Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
70101	Find the Domain and Range	f(x)=\|2x\| if -2<=x<0; x^3 if x>=0	$f (x) = {\begin{cases} \| 2 x \| & - 2 \leq x < 0 \\ x^{3} & x \geq 0 \end{cases}$
70102	Find the Tangent Line at (1,0)	(x^2-1)/(x^2+x+1) , (1,0)	$\frac{x^{2} - 1}{x^{2} + x + 1}$ , $(1, 0)$
70103	Find dy/dx	y=-x^2+3	$y = - x^{2} + 3$
70104	Find the Tangent Line at (0,8)	y=8e^x+x , (0,8)	$y = 8 e^{x} + x$ , $(0, 8)$
70105	Find the Derivative - d/dx	e^x(x+x square root of x)	$e^{x} (x + x \sqrt{x})$
70106	Evaluate the Integral	integral of (5x^2+1)(5x^3+3x-8)^6 with respect to x	$\int (5 x^{2} + 1) {(5 x^{3} + 3 x - 8)}^{6} d x$
70107	Evaluate the Limit	limit as t approaches 0 of (1-cos(t))/t	$lim_{t \to 0} \frac{1 - \cos (t)}{t}$
70108	Evaluate the Integral	integral from 1 to infinity of xe^(-x^2) with respect to x	$\int_{1}^{\infty} x e^{- x^{2}} d x$
70109	Use Logarithmic Differentiation to Find the Derivative	y = natural log of e^(-x)+xe^(-x)	$y = \ln (e^{- x} + x e^{- x})$
70110	Find the Second Derivative	(d^2y)/(dx^2)	$\frac{d^{2} y}{d x^{2}}$
70111	Find dy/dx	xy+e^y=e	$x y + e^{y} = e$
70112	Find the Relative Extrema	f(x)=x^3-27x	$f (x) = x^{3} - 27 x$
70113	Evaluate the Integral	integral of (sin(u)+u) with respect to u	$\int (\sin (u) + u) d u$
70114	Find the Antiderivative	1/((1-x)^2)	$\frac{1}{{(1 - x)}^{2}}$
70115	Use Logarithmic Differentiation to Find the Derivative	y=( natural log of x)^( natural log of x)	$y = {(\ln (x))}^{\ln (x)}$
70116	Find Where Increasing/Decreasing	f(x)=1/2x^4-4x^2+3	$f (x) = \frac{1}{2} x^{4} - 4 x^{2} + 3$
70117	Integrate Using Partial Fractions	integral of (x^2+12x+12)/(x^3-4x) with respect to x	$\int \frac{x^{2} + 12 x + 12}{x^{3} - 4 x} d x$
70118	Find the Derivative - d/dx	y=(3-2x)/(3+2x)	$y = \frac{3 - 2 x}{3 + 2 x}$
70119	Evaluate the Limit	limit as x approaches -2 of (x^4+5x^3+6x^2)/(x^2(x+1)-4(x+1))	$lim_{x \to - 2} \frac{x^{4} + 5 x^{3} + 6 x^{2}}{x^{2} (x + 1) - 4 (x + 1)}$
70120	Find dy/dx	x=e^y	$x = e^{y}$
70121	Evaluate the Integral	integral of (tan(x)+sec(x)^2) with respect to x	$\int (\tan (x) + \sec^{2} (x)) d x$
70122	Evaluate the Limit	limit as n approaches infinity of (n/(n+1))^n	$lim_{n \to \infty} {(\frac{n}{n + 1})}^{n}$
70123	Find the Upper and Lower Bounds	f(x)=4x^4-25x^2-5x-13	$f (x) = 4 x^{4} - 25 x^{2} - 5 x - 13$
70124	Evaluate the Limit	limit as x approaches infinity of (x^2+4x-12)/(x^2-4)	$lim_{x \to \infty} \frac{x^{2} + 4 x - 12}{x^{2} - 4}$
70125	Solve the Differential Equation	(2dy)/(3dx)=(x-2)^2	$\frac{2 d y}{3 d x} = {(x - 2)}^{2}$
70126	Find the Linearization at a=1	f(x)=x+1/x , a=1	$f (x) = x + \frac{1}{x}$ , $a = 1$
70127	Evaluate the Integral	integral of 10w square root of w with respect to w	$\int 10 w \sqrt{w} d w$
70128	Evaluate the Limit	limit as x approaches negative infinity of ( square root of x^2+1)/(x+1)	$lim_{x \to - \infty} \frac{\sqrt{x^{2} + 1}}{x + 1}$
70129	Find Where Increasing/Decreasing	f(x)=-\|2x-5\|+6	$f (x) = - \| 2 x - 5 \| + 6$
70130	Find the Derivative - d/dx	pi-x	$π - x$
70131	Find Where Increasing/Decreasing	f(x)=-1/(x-4)+3	$f (x) = \frac{- 1}{x - 4} + 3$
70132	Find dy/dx	y^5+x^2y^3=1+x^4y	$y^{5} + x^{2} y^{3} = 1 + x^{4} y$
70133	Evaluate the Integral	integral of (-4/( square root of 3-3x^2)) with respect to x	$\int (- \frac{4}{\sqrt{3 - 3 x^{2}}}) d x$
70134	Evaluate the Integral	integral from negative infinity to 0 of e^(2x) with respect to x	$\int_{- \infty}^{0} e^{2 x} d x$
70135	Find the Derivative - d/dx	x^2(e^x-1)	$x^{2} (e^{x} - 1)$
70136	Evaluate the Integral	integral of 1/(x natural log of x natural log of natural log of x) with respect to x	$\int \frac{1}{x \ln (x) \ln (\ln (x))} d x$
70137	Find the Derivative - d/dx	y=ax^4	$y = a x^{4}$
70138	Find dy/dx	x+y=e^(2x+2y)	$x + y = e^{2 x + 2 y}$
70139	Evaluate the Integral	integral of (x-1)^2x with respect to x	$\int {(x - 1)}^{2} x d x$
70140	Verify the Differential Equation Solution	y''''+2y=0 , y=3e^(-2x)	$y'' + 2 y = 0$ , $y = 3 e^{- 2 x}$
70141	Evaluate the Limit	limit as x approaches infinity of (x^2+5x+6)/(x+1)	$lim_{x \to \infty} \frac{x^{2} + 5 x + 6}{x + 1}$
70142	Evaluate the Limit	limit as theta approaches pi/2 of (cos(theta)^2)/(1-sin(theta))	$lim_{θ \to \frac{π}{2}} \frac{\cos^{2} (θ)}{1 - \sin (θ)}$
70143	Find the Derivative - d/dx	x( square root of x)	$x (\sqrt{x})$
70144	Find the Second Derivative	f(x)=(x^3)/3	$f (x) = \frac{x^{3}}{3}$
70145	Find the Derivative - d/dx	(sin(x)+cos(x))/(sin(x)-cos(x))	$\frac{\sin (x) + \cos (x)}{\sin (x) - \cos (x)}$
70146	Find the Derivative - d/dx	d/(dx)(-2x^4+3x^3-x^2)	$\frac{d}{d x} (- 2 x^{4} + 3 x^{3} - x^{2})$
70147	Find the Center and Radius	x^2+y^2-4x+2y=b	$x^{2} + y^{2} - 4 x + 2 y = b$
70148	Find the Derivative - d/dx	sin(x)^2+sin(x)	$\sin^{2} (x) + \sin (x)$
70149	Find the Derivative - d/dx	y=ax	$y = a x$
70150	Evaluate the Limit	limit as h approaches 0 of 1/h(1/(x+h)-1/x)	$lim_{h \to 0} \frac{1}{h} (\frac{1}{x + h} - \frac{1}{x})$
70151	Evaluate the Limit	limit as x approaches negative infinity of (x^2+4x-12)/(x^2-4)	$lim_{x \to - \infty} \frac{x^{2} + 4 x - 12}{x^{2} - 4}$
70152	Evaluate the Limit	limit as x approaches infinity of x/(2x+1)	$lim_{x \to \infty} \frac{x}{2 x + 1}$
70153	Find dy/dx	y = log base 3 of x	$y = \log_{3} (x)$
70154	Find the Derivative - d/dx	f(x)1/x	$f (x) \frac{1}{x}$
70155	Solve the Differential Equation	(dy)/(dx)=x^2y	$\frac{d y}{d x} = x^{2} y$
70156	Find the Center and Radius	y^2+x^2-6y+5=0	$y^{2} + x^{2} - 6 y + 5 = 0$
70157	Integrate Using u-Substitution	integral of x square root of x+6 with respect to x	$\int x \sqrt{x + 6} d x$
70158	Find dy/dx	9y+x=4y	$9 y + x = 4 y$
70159	Find dy/dx	7sin(xy^2)=5	$7 \sin (x y^{2}) = 5$
70160	Evaluate the Limit	limit as x approaches infinity of (3-2x)/(3x^3-1)	$lim_{x \to \infty} \frac{3 - 2 x}{3 x^{3} - 1}$
70161	Find Where Increasing/Decreasing	f(x)=e^(6x)+e^(-x)	$f (x) = e^{6 x} + e^{- x}$
70162	Find dy/dx	xy^2-x^2+4=0	$x y^{2} - x^{2} + 4 = 0$
70163	Evaluate the Integral	integral of ((( square root of 5- square root of x)^2)/( square root of x)) with respect to x=10 square root of x-2x square root of 5+2/3 square root of x^3+C	$\int (\frac{{(\sqrt{5} - \sqrt{x})}^{2}}{\sqrt{x}}) d x = 10 \sqrt{x} - 2 x \sqrt{5} + \frac{2}{3} \sqrt{x^{3}} + C$
70164	Evaluate the Integral	integral from 0 to pi/2 of tan(x) with respect to x	$\int_{0}^{\frac{π}{2}} \tan (x) d x$
70165	Find dy/dx	y=e^(x^6)	$y = e^{x^{6}}$
70166	Find dx/dy	y=x^(2x)	$y = x^{2 x}$
70167	Find the Tangent Line at (4,2)	y = square root of x , (4,2)	$y = \sqrt{x}$ , $(4, 2)$
70168	Find dy/dx	y=2sin(x)cos(x)	$y = 2 \sin (x) \cos (x)$
70169	Evaluate the Integral	integral of (2sin(x)+3cos(x)) with respect to x	$\int (2 \sin (x) + 3 \cos (x)) d x$
70170	Find dy/dx	4x^2+y^2=8	$4 x^{2} + y^{2} = 8$
70171	Find Where Increasing/Decreasing	f(x)=(2x^2)/(x^2-1)	$f (x) = \frac{2 x^{2}}{x^{2} - 1}$
70172	Find the Derivative - d/dx	y = natural log of ax^2+b	$y = \ln (a x^{2} + b)$
70173	Find the Derivative - d/dy	(xy)/(x+y)	$\frac{x y}{x + y}$
70174	Find the Derivative - d/dx	y=(x-x^2)/( square root of x)	$y = \frac{x - x^{2}}{\sqrt{x}}$
70175	Find the Derivative - d/dr	V=pir^2h	$V = π r^{2} h$
70176	Evaluate the Integral	integral of (pi^2-1) with respect to x	$\int (π^{2} - 1) d x$
70177	Find the Derivative - d/dx	d/(dx)(f(g(x)))	$\frac{d}{d x} (f (g (x)))$
70178	Evaluate the Integral	integral of (-3x^4-6x^2+8) with respect to x	$\int (- 3 x^{4} - 6 x^{2} + 8) d x$
70179	Evaluate the Integral	integral from 5 to infinity of 1/(x^2+x) with respect to x	$\int_{5}^{\infty} \frac{1}{x^{2} + x} d x$
70180	Use Logarithmic Differentiation to Find the Derivative	f(x)=x^(5x)	$f (x) = x^{5 x}$
70181	Find the Derivative - d/dx	d/(dx)(1+8/x)^x	$\frac{d}{d x} {(1 + \frac{8}{x})}^{x}$
70182	Find the Second Derivative	x^3-5x^2+x=0	$x^{3} - 5 x^{2} + x = 0$
70183	Find dy/dx	y = square root of 3-2x	$y = \sqrt{3 - 2 x}$
70184	Find the Domain and Range	f(x)=\|x\| if -2<=x<0; x^3 if x>=0	$f (x) = {\begin{cases} \| x \| & - 2 \leq x < 0 \\ x^{3} & x \geq 0 \end{cases}$
70185	Find the Linearization at a=25	f(x) = square root of x , a=25	$f (x) = \sqrt{x}$ , $a = 25$
70186	Find dy/dx	y=sin(x)^(cos(x))	$y = {\sin (x)}^{\cos (x)}$
70187	Evaluate the Limit	limit as x approaches infinity of (-2x^2+18x)/(4x^9-3)	$lim_{x \to \infty} \frac{- 2 x^{2} + 18 x}{4 x^{9} - 3}$
70188	Find dy/dx	5x-3y=15	$5 x - 3 y = 15$
70189	Find the Derivative - d/dx	y=tan( square root of x)	$y = \tan (\sqrt{x})$
70190	Find the Derivative - d/dx	(2x^2+x-3)/(2x+7)	$\frac{2 x^{2} + x - 3}{2 x + 7}$
70191	Evaluate the Limit	limit as x approaches 0 from the right of x-1/(x^3)	$lim_{x \to 0^{+}} x - \frac{1}{x^{3}}$
70192	Find dy/dx	y=1/(5x)	$y = \frac{1}{5 x}$
70193	Find the Derivative - d/dy	1/(2y^3)	$\frac{1}{2 y^{3}}$
70194	Integrate Using u-Substitution	integral of square root of 25-x^2(-2x) with respect to x	$\int \sqrt{25 - x^{2}} (- 2 x) d x$
70195	Find dx/dy	y^2=4x	$y^{2} = 4 x$
70196	Find the Derivative - d/dx	(3x-2x^2)(5+4x)	$(3 x - 2 x^{2}) (5 + 4 x)$
70197	Find the Derivative - d/dx	x square root of 2	$x \sqrt{2}$
70198	Evaluate the Limit	limit as x approaches infinity of (2^x-5)/(2^x+7)	$lim_{x \to \infty} \frac{2^{x} - 5}{2^{x} + 7}$
70199	Evaluate the Integral	integral of (-3x+4)e^(-x) with respect to x	$\int (- 3 x + 4) e^{- x} d x$
70200	Evaluate the Limit	limit as h approaches 0 of (arcsin(x+h)-arcsin(x))/h	$lim_{h \to 0} \frac{\arcsin (x + h) - \arcsin (x)}{h}$