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Free Examples Solved Step-by-Step
Arithmetic
Addition3+5+73+5+73+5+7 Multiplication2⋅(10−6)2\cdot\left(10-6\right)2⋅(10−6) Square root24⋅6\sqrt{24\cdot6}24⋅6
Algebra
Simplificationx2+x−2x2+5x+6\frac{x^2+x-2}{x^2+5x+6}x2+5x+6x2+x−2 Quadratic equations−x2+7x−10=0-x^2+7x-10=0−x2+7x−10=0 Division of polynomialsx5−x4+x2−2x2+1\frac{x^5-x^4+x^2-2}{x^2+1}x2+1x5−x4+x2−2
Trigonometry
Trigonometric Equationssin(x)−22=0\sin\left(x\right)-\frac{\sqrt{2}}{2}=0sin(x)−22=0 Prove identity from LHScot(x)⋅sec(x)=csc(x)\cot\left(x\right)\cdot\sec\left(x\right)=\csc\left(x\right)cot(x)⋅sec(x)=csc(x) Prove identity from RHSsec(x)=sin(2x)sin(x)−cos(2x)cos(x)\sec \left(x\right)=\frac{\sin \left(2x\right)}{\sin \left(x\right)}-\frac{\cos \left(2x\right)}{\cos \left(x\right)}sec(x)=sin(x)sin(2x)−cos(x)cos(2x)
Limits
Direct Substitutionlimx→0(3x+1)\lim_{x\to 0}\left(3x+1\right)x→0lim(3x+1) Factorizationlimx→5(x2−25x−5)\lim_{x\to 5}\left(\frac{x^2-25}{x-5}\right)x→5lim(x−5x2−25) LHôpitals rulelimx→0(1−cos(x)x2)\lim_{x\to 0}\left(\frac{1-\cos\left(x\right)}{x^2}\right)x→0lim(x21−cos(x))
Derivatives
Basic Derivativesddx(x2)\frac{d}{dx}\left(x^2\right)dxd(x2) Chain Ruleddx(tan(x+1))\frac{d}{dx}\left(\tan\left(x+1\right)\right)dxd(tan(x+1)) Logarithmic Differentiationddx(xx)\frac{d}{dx}\left(x^x\right)dxd(xx)
Integrals
U-substitution∫x⋅cos(2x2+3)dx\int x\cdot\cos\left(2x^2+3\right)dx∫x⋅cos(2x2+3)dx Integration by Parts∫(x⋅e2x)dx\int\left(x\cdot e^{2x}\right)dx∫(x⋅e2x)dx Trigonometric Substitution∫x2x2+6dx\int\frac{x^2}{\sqrt{x^2+6}}dx∫x2+6x2dx
Differential Equations
Separable Equationsdydx=2x3y2\frac{dy}{dx}=\frac{2x}{3y^2}dxdy=3y22x Linear Equationsdydx+3xy=1x2\frac{dy}{dx}+\frac{3}{x}y=\frac{1}{x^2}dxdy+x3y=x21 Bernoulli Equationsdydx−yx=x3y\frac{dy}{dx}\:-\frac{y}{x}=\frac{x}{3y}dxdy−xy=3yx
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