Callisto
  • Callisto
Just for practice
LaTeX Practicing! :)
  • Stacey Warren - Expert brainly.com
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
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Callisto
  • Callisto
(A) Four basic operations (i) Addition => + \(+\) (ii) Subtraction => - \(-\) (iii) Multiplication => \times \(\times\) or \cdot \(\cdot\) (iv) Division => \div \(\div\) or / \(/\) ** (v) plus / minus => \pm \(\pm\) ** (vi) minus/plus => \mp \(\mp\)
Callisto
  • Callisto
(B) ''Equal'' signs (i) Equal => = \(=\) (ii) Not equal to => \ne \(\ne\) (iii) Approximately equal to => \approx \(\approx\) (iv) Similar to => \sim \(\sim\) (v) Congruent to => \cong \(\cong\)
Callisto
  • Callisto
(C) Inequality signs (i) less than => < \(<\) (ii) less than or equal to => \le \(\le\) (iii) greater than => > \(>\) (vi) greater than or equal to => \ge \(\ge\)

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Callisto
  • Callisto
(D) Exponent and logarithm (i) power => x^{n} \(x^{n}\) (ii) base => x_{n} \(x_{n}\) (iii) square root => \sqrt{x} \(\sqrt{x}\) (iv) nth root => \sqrt[n]{x} \(\sqrt[n]{x}\) (v) common log => \log x \(\log x\) (vi) common log with base n => \log_{n}x \(\log_{n}x\) (vii) natural log => \ln x \(\ln x\)
Callisto
  • Callisto
(E) Binomial expansion (i) summation => \sum_{}^{} \(\sum_{n=0}^{\infty}\) (ii) combination => _{n}C_{r} \(_{n}C_{r}\)
Callisto
  • Callisto
(F) Probability (i) Combination => _{n}C_{r} \(_{n}C_{r}\) (ii) Permutation => _{n}P_{r} \(_{n}P_{r}\) (iii) A∪B => A\cup B \(A\cup B\) (iv)
Callisto
  • Callisto
(F) Probability (i) Combination => _{n}C_{r} \(_{n}C_{r}\) (ii) Permutation => _{n}P_{r} \(_{n}P_{r}\) (iii) A∪B => A\cup B \(A\cup B\) (iv) A∩B => A \cap B \(A \cap B\)
Callisto
  • Callisto
\[\int_{-2}^{2}\sqrt{4-x^2}dx\] Using trigo substitution: Let x = 2sinθ , dx = 2cosθ dθ When x = 2, θ = π/2 When x = -2, θ = -π/2 The integral becomes \[\int_{-\frac{π}{2}}^{ \frac{π}{2}}\sqrt{4-(2\sin\theta)^2}(2\cos\theta d\theta)\]\[=4\int_{-\frac{π}{2}}^{ \frac{π}{2}}\cos^2\theta d\theta\]\[=4\int_{-\frac{π}{2}}^{ \frac{π}{2}}\frac{\cos(2\theta)+1}{2} d\theta\]\[=2\int_{-\frac{π}{2}}^{ \frac{π}{2}}(\cos(2\theta)+1)d\theta\]\[=2(\frac{1}{2}sin(2\theta)+\theta|_{-\frac{π}{2}}^{ \frac{π}{2}})\]\[=2(\frac{\pi}{2}-(-\frac{\pi}{2}))\]\[ = 2\pi\] This is not really I want to show LOL! Suppose \(y=f(x)=\sqrt{4-x^2}\) |dw:1383399191453:dw| It's clear that integrating the function y=f(x) from -2 to 2 is the same as finding the area of the semi-circle with radius = 2. So, immediately, we get \[\int_{-2}^{2}\sqrt{4-x^2}dx=\pi(2^2) /2 = 2\pi\] Geometry has its role here :D

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