Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
83301	Evaluate the Limit	limit as x approaches infinity of (2-x^3)/(4x^5+1)	$lim_{x \to \infty} \frac{2 - x^{3}}{4 x^{5} + 1}$
83302	Integrate By Parts	integral from 0 to 1 of arctan(4x) with respect to x	$\int_{0}^{1} \arctan (4 x) d x$
83303	Find the Antiderivative	x/(1-x)	$\frac{x}{1 - x}$
83304	Find dy/dx	-4x^2+3-y+x=y^3	$- 4 x^{2} + 3 - y + x = y^{3}$
83305	Evaluate Using L'Hospital's Rule	limit as x approaches -3 of (e^(x+3)-1)/(3 natural log of -5-2x)	$lim_{x \to - 3} \frac{e^{x + 3} - 1}{3 \ln (- 5 - 2 x)}$
83306	Find the Derivative - d/dx	d/(dx)cos(x^3)^2	$\frac{d}{d x} \cos^{2} (x^{3})$
83307	Find the Antiderivative	6 square root of x- sixth root of x	$6 \sqrt{x} - \sqrt[6]{x}$
83308	Find the Maximum/Minimum Value	f(x)=3sin(5x-4)	$f (x) = 3 \sin (5 x - 4)$
83309	Find the Local Maxima and Minima	f(x)=3/4x^4-3x^3-81x^2-16	$f (x) = \frac{3}{4} x^{4} - 3 x^{3} - 81 x^{2} - 16$
83310	Evaluate the Integral	integral from -1 to 5 of [4y-(y^2-5)] with respect to y	$\int_{- 1}^{5} [4 y - (y^{2} - 5)] d y$
83311	Evaluate the Limit	limit as x approaches -3 of \|x+3\|-8x	$lim_{x \to - 3} \| x + 3 \| - 8 x$
83312	Find the Derivative - d/dx	x2/3	$x \frac{2}{3}$
83313	Evaluate the Limit	limit as x approaches -3 of (9-7x) square root of 6-4x	$lim_{x \to - 3} (9 - 7 x) \sqrt{6 - 4 x}$
83314	Evaluate the Limit	limit as x approaches infinity of (10x^3+x^2-1)/(2x^3+7x-8)	$lim_{x \to \infty} \frac{10 x^{3} + x^{2} - 1}{2 x^{3} + 7 x - 8}$
83315	Evaluate Using L'Hospital's Rule	limit as x approaches 3 of (4 natural log of 3x-8)/(2e^(2x-6)-2)	$lim_{x \to 3} \frac{4 \ln (3 x - 8)}{2 e^{2 x - 6} - 2}$
83316	Find dx/dy	y^3x^5=e^(3x)	$y^{3} x^{5} = e^{3 x}$
83317	Evaluate the Limit	limit as x approaches 1/2 of x	$lim_{x \to \frac{1}{2}} x$
83318	Find the Derivative - d/dt	natural log of 2e^t-1	$\ln (2 e^{t} - 1)$
83319	Evaluate Using Summation Formulas	limit as n approaches infinity of 1/n sum from i=1 to n of 1/(1+(i/n)^2)	$lim_{n \to \infty} \frac{1}{n} \sum_{i = 1}^{n} \frac{1}{1 + {(\frac{i}{n})}^{2}}$
83320	Find the Area Between the Curves	y=sin(x) , y=5x , x=pi/2 , x=pi	$y = \sin (x)$ , $y = 5 x$ , $x = \frac{π}{2}$ , $x = π$
83321	Find the Second Derivative	f(x)=x+3(1-x)^(1/3)	$f (x) = x + 3 {(1 - x)}^{\frac{1}{3}}$
83322	Evaluate the Integral	integral from -3 to 5 of (5x^2-e^(5x)) with respect to x	$\int_{- 3}^{5} (5 x^{2} - e^{5 x}) d x$
83323	Integrate Using u-Substitution	integral of x square root of 1+x with respect to x	$\int x \sqrt{1 + x} d x$
83324	Evaluate the Limit	limit as x approaches infinity of (x^3+71x)/(x+1)	$lim_{x \to \infty} \frac{x^{3} + 71 x}{x + 1}$
83325	Evaluate the Integral	integral from -1 to 2 of (3u-2)(u+1) with respect to u	$\int_{- 1}^{2} (3 u - 2) (u + 1) d u$
83326	Evaluate the Integral	integral of (3+e^(x^2)) with respect to x	$\int (3 + e^{x^{2}}) d x$
83327	Find dy/dx	3x^3-3y^3=-4x^2y	$3 x^{3} - 3 y^{3} = - 4 x^{2} y$
83328	Find dy/dx	3y^3=-3+3x^2	$3 y^{3} = - 3 + 3 x^{2}$
83329	Integrate By Parts	integral of square root of x with respect to x	$\int \sqrt{x} d x$
83330	Find the Third Derivative	f(x)=5/7x-1/10x^6+1/6x^-1-1/10x^5	$f (x) = \frac{5}{7} x - \frac{1}{10} x^{6} + \frac{1}{6} x^{- 1} - \frac{1}{10} x^{5}$
83331	Evaluate the Integral	integral of -(14x^(5/2))/2 with respect to x	$\int - \frac{14 x^{\frac{5}{2}}}{2} d x$
83332	Find the Derivative - d/dx	-2/(x^(1/2))	$- \frac{2}{x^{\frac{1}{2}}}$
83333	Find the Antiderivative	f(x)=2/5+cos(x)	$f (x) = \frac{2}{5} + \cos (x)$
83334	Find the Derivative - d/dt	1-arctan(e^t)	$1 - \arctan (e^{t})$
83335	Find the Derivative - d/dx	(x+4)/((x-1)(x+3))	$\frac{x + 4}{(x - 1) (x + 3)}$
83336	Find the Derivative - d/dx	e^xsin(x^2)	$e^{x} \sin (x^{2})$
83337	Find the Derivative - d/dx	\|2x\|	$\| 2 x \|$
83338	Find the Derivative - d/dx	-(x+1)^(2/3)	$- {(x + 1)}^{\frac{2}{3}}$
83339	Solve the Differential Equation	(1+e^x)y*(dy)/(dx)=e^x	$(1 + e^{x}) y \cdot \frac{d y}{d x} = e^{x}$
83340	Find Where Increasing/Decreasing	f(x)=5+12x-x^3	$f (x) = 5 + 12 x - x^{3}$
83341	Find the Concavity	1/6x^4+x^3-18x^2	$\frac{1}{6} x^{4} + x^{3} - 18 x^{2}$
83342	Evaluate the Limit	limit as x approaches infinity of (x^2-5x+4)/(2x^2-8x)	$lim_{x \to \infty} \frac{x^{2} - 5 x + 4}{2 x^{2} - 8 x}$
83343	Find the Derivative - d/dx	y=cos(2x+1)	$y = \cos (2 x + 1)$
83344	Find the Derivative - d/dx	y=1/2(e^x+e^(-x))	$y = \frac{1}{2} (e^{x} + e^{- x})$
83345	Find dy/dx	e^(xy)=e^(4x)-e^(5y)	$e^{x y} = e^{4 x} - e^{5 y}$
83346	Find Where Increasing/Decreasing	f(x)=-2^x+6	$f (x) = - 2^{x} + 6$
83347	Find the Maximum/Minimum Value	f(x) = natural log of x^2-1	$f (x) = \ln (x^{2} - 1)$
83348	Evaluate the Integral	integral of 5x^2(3x-4)(x-1) with respect to x	$\int 5 x^{2} (3 x - 4) (x - 1) d x$
83349	Find the Derivative - d/dx	\| natural log of x\|	$\| \ln (x) \|$
83350	Find the Derivative - d/dx	y=(4 square root of x)/(x^2-2)	$y = \frac{4 \sqrt{x}}{x^{2} - 2}$
83351	Evaluate the Limit	limit as x approaches -1 of (-5/x-5)/(x+1)	$lim_{x \to - 1} \frac{- \frac{5}{x} - 5}{x + 1}$
83352	Find Where Increasing/Decreasing	300x-x^3	$300 x - x^{3}$
83353	Evaluate Using L'Hospital's Rule	limit as x approaches 3 from the right of (x-3)/(\|x^3-3x^2\|)	$lim_{x \to 3^{+}} \frac{x - 3}{\| x^{3} - 3 x^{2} \|}$
83354	Find the Antiderivative	f(x)=1/(x^3)-2	$f (x) = \frac{1}{x^{3}} - 2$
83355	Evaluate the Limit	limit as x approaches 1 of (x^2+4x-5)/(1- square root of x)	$lim_{x \to 1} \frac{x^{2} + 4 x - 5}{1 - \sqrt{x}}$
83356	Find dy/dx	sin(x^2y)=x	$\sin (x^{2} y) = x$
83357	Find the Derivative - d/dx	2^xsin(x)	$2^{x} \sin (x)$
83358	Integrate Using u-Substitution	integral from 0 to 2 of (3x^2-1)/(x^2) with respect to x	$\int_{0}^{2} \frac{3 x^{2} - 1}{x^{2}} d x$
83359	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (e^x+e^(-x)-2)/(1-cos(2x))	$lim_{x \to 0} \frac{e^{x} + e^{- x} - 2}{1 - \cos (2 x)}$
83360	Evaluate the Limit	limit as x approaches 4 of (f(x)-5)/(x-2)	$lim_{x \to 4} \frac{f (x) - 5}{x - 2}$
83361	Find dy/dx	y=tan(x)^2	$y = \tan^{2} (x)$
83362	Find the Integral	(12x^2-4x)dx	$(12 x^{2} - 4 x) d x$
83363	Find the Inflection Points	f(x)=-0.5*x^4+3x^2	$f (x) = - 0.5 \cdot x^{4} + 3 x^{2}$
83364	Find Where Increasing/Decreasing	-3/4x^4-16x^3-90x^2+25	$- \frac{3}{4} x^{4} - 16 x^{3} - 90 x^{2} + 25$
83365	Find dy/dx	y=2 fifth root of x^2	$y = 2 \sqrt[5]{x^{2}}$
83366	Find the Antiderivative	e^(x+y)	$e^{x + y}$
83367	Find dy/dx	0=-x^3+y^3-x^2	$0 = - x^{3} + y^{3} - x^{2}$
83368	Evaluate the Integral	integral of 3x(4x+3)^2 with respect to x	$\int 3 x {(4 x + 3)}^{2} d x$
83369	Find dy/dx	-xy+2x=4	$- x y + 2 x = 4$
83370	Evaluate the Limit	limit as x approaches -1 of (x^3-7x^2+14x-8)/(2x^2-3x-4)	$lim_{x \to - 1} \frac{x^{3} - 7 x^{2} + 14 x - 8}{2 x^{2} - 3 x - 4}$
83371	Find the Inflection Points	f(x) = cube root of x-1	$f (x) = \sqrt[3]{x - 1}$
83372	Evaluate the Integral	integral of (x^5+2x^4-x^2)/(x^4) with respect to x	$\int \frac{x^{5} + 2 x^{4} - x^{2}}{x^{4}} d x$
83373	Find the Derivative - d/dx	y=(a+b/(x^2))^3	$y = {(a + \frac{b}{x^{2}})}^{3}$
83374	Find dy/dx	(3x^2+y)^4=y	${(3 x^{2} + y)}^{4} = y$
83375	Evaluate the Limit	limit as x approaches 4 of (5x-20)/(9-3x)	$lim_{x \to 4} \frac{5 x - 20}{9 - 3 x}$
83376	Evaluate the Integral	integral of -1/x with respect to x	$\int \frac{- 1}{x} d x$
83377	Evaluate the Limit	limit as x approaches -1 of (1/(4x+3)+1)/(4x+4)	$lim_{x \to - 1} \frac{\frac{1}{4 x + 3} + 1}{4 x + 4}$
83378	Find the Maximum/Minimum Value	f(x)=-x^4-8x^3-18x^2+6	$f (x) = - x^{4} - 8 x^{3} - 18 x^{2} + 6$
83379	Evaluate the Integral	integral from 0 to 1/2 of arccos(x) with respect to x	$\int_{0}^{\frac{1}{2}} \arccos (x) d x$
83380	Find the Concavity	1/10x^5+2x^4+12x^3	$\frac{1}{10} x^{5} + 2 x^{4} + 12 x^{3}$
83381	Find the Derivative - d/dx	y=3x^(-1/2)	$y = 3 x^{- \frac{1}{2}}$
83382	Find the Center and Radius	x^2+y^2=4^2	$x^{2} + y^{2} = 4^{2}$
83383	Find the Derivative - d/dx	-1/3(x^7+2x-9)	$- \frac{1}{3} (x^{7} + 2 x - 9)$
83384	Evaluate the Limit	limit as h approaches 0 of (arctan(x+h)-arctan(x))/h	$lim_{h \to 0} \frac{\arctan (x + h) - \arctan (x)}{h}$
83385	Evaluate the Integral	integral of 3x(x+6)^2 with respect to x	$\int 3 x {(x + 6)}^{2} d x$
83386	Find the Tangent Line at (1,-4)	y=x^3-3x^2-2 , (1,-4)	$y = x^{3} - 3 x^{2} - 2$ , $(1, - 4)$
83387	Evaluate the Integral	integral from 0 to 1 of x*5^x with respect to x	$\int_{0}^{1} x \cdot 5^{x} d x$
83388	Evaluate Using L'Hospital's Rule	limit as x approaches -3 of (4 natural log of 2x+7)/(2tan(-6-2x))	$lim_{x \to - 3} \frac{4 \ln (2 x + 7)}{2 \tan (- 6 - 2 x)}$
83389	Find the Antiderivative	(x^3+3x^2+3x-1)/(x^2+2x+1)	$\frac{x^{3} + 3 x^{2} + 3 x - 1}{x^{2} + 2 x + 1}$
83390	Evaluate the Integral	integral of sin(x)sin(cos(x)) with respect to x	$\int \sin (x) \sin (\cos (x)) d x$
83391	Find the Antiderivative	f(x)=-e^(-x)	$f (x) = - e^{- x}$
83392	Find the Derivative - d/dx	square root of (4x^2)/(6+2x)	$\sqrt{\frac{4 x^{2}}{6 + 2 x}}$
83393	Find Where Increasing/Decreasing	y=2x^3+3x^2-12x	$y = 2 x^{3} + 3 x^{2} - 12 x$
83394	Integrate By Parts	integral of x^3e^(x^4) with respect to x	$\int x^{3} e^{x^{4}} d x$
83395	Evaluate the Limit	limit as x approaches -5/2 of (6x^2+11x-10)/(8x^2-18x-5)	$lim_{x \to - \frac{5}{2}} \frac{6 x^{2} + 11 x - 10}{8 x^{2} - 18 x - 5}$
83396	Evaluate the Limit	limit as x approaches 1 of (3x+x^2-4)/(x-1)	$lim_{x \to 1} \frac{3 x + x^{2} - 4}{x - 1}$
83397	Evaluate the Limit	limit as x approaches 0 of (sin(x))/(x^2+x)	$lim_{x \to 0} \frac{\sin (x)}{x^{2} + x}$
83398	Find dy/dx	x^y=e^(x-y)	$x^{y} = e^{x - y}$
83399	Evaluate the Limit	limit as x approaches infinity of 5+x^-1-2x^-2	$lim_{x \to \infty} 5 + x^{- 1} - 2 x^{- 2}$
83400	Find the Maximum/Minimum Value	f(x)=sin(x)^2	$f (x) = \sin^{2} (x)$