Precalculus Solutions | Expert Assistance for Problems & Examples

Find the value of $\log \frac{a + b i}{a - b i}$

Kinsley Moon 2022-01-24

Why is $\frac{\cos (α + β) + \cos (- α)}{\sin (α + β) + \sin (- α)}$ independent of $α$ ?

poveli1e 2022-01-24

Write $\cos^{2} (x)$ as linear combination of $x \mapsto \sin (x)$ and $x \mapsto \cos (x)$

Lainey Goodwin 2022-01-24

Consider the following equality:
$a_{1} \sin (x) + a_{2} \sin^{2} (x) + \dots + a_{n} \sin^{n} (x) = a_{1} \sin (x) + a_{2} \sin (2 x) + \dots + a_{n} \sin (n x)$
where $a_{1}, a_{2} \dots, a_{n} \in C, n \in N$
This equality clearly holds for n=1 and for any $a_{1} \in C$ . The trivial equality ( $a_{1} = a_{2} = \dots = a_{n} = 0$ ) also holds.
Do there exists any other solutions? If so, are there infinitely many of such solutions?
Do there exist other solutions if we constrain the domain of coefficients to Q, R or Z?

Mlejd5 2022-01-24

Find the number of roots of the equation, $x^{3} + x^{2} + 2 x + \sin x = 0$ in $[- 2 π, 2 π]$

Jessie Jenkins 2022-01-24

Reaching upon 9=1 while solving x for $3 \tan (x - 15^{\circ}) = \tan (x + 15^{\circ})$
Substituting $y = x + 45^{\circ}$ , we get
$3 \tan (y - 60^{\circ}) = \tan (y - 30^{\circ})$
$3 \frac{\tan y - \sqrt{3}}{1 + \sqrt{3} \tan y} = \frac{\tan y - \frac{1}{\sqrt{3}}}{1 + \frac{1}{\sqrt{3}} \cdot \tan y}$

$3 (\tan^{2} y - 3) = 3 \tan^{2} - 1$

9=1

The solution provided by the book $x = n π + \frac{π}{4}$ fits, so why did i get 9=1?

Rudy Koch 2022-01-24

If $2 (\sin a + \cos a) \sin b = 3 - \cos b$ , then find $3 \tan^{2} a + 4 \tan^{2} b$
I doubt there is a solution on the internet now, but they do have a number 35 as the final answer.
My tiny little progress:
Use simple simplification,
$3 \tan^{2} a + 4 \tan^{2} b = \frac{3}{\cos^{2} a} + \frac{4}{\cos^{2} b} - 7$
Intuitively, in order to get this, the given equation should be squared. But that is where I got stuck, because the term cosb seems hard to handle; it just seems different from other terms.

Berasiniz1 2022-01-24

Finding value of $\int_{0}^{\infty} \frac{x \sin x}{{(x^{2} + 1)}^{3}} d x$

Maximus George 2022-01-24

$x^{2} + y^{2} + x y = 1$ , then find the minimum of $x^{3} y + x y^{3} + 4$

Hailee Cline 2022-01-24

Volume of a solid $y = \cos (x)$ and y=0 for the interval $0 \leq x \leq \frac{π}{2}$
I used method of shells to get:
$2 π \int_{0}^{\frac{π}{2}} x \cos (x) d x$
And I got:
$2 π \int_{0}^{\frac{π}{2}} x \cos (x) d x = 2 π {[x \sin (x) + \cos (x)]}_{0}^{\frac{π}{2}}$
$= 2 π [\frac{π}{2} \sin (\frac{π}{2}) - \cos (0)]$
$= 2 π (\frac{π}{2} - 1)$
$2 π \int_{0}^{\frac{π}{2}} x \cos (x) d x = π^{2} - 2 π$
Then I am doing it by method of slicing and got this as an answer

Duncan Reed 2022-01-23

What is the continuity of the composite function $f (g (x))$ given $f (x) = \frac{1}{x - 6}$ and $g (x) = x^{2} + 5$

Kinsley Moon 2022-01-23

How to simplify the ratio $\frac{1 - \cos 2 x + i \sin 2 x}{1 + \cos 2 x - i \sin 2 x}$

treslagosnv 2022-01-23

I have troubles with such limit
$lim_{(x, y) \to (0, 0)} \frac{x^{3}}{y^{4} + 2 \sin^{2} x}$
I approach on any line or curve I get limit equal to 0. I try polar coordinates - also nothing, still 0. I try to bound it somehow - I get infinity. However, wolfram tells that there is no limit for the function in (0,0)

Connor Randall 2022-01-23

Evaluating $lim_{x \to 0} {(\sin x)}^{x}$

Alex Cervantes 2022-01-23

How do you evaluate $C_{4}^{6}$ ?

Gabriela Duarte 2022-01-23

How many 4 person committees are possible from a group of 9 people if ?
A) there are no restrictions?
B) Both John and Barbara must be on the committee?
C) Either John or Barbara (but not both) must be on the committee?

meteraiqn 2022-01-23

How do you find the $(f \circ g \circ h) (x)$ for $f (x) = \frac{x - 2}{2 x + 1}, g (x) = 3 x + 1, h (x) = x^{2}$ ,

Branden Valentine 2022-01-23

How do you find (f of g of h) if $f (x) = x^{2} + 1$ and $h (x) = x - 1$ ?

siutulysr5 2022-01-23

How do you find the composition of function given $f (x) = \sqrt{x + 8}$ and $g (x) = 4 x + 1$

kejpsy 2022-01-23

What is the continuity of the composite function $f (g (x))$ given $f (x) = \sin x$ and $g (x) = x^{2}$ ?

Precalculus problems and solutions are hard to find online even though this topic is quite popular among college students majoring in Engineering. Keeping this fact in mind, we decided to provide you with a list of questions and answers that will help you with various precalculus problems. Regardless if it is related to equations or any other problem, these precalculus problems and composite functions examples and solutions below will help you see the logic and compare solutions as you check your original task.

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