)^3(x^5-1))/(x^8(5x-1))	$lim_{x \to \infty} \frac{2 x {(2 x + 1)}^{3} (x^{5} - 1)}{x^{8} (5 x - 1)}$
67452	Find dy/dx	square root of x+ square root of y=9	$\sqrt{x} + \sqrt{y} = 9$
67453	Find the Constant Using Slope	3y=2kx-3 , m=-2	$3 y = 2 k x - 3$ , $m = - 2$
67454	Use Logarithmic Differentiation to Find the Derivative	y=( square root of x)^(7x)	$y = {(\sqrt{x})}^{7 x}$
67455	Find the Derivative - d/dx	d/(dx)(-4e^x-sin(x)-9)	$\frac{d}{d x} (- 4 e^{x} - \sin (x) - 9)$
67456	Find dy/dx	y^4=y^2-x^2	$y^{4} = y^{2} - x^{2}$
67457	Evaluate the Integral	integral from negative infinity to 0 of xe^x with respect to x	$\int_{- \infty}^{0} x e^{x} d x$
67458	Determine if Continuous	f(x)=x-3 if x<=2; -5x+4 if x>2	$f (x) = {\begin{cases} x - 3 & x \leq 2 \\ - 5 x + 4 & x > 2 \end{cases}$
67459	Evaluate the Limit	limit as x approaches 0 of (csc(7x))/(csc(3x))	$lim_{x \to 0} \frac{\csc (7 x)}{\csc (3 x)}$
67460	Evaluate the Integral	integral of (7/( square root of x)+7 square root of x) with respect to x	$\int (\frac{7}{\sqrt{x}} + 7 \sqrt{x}) d x$
67461	Evaluate the Limit	limit as x approaches negative infinity of xe^x	$lim_{x \to - \infty} x e^{x}$
67462	Find the Derivative - d/dx	y=2/3(x^2+1)^(3/2)	$y = \frac{2}{3} {(x^{2} + 1)}^{\frac{3}{2}}$
67463	Find the Antiderivative	xdx	$x d x$
67464	Evaluate the Limit	limit as x approaches 5 from the right of (x-5)/(x^2-25)	$lim_{x \to 5^{+}} \frac{x - 5}{x^{2} - 25}$
67465	Evaluate the Limit	limit as x approaches 0 of (cos(5x))/(8xcot(2x))	$lim_{x \to 0} \frac{\cos (5 x)}{8 x \cot (2 x)}$
67466	Find the Derivative - d/dx	square root of 1+e^x	$\sqrt{1 + e^{x}}$
67467	Find the Derivative - d/dx	e^xcos(y)	$e^{x} \cos (y)$
67468	Find the Maximum/Minimum Value	f(x)=(x^2)/(x-1)	$f (x) = \frac{x^{2}}{x - 1}$
67469	Find the Domain and Range	f(x)=-x+3 if x<1; 3x-1 if x>=1	$f (x) = {\begin{cases} - x + 3 & x < 1 \\ 3 x - 1 & x \geq 1 \end{cases}$
67470	Find the Derivative - d/dx	square root of 1+x^3	$\sqrt{1 + x^{3}}$
67471	Find dy/dx	y=3e^x	$y = 3 e^{x}$
67472	Integrate By Parts	integral of x square root of x+1 with respect to x	$\int x \sqrt{x + 1} d x$
67473	Evaluate the Limit	limit as x approaches infinity of ( square root of 16x^4-3)/(2x^2+3)	$lim_{x \to \infty} \frac{\sqrt{16 x^{4} - 3}}{2 x^{2} + 3}$
67474	Integrate Using u-Substitution	integral of xe^(x^2) with respect to x	$\int x e^{x^{2}} d x$
67475	Evaluate Using L'Hospital's Rule	limit as x approaches pi/(()/())*2 from the right of (cos(x))/(1-sin(x))	$lim_{x \to {(\frac{π}{\frac{}{}} \cdot 2)}^{+}} \frac{\cos (x)}{1 - \sin (x)}$
67476	Evaluate the Integral	integral from 0 to 13 of 1/( cube root of (1+2x)^2) with respect to x	$\int_{0}^{13} \frac{1}{\sqrt[3]{{(1 + 2 x)}^{2}}} d x$
67477	Find the Derivative - d/dx	d/(dx)( natural log of (2x+1)/(2x-1))	$\frac{d}{d x} (\ln (\frac{2 x + 1}{2 x - 1}))$
67478	Find the Derivative - d/dx	cos(-x)	$\cos (- x)$
67479	Evaluate the Integral	integral from 0 to infinity of 1/( fourth root of 1+x) with respect to x	$\int_{0}^{\infty} \frac{1}{\sqrt[4]{1 + x}} d x$
67480	Find the Derivative - d/dx	e^x-sin(x)-1	$e^{x} - \sin (x) - 1$
67481	Find dy/dx	y = natural log of 3x+4y	$y = \ln (3 x + 4 y)$
67482	Find the Derivative - d/dx	f(0)	$f (0)$
67483	Evaluate the Integral	e^( integral of 1/x with respect to x)	$e^{\int \frac{1}{x} d x}$
67484	Integrate Using Trig Substitution	integral of square root of 4-x^2 with respect to x	$\int \sqrt{4 - x^{2}} d x$
67485	Find dy/dx	y=e^xsin(x)	$y = e^{x} \sin (x)$
67486	Use Logarithmic Differentiation to Find the Derivative	y=( square root of x)^(9x)	$y = {(\sqrt{x})}^{9 x}$
67487	Find the Tangent Line at (9,3)	y = square root of x , (9,3)	$y = \sqrt{x}$ , $(9, 3)$
67488	Integrate Using u-Substitution	integral of x^2e^(x^3) with respect to x	$\int x^{2} e^{x^{3}} d x$
67489	Solve the Differential Equation	(dy)/(dx)=(x-2)^2	$\frac{d y}{d x} = {(x - 2)}^{2}$
67490	Evaluate the Limit	limit as x approaches infinity of ( square root of 9x^6+4x^2)/(x^3-1)	$lim_{x \to \infty} \frac{\sqrt{9 x^{6} + 4 x^{2}}}{x^{3} - 1}$
67491	Find the Derivative - d/dx	1/(x square root of x)	$\frac{1}{x \sqrt{x}}$
67492	Find dy/dx	x^2+xy+y^3=1	$x^{2} + x y + y^{3} = 1$
67493	Evaluate the Integral	integral from 15 to 35 of (x^2x) with respect to x	$\int_{15}^{35} (x^{2} x) d x$
67494	Find the Integral	1dx	$1 d x$
67495	Find Where Increasing/Decreasing	f(x)=(5-x)(x+1)^2	$f (x) = (5 - x) {(x + 1)}^{2}$
67496	Find the Domain and Range	f(x)=4+2x if x<0; x^2 if x>=0	$f (x) = {\begin{cases} 4 + 2 x & x < 0 \\ x^{2} & x \geq 0 \end{cases}$
67497	Find the Derivative - d/dx	2x square root of x^2+7	$2 x \sqrt{x^{2} + 7}$
67498	Find dy/dx	x^2y^2=100	$x^{2} y^{2} = 100$
67499	Evaluate the Integral	integral of (x^2-x)/(1+3x^2-2x^3) with respect to x	$\int \frac{x^{2} - x}{1 + 3 x^{2} - 2 x^{3}} d x$
67500	Integrate Using u-Substitution	integral of x^3(x^4+3)^2 with respect to x	$\int x^{3} {(x^{4} + 3)}^{2} d x$