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Free Examples Solved Step-by-Step

Arithmetic

Addition $3+5+7$ Multiplication $2\cdot\left(10-6\right)$ Square root $\sqrt{24\cdot6}$

Algebra

Simplification $\frac{x^2+x-2}{x^2+5x+6}$ Quadratic equations $-x^2+7x-10=0$ Division of polynomials $\frac{x^5-x^4+x^2-2}{x^2+1}$

Trigonometry

Trigonometric Equations $\sin\left(x\right)-\frac{\sqrt{2}}{2}=0$ Prove identity from LHS $\cot\left(x\right)\cdot\sec\left(x\right)=\csc\left(x\right)$ Prove identity from RHS $\sec \left(x\right)=\frac{\sin \left(2x\right)}{\sin \left(x\right)}-\frac{\cos \left(2x\right)}{\cos \left(x\right)}$

Limits

Direct Substitution $\lim_{x\to 0}\left(3x+1\right)$ Factorization $\lim_{x\to 5}\left(\frac{x^2-25}{x-5}\right)$ LHôpitals rule $\lim_{x\to 0}\left(\frac{1-\cos\left(x\right)}{x^2}\right)$

Derivatives

Basic Derivatives $\frac{d}{dx}\left(x^2\right)$ Chain Rule $\frac{d}{dx}\left(\tan\left(x+1\right)\right)$ Logarithmic Differentiation $\frac{d}{dx}\left(x^x\right)$

Integrals

U-substitution $\int x\cdot\cos\left(2x^2+3\right)dx$ By Parts $\int\left(x\cdot e^{2x}\right)dx$ Trigonometric Substitution $\int\frac{x^2}{\sqrt{x^2+6}}dx$

Differential Equations

Separable Equations $\frac{dy}{dx}=\frac{2x}{3y^2}$ Linear Equations $\frac{dy}{dx}+\frac{3}{x}y=\frac{1}{x^2}$ Bernoulli Equations $\frac{dy}{dx}\:-\frac{y}{x}=\frac{x}{3y}$

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