Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
69301	Evaluate the Limit	limit as x approaches infinity of ( square root of 9x^4+1)/(x^2-3x+5)	$lim_{x \to \infty} \frac{\sqrt{9 x^{4} + 1}}{x^{2} - 3 x + 5}$
69302	Find the Derivative - d/dx	f(x)^2	$f {(x)}^{2}$
69303	Find the Derivative - d/dx	integral of ((3x^2-2x^3)/(6x)) with respect to x	$\int (\frac{3 x^{2} - 2 x^{3}}{6 x}) d x$
69304	Evaluate the Summation	sum from n=4 to infinity of 1/( square root of n)-1/( square root of n+1)	$\sum_{n = 4}^{\infty} \frac{1}{\sqrt{n}} - \frac{1}{\sqrt{n + 1}}$
69305	Find the Derivative - d/dx	y=pix^2	$y = π x^{2}$
69306	Find Where Increasing/Decreasing	f(x)=(x^2-8)/(x-3)	$f (x) = \frac{x^{2} - 8}{x - 3}$
69307	Evaluate the Limit	limit as x approaches 0 of (e^x-x-1)/(x^2)	$lim_{x \to 0} \frac{e^{x} - x - 1}{x^{2}}$
69308	Find dx/dt	x = square root of t	$x = \sqrt{t}$
69309	Solve the Differential Equation	(dy)/(dx)=y	$\frac{d y}{d x} = y$
69310	Evaluate the Integral	integral of (x-1)/(x^2) with respect to x	$\int \frac{x - 1}{x^{2}} d x$
69311	Evaluate the Limit	limit as x approaches 0 of (1-cos(x))/(xsin(x))	$lim_{x \to 0} \frac{1 - \cos (x)}{x \sin (x)}$
69312	Find the Derivative - d/dx	x*sin(x)	$x \cdot \sin (x)$
69313	Evaluate the Integral	integral from ( square root of 2)/3 to 2/3 of 1/(x^5 square root of 9x^2-1) with respect to x	$\int_{\frac{\sqrt{2}}{3}}^{\frac{2}{3}} \frac{1}{x^{5} \sqrt{9 x^{2} - 1}} d x$
69314	Find dy/dx	x+sin(y)=xy	$x + \sin (y) = x y$
69315	Evaluate the Limit	limit as x approaches 2 of ( square root of x^2+5-3)/(x^2-2x)	$lim_{x \to 2} \frac{\sqrt{x^{2} + 5} - 3}{x^{2} - 2 x}$
69316	Find the Derivative - d/dx	x-e^x	$x - e^{x}$
69317	Evaluate the Derivative at a=9	h(x)=x^( square root of x) , a=9	$h (x) = x^{\sqrt{x}}$ , $a = 9$
69318	Find the Derivative - d/dx	y=1/2 cube root of x^2+( fourth root of x^5)/3	$y = \frac{1}{2} \sqrt[3]{x^{2}} + \frac{\sqrt[4]{x^{5}}}{3}$
69319	Find the Tangent Line at (0,1)	y=sin(x)+cos(x) , (0,1)	$y = \sin (x) + \cos (x)$ , $(0, 1)$
69320	Find dy/dx	cos(3y)+sin(2x)=2x+3y	$\cos (3 y) + \sin (2 x) = 2 x + 3 y$
69321	Find the Area Between the Curves	y=9x , y=x^3 , x=0 , x=3	$y = 9 x$ , $y = x^{3}$ , $x = 0$ , $x = 3$
69322	Evaluate the Integral	integral of (y^4+2y^2-1)/( square root of y) with respect to y	$\int \frac{y^{4} + 2 y^{2} - 1}{\sqrt{y}} d y$
69323	Find the Antiderivative	f(x)=1/((x/5+1)^6)	$f (x) = \frac{1}{{(\frac{x}{5} + 1)}^{6}}$
69324	Find the Derivative - d/dx	y=(x+6)/(x^3)	$y = \frac{x + 6}{x^{3}}$
69325	Find the Derivative - d/dx	d/(dx)sin(2x)	$\frac{d}{d x} \sin (2 x)$
69326	Find dx/dy	y=3e^x	$y = 3 e^{x}$
69327	Evaluate the Integral	integral of (x^2+3x-1)e^(2x) with respect to x	$\int (x^{2} + 3 x - 1) e^{2 x} d x$
69328	Evaluate the Limit	limit as x approaches infinity of (1+1/x)^(3x)	$lim_{x \to \infty} {(1 + \frac{1}{x})}^{3 x}$
69329	Find dy/dx	y=x^2sin(6x)	$y = x^{2} \sin (6 x)$
69330	Find dy/dx	y = fifth root of 6x	$y = \sqrt[5]{6 x}$
69331	Find dy/dx	x=y^4	$x = y^{4}$
69332	Find the Derivative - d/dt	y=2t^4-10t^2+13t	$y = 2 t^{4} - 10 t^{2} + 13 t$
69333	Evaluate the Integral	integral from -1 to 1 of 1/x with respect to x	$\int_{- 1}^{1} \frac{1}{x} d x$
69334	Find dy/dx	y=cos(3x)^2	$y = \cos^{2} (3 x)$
69335	Find the Derivative - d/dx	1/( square root of x)+ fifth root of x	$\frac{1}{\sqrt{x}} + \sqrt[5]{x}$
69336	Find the Maximum/Minimum Value	f(x)=3-2sin(2x-pi/4)	$f (x) = 3 - 2 \sin (2 x - \frac{π}{4})$
69337	Find the Slope	f(x)=4	$f (x) = 4$
69338	Evaluate the Limit	limit as x approaches infinity of (1-2x+2x^3)/(x^3+x+1)	$lim_{x \to \infty} \frac{1 - 2 x + 2 x^{3}}{x^{3} + x + 1}$
69339	Find the Second Derivative	1/( square root of x)	$\frac{1}{\sqrt{x}}$
69340	Find the Derivative - d/dx	d/(dx)arctan(x)	$\frac{d}{d x} \arctan (x)$
69341	Find dy/dx	8x^2+y^2=10	$8 x^{2} + y^{2} = 10$
69342	Find dy/dx	y = log base 2 of x	$y = \log_{2} (x)$
69343	Evaluate the Integral	integral from -1 to 2 of (f(x)+6x) with respect to x=15	$\int_{- 1}^{2} (f (x) + 6 x) d x = 15$
69344	Find the Derivative - d/dy	4 square root of y^2+7x^2	$4 \sqrt{y^{2} + 7 x^{2}}$
69345	Find dy/dx	x+4y=1	$x + 4 y = 1$
69346	Evaluate the Summation	sum from n=1 to infinity of 4(0.2)^(n-1)	$\sum_{n = 1}^{\infty} 4 {(0.2)}^{n - 1}$
69347	Find the Derivative - d/dx	e^( square root of 2x)	$e^{\sqrt{2 x}}$
69348	Evaluate the Limit	limit as x approaches -2 from the left of (-3(x+2))/(x^2+4x+4)	$lim_{x \to {(- 2)}^{-}} \frac{- 3 (x + 2)}{x^{2} + 4 x + 4}$
69349	Find dy/dx	y=e^(x^4)	$y = e^{x^{4}}$
69350	Find the Derivative - d/dx	cos(x)x^3	$\cos (x) x^{3}$
69351	Find the Second Derivative	y=cos(x)	$y = \cos (x)$
69352	Evaluate the Integral	integral from a to a of f(x) with respect to x	$\int_{a}^{a} f (x) d x$
69353	Find Where Increasing/Decreasing	f(x)=(x^2)/(x^2-36)	$f (x) = \frac{x^{2}}{x^{2} - 36}$
69354	Evaluate the Summation	sum from i=4 to 16 of 9i	$\sum_{i = 4}^{16} 9 i$
69355	Evaluate the Derivative at a=4	h(x)=x^( square root of x) , a=4	$h (x) = x^{\sqrt{x}}$ , $a = 4$
69356	Evaluate the Summation	sum from i=1 to n of (3i-1)^2	$\sum_{i = 1}^{n} {(3 i - 1)}^{2}$
69357	Find the Arc Length	y=1+6x^(3/2) , 0<=x<=1	$y = 1 + 6 x^{\frac{3}{2}}$ , $0 \leq x \leq 1$
69358	Find the Derivative - d/dx	2Ax+B	$2 A x + B$
69359	Evaluate the Integral	integral of (2e^x-6^x) with respect to x	$\int (2 e^{x} - 6^{x}) d x$
69360	Find the Derivative - d/dx	(3x^2+1)/(x+2)	$\frac{3 x^{2} + 1}{x + 2}$
69361	Evaluate the Integral	integral from 0 to infinity of 1/( square root of e^x) with respect to x	$\int_{0}^{\infty} \frac{1}{\sqrt{e^{x}}} d x$
69362	Find dr/dθ	r=tan(theta)sec(theta)	$r = \tan (θ) \sec (θ)$
69363	Find the Derivative - d/dx	y = cube root of (2x-3)^2	$y = \sqrt[3]{{(2 x - 3)}^{2}}$
69364	Find dy/dx	y=sin(x^2)	$y = \sin (x^{2})$
69365	Find dx/dy	x^3+y^3-6xy=0	$x^{3} + y^{3} - 6 x y = 0$
69366	Find dy/dx	y=x^2+1	$y = x^{2} + 1$
69367	Evaluate the Integral	integral of (5x^4+3x^3+6) with respect to x	$\int (5 x^{4} + 3 x^{3} + 6) d x$
69368	Find dy/dx	y^3-2xy^2=x^3y+5x^2y^2-y	$y^{3} - 2 x y^{2} = x^{3} y + 5 x^{2} y^{2} - y$
69369	Evaluate the Limit	limit as x approaches infinity of (x^2-3x)/(4x^2+5)	$lim_{x \to \infty} \frac{x^{2} - 3 x}{4 x^{2} + 5}$
69370	Evaluate the Integral	integral from 0 to pi/2 of tan(theta)^2 with respect to theta	$\int_{0}^{\frac{π}{2}} \tan^{2} (θ) d θ$
69371	Evaluate the Limit	limit as x approaches square root of 2 of (x^2-2)/(x- square root of 2)	$lim_{x \to \sqrt{2}} \frac{x^{2} - 2}{x - \sqrt{2}}$
69372	Evaluate the Integral	integral from 2 to 4 of x^(1/3)(1-2x) with respect to x	$\int_{2}^{4} x^{\frac{1}{3}} (1 - 2 x) d x$
69373	Find dy/dx	cos(x^2y^2)=3x	$\cos (x^{2} y^{2}) = 3 x$
69374	Find the Derivative - d/dx	(e^x-1)/x	$\frac{e^{x} - 1}{x}$
69375	Evaluate the Limit	limit as n approaches infinity of n root of \|a_n\|	$lim_{n \to \infty} \sqrt[n]{\| a_{n} \|}$
69376	Evaluate the Integral	integral of (7x^2+2x-7)/(x^3-x) with respect to x	$\int \frac{7 x^{2} + 2 x - 7}{x^{3} - x} d x$
69377	Find the Tangent Line at (1,1)	y=x^3 , (1,1)	$y = x^{3}$ , $(1, 1)$
69378	Evaluate the Integral	integral of x^2(x+1)^3 with respect to x	$\int x^{2} {(x + 1)}^{3} d x$
69379	Evaluate the Limit	limit as x approaches 2 from the left of (x^2+x-6)/(\|x-2\|)	$lim_{x \to 2^{-}} \frac{x^{2} + x - 6}{\| x - 2 \|}$
69380	Find the Derivative - d/dx	xe^(ax)	$x e^{a x}$
69381	Integrate By Parts	integral of e^x with respect to x	$\int e^{x} d x$
69382	Evaluate the Limit	limit as x approaches 0 of (x^2+x)/(x^2+8x)	$lim_{x \to 0} \frac{x^{2} + x}{x^{2} + 8 x}$
69383	Evaluate the Integral	integral of ( square root of x) with respect to x	$\int (\sqrt{x}) d x$
69384	Integrate Using u-Substitution	integral of natural log of x with respect to x	$\int \ln (x) d x$
69385	Find dy/dx	y^3=x^5	$y^{3} = x^{5}$
69386	Find the Derivative - d/dt	(-te^(-t)+e^(-t))/(e^t)	$\frac{- t e^{- t} + e^{- t}}{e^{t}}$
69387	Find the Derivative - d/dx	d/(dx)(2sin( square root of x)^2)	$\frac{d}{d x} (2 \sin^{2} (\sqrt{x}))$
69388	Find the Domain and Range	f(x)=x^2+1 , x<=0	$f (x) = x^{2} + 1$ , $x \leq 0$
69389	Find the Derivative - d/dy	y natural log of x	$y \ln (x)$
69390	Evaluate the Integral	integral of 1/(at+b) with respect to t	$\int \frac{1}{a t + b} d t$
69391	Evaluate the Limit	limit as x approaches infinity of (-6x^2+x-1)/(x^2+3)	$lim_{x \to \infty} \frac{- 6 x^{2} + x - 1}{x^{2} + 3}$
69392	Find dx/dy	x^4y^2-x^3y+2xy^3=0	$x^{4} y^{2} - x^{3} y + 2 x y^{3} = 0$
69393	Find the Derivative - d/dx	log of 1+x	$\log (1 + x)$
69394	Evaluate the Limit	limit as x approaches -1 of (1-x)/(-1+x)	$lim_{x \to - 1} \frac{1 - x}{- 1 + x}$
69395	Find dx/dy	y = square root of 2x+1	$y = \sqrt{2 x + 1}$
69396	Find dy/dx	y=x^3cos(x)	$y = x^{3} \cos (x)$
69397	Find the Linearization at a=0	f(x) = square root of 1-x at a=0	$f (x) = \sqrt{1 - x}$ at $a = 0$
69398	Find Where Increasing/Decreasing	A=1200(0.85)^6	$A = 1200 {(0.85)}^{6}$
69399	Find dx/dy	x^4+y^4=16	$x^{4} + y^{4} = 16$
69400	Evaluate the Limit	limit as x approaches infinity of (-3x^4+4x^3+8x^2-8x)/(4x^3-7x^2+4x-3)	$lim_{x \to \infty} \frac{- 3 x^{4} + 4 x^{3} + 8 x^{2} - 8 x}{4 x^{3} - 7 x^{2} + 4 x - 3}$