A community for students.
Here's the question you clicked on:
 0 viewing
Callisto
 2 years ago
Just for practice
Callisto
 2 years ago
Just for practice

This Question is Closed

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.5(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
 2 years ago
Best ResponseYou've already chosen the best response.5(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
 2 years ago
Best ResponseYou've already chosen the best response.5(C) Inequality signs (i) less than => < \(<\) (ii) less than or equal to => \le \(\le\) (iii) greater than => > \(>\) (vi) greater than or equal to => \ge \(\ge\)

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.5(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
 2 years ago
Best ResponseYou've already chosen the best response.5(E) Binomial expansion (i) summation => \sum_{}^{} \(\sum_{n=0}^{\infty}\) (ii) combination => _{n}C_{r} \(_{n}C_{r}\)

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.5(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
 2 years ago
Best ResponseYou've already chosen the best response.5(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
 one year ago
Best ResponseYou've already chosen the best response.5\[\int_{2}^{2}\sqrt{4x^2}dx\] 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 \(y=f(x)=\sqrt{4x^2}\) 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 semicircle with radius = 2. So, immediately, we get \[\int_{2}^{2}\sqrt{4x^2}dx=\pi(2^2) /2 = 2\pi\] Geometry has its role here :D
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.