Mathematica: Trigonometric e Logarithmique Identitates

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Questions and Answers

Qual del sequente expressiones es equivalente a $\sin(\theta + \beta)$?

$\cos \theta \cos \beta - \sin \theta \sin \beta$

$\cos \theta \cos \beta + \sin \theta \sin \beta$

$\sin \theta \cos \beta - \cos \theta \sin \beta$

$\sin \theta \cos \beta + \cos \theta \sin \beta$ (correct)

Es ver que $\cos(-\theta) = -\cos(\theta)$?

False (B)

Simplifica le expression: $\tan(\theta - \beta)$

$\frac{\tan \theta - \tan \beta}{1 + \tan \theta \tan \beta}$

$\sin(2\theta) = $ ______

$2 \sin \theta \cos \theta$ Signup and view all the answers

Qual es le identitate de co-function pro $\cos(\frac{\pi}{2} - \theta)$?

$\sin(\theta)$ (A) Signup and view all the answers

Es $\tan(-\theta) = \tan(\theta)$?

False (B) Signup and view all the answers

Associa le sequente identitates trigonometric con lor expressiones correcte:

$\sin(\theta + \beta)$ = $\sin \theta \cos \beta + \cos \theta \sin \beta$ $\cos(\theta + \beta)$ = $\cos \theta \cos \beta - \sin \theta \sin \beta$ $\tan(\theta + \beta)$ = $\frac{\tan \theta + \tan \beta}{1 - \tan \theta \tan \beta}$ Signup and view all the answers

Qual del sequente affirmationes es correcte re le logarithmo natural?

ln e = 1 (B) Signup and view all the answers

Es ver que $e^{ln x} = x$ pro omne valores de x?

False (B) Signup and view all the answers

Simplifica le expression: $ln(e^5)$

5 Signup and view all the answers

Secundo le formulas de cambio de base, $log_b a = \frac{ln a}{______}$

ln b Signup and view all the answers

Qual es le equivalente de $ln(xy)$ ?

$ln(x) + ln(y)$ (B) Signup and view all the answers

Es ver que $a^m * a^n = a^{m*n}$?

False (B) Signup and view all the answers

$a^0 = ______$, ubi a ≠ 0.

1 Signup and view all the answers

Associa le proprietates del exponentes con lor expressiones:

$a^m a^n$ = $a^{m+n}$ $(a^m)^n$ = $a^{mn}$ $\frac{a^m}{a^n}$ = $a^{m-n}$ Signup and view all the answers

Qual es le objectivo de Emmanuel con le 'Maths Handbook and Study Guides'?

A demystificar le mathematicas e adjutar studentes a attinger lor potential. (C) Signup and view all the answers

Le libros de Emmanuel es solmente compatibile con certe libros de calculo.

False (B) Signup and view all the answers

Quales characteristicas distingue le libros de Emmanuel?

Clar, simple, visual e logic Signup and view all the answers

Emmanuel usa codification de colores pro facilitar ______, definitiones, formulas e recapitos de travalio passate.

explicationes Signup and view all the answers

Associa le sequente personas con lor rolos mentionate in le texto:

Emmanuel Chauke = Autor de 'Maths Handbook and Study Guides' Mr. Chauke T.E = Mentor de Emmanuel Prof Gopal Raja = Un del lecturers passate de Emmanuel Dr K.Adem = Un del lecturers passate de Emmanuel Signup and view all the answers

Qual es un characteristic principal del scriptura de Emmanuel?

Claritate e simplicitate. (C) Signup and view all the answers

Emmanuel solmente adjuta studentes qui ama le mathematicas e le logica.

False (B) Signup and view all the answers

Que assecura Emmanuel con su travalio?

Es actualisate e convenibile pro cursos de calculo e studentes del Curriculum National. Signup and view all the answers

In le exemplo a), qual identitate trigonometric es usate pro simplificar le equation?

cos 2𝑥 = 1 − 2sin2 𝑥 (C) Signup and view all the answers

In le equation sin 𝑥 + 2 = 0 del exemplo a), il existe un solution valide pro 𝑥.

False (B) Signup and view all the answers

In le exemplo b), post substituer sin 2𝑥, que es le proxime passo pro solver le equation?

Subtraher $6\cos x$ e $3$ de ambe lateres. Signup and view all the answers

In le exemplo a), le factores del equation quadratic $2sin^2 x + 3 sin x - 2 = 0$ es $(2 sin x - 1)$ e $(sin x + ______)$.

2 Signup and view all the answers

Qual es le rango de $x$ in exemplo a)?

$-2π ≤ x ≤ 2π$ (B) Signup and view all the answers

In le exemplo b), le factor $(2 cos 𝑥 + 1)$ debe equalar a zero pro solver le equation.

True (A) Signup and view all the answers

In le exemplo b), que valor de `sin x` face le secunde factor equal a zero?

3 Signup and view all the answers

Combine le equation trigonometric con le passo initial associate pro solver lo:

cos 2𝑥 − 3 sin 𝑥 = −1 = Applica le identitate de angulo duple sin 2𝑥 + sin 𝑥 = 6 cos 𝑥 + 3 = Subtrahe terminos pro equalisar a zero 4cos2 𝑥 + sin 2𝑥 − 1 = 0 = Reorganisa e factorisa sin 2𝑥 + 2 sin 𝑥 + cos 2 𝑥 + cos 𝑥 = 0 = Factorisa per gruppos Signup and view all the answers

Qual del sequente es un proprietate de un function?

Asymptotas (D) Signup and view all the answers

Un function assigna a cata elemento x in un insimul D exactemente duo elementos in un insimul E.

False (B) Signup and view all the answers

Qual es le formato general de un function linear?

f(x) = mx + c Signup and view all the answers

Le insimul de tote le valores de output (valores de f(x)) de un function es appellate le ______.

ambito Signup and view all the answers

Associa le sequente conceptos con lor definitiones:

Dominio = Le insimul de tote le valores de input (x) pro un function. Ambito = Le insimul de tote le valores de output (f(x)) pro un function. Asymptota = Un linea que le graphico de un function approxima ma nunquam crucia. Periodo = Le intervallo super qual un function periodic repete su valores. Signup and view all the answers

Solver pro x: $tan(x) = 3$

$x = 1.23 + \pi k, k \in \mathbb{Z}$ (B) Signup and view all the answers

Si $cos(x) = -1$, alora $x = 0 + 2\pi k, k \in \mathbb{Z}$

False (B) Signup and view all the answers

Solve pro $x$: $2 sin x + cos x = 0$

x = 0.464 + πk , k ∈ ℤ Signup and view all the answers

Qual es le dominio del function $f(x) = \sqrt{x+4}$?

$[-4, \infty)$ (A) Signup and view all the answers

Es le rango del function $f(x) = 2x - 1$ con dominio $[-1, 1]$ equal a $[-3, 1]$?

True (A) Signup and view all the answers

Si $f(x) = x^2$ con dominio $[-1, 3]$, qual es le maximo valor del rango?

9 Signup and view all the answers

Pro le function $f(x) = \frac{x}{x-2}$, le function es indefinite quando $x$ es equal a ______.

2 Signup and view all the answers

Qual es le rango del function $f(x) = x^2$ con dominio $[-1,3]$?

$[0, 9]$ (B) Signup and view all the answers

Es le dominio del function $f(x) = \frac{x+1}{x-1}$ equal a $[1, \infty)$?

False (B) Signup and view all the answers

Qual es le valor de $f(2)$ pro le function $f(x) = \frac{2x + 1}{2x}$?

1.25 Signup and view all the answers

Apparea le functiones con lor dominio correspondente:

$f(x) = 2x - 1$, $-1 \leq x \leq 1$ = $[-1, 1]$ $f(x) = x^2$, $-1 \leq x \leq 3$ = $[-1, 3]$ $f(x) = \sqrt{x + 4}$ = $[-4, \infty)$ $f(x) = \frac{2x + 1}{2x}$, $1 \leq x \leq 4$ = $[1, 4]$ Signup and view all the answers

Flashcards

log e x

Equivalente a ln x, la logarithm natural de x.

Emmanuel Chauke

An informative tutor skilled in math and logic education.