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Find all the points of discontinuity of the function $\frac{x^{2} - 23 x + 132}{x^{5} - 6 x^{4} - 37 x^{3} + 306 x^{2} - 504 x}$ .

Fescoisyncsibgyp8b 2022-04-10

Calculate all the points of discontinuity of $\frac{v^{2} - 23 v + 132}{(v^{2} - 4 v - 5) (v^{3} + 14 v^{2} + 55 v + 42)}$ .

London Ware 2022-04-10

Calculate all the points of discontinuity of $\frac{u^{2} - 11 u + 24}{(u + 3) (u^{3} - 8 u^{2} - 12 u + 144)}$ .

Kendal Day 2022-04-10

How do you multiply this radical equation, $\sqrt[3]{9} (\sqrt[3]{3} + \sqrt[3]{9})$ ?

Braden Hatfield 2022-04-10

Use the properties of logarithms to simplify the following function before computing $f^{'} (x) . f (x) = {{\ln (4 x + 3)}^{2} f}^{'} (x) =$

Kendal Day 2022-04-10

Unknown in logarithm base $\frac{122312}{100000} = {(1 + t)}^{5}$
I am new to exponents and logarithms, and have been stuck with this for a quite long time.
The problem is:
$\frac{122312}{100000} = {(1 + t)}^{5}$
or
$\log_{1 + t} \frac{122312}{100000} = 5$
I have no idea, how to solve this. Hints or tips would be very very welcomed.
Thank You (a lot) in advance!(also apologies for my poor english)

Osmarq5ltp 2022-04-10

As shown in the title, I want to show that if a rational function satisfies $h (t) = h (1 / t)$ , then h(t) can be express in the variable $1 + 1 / t$ , that is, $h (t) = f (t + 1 / t)$ for some rational function $f$ . Any help is apreciated.

Edith Mayer 2022-04-10

Solve $2 \log_{3} (x) - \log_{3} (x + 6) = 1$
just getting going with logarithms, having trouble with this question.
$2 \log_{3} (x) - \log_{3} (x + 6) = 1$
$\log_{3} x^{2} - \log_{3} (x + 6) = 1$
Stuck at this point: What do I do next?
$\log_{3} (\frac{x^{2}}{x + 6}) = 1$
Edit: Got it!
$\frac{x^{2}}{x + 6} = 3^{1}$
$\frac{x^{2}}{x + 6} = 3$
$x^{2} = 3 (x + 6)$
$x^{2} = 3 x + 18$
$x^{2} - 3 x - 18 = 0$
$(x - 6) (x + 3) = 0$
$x = 6$ and cannot equal $\neq 3$ as $2 \log_{3} (- 3) < 0$

hovudverkocym6 2022-04-10

Here is the problem.
A nonconstant rational function over the real numbers(a rational function is a function that can be expressed as $\frac{p (x)}{q (x)}$ , with $p (x)$ , $q (x)$ as polynomial function) $f (x)$ , is defined such that:
$(f (x))^{2} - a = f (x^{2})$ for all $x$ ( $a$ is a constant value)
Prove that $f (x)$ must be of the form $x^{k}$ for some constant $k$ .
I have an idea of how to prove it, but I can't do so rigorously. I can prove that any polynomial with more than 2 terms, or monomials, would not work. But I can't prove it won't work for any rational function.

Devin Dougherty 2022-04-09

How do you solve the integral of $\frac{\sqrt{x}}{\sqrt{x} + \sqrt{8 - x}} d x$ ?

George Michael 2022-04-09

I was trying to prove that

where w is a complex number with absolute value smaller than 1 and $r \in R$ , r<1. I saw some solution online, which says we substitute $w = m e^{i x}$ so that the LHS becomes ${(m - r)}^{2}$ . How is that true?
We have
$(w - r) (\overset{―}{w} - r) = (m e^{i x} - r) (m e^{- i x} - r) = e^{i x} e^{- i x} (m - r e^{- i x}) (m - r e^{i x}) = (m - r e^{- i x}) (m - r e^{i x})$

Jefferson Pacheco 2022-04-09

I want to simplify the following expression.
$Y = Bottom + \frac{Top - Bottom}{1 + 10^{((\log E C 50 - X))}}$
log is base of 10. Some may know that it's a dose response curve, and I want to solve for EC50.
I tried simplifying it but I forgot math long time ago and I couldn't find the answer online.
My problem was the exponential and logarithms part.
Can someone simplify the expression to solve for EC50?
Thank you very much.
Edit : And if someone could explain simplifying exponential and logarithm on this one, it would be great as well. I forgot all the math and I would appreciate it.

Alessandra Carrillo 2022-04-09

How to simplify $\frac{\log_{2} 625}{\log_{2} 125}$

Christopher Stone 2022-04-09

How to prove the inequality
$\frac{1}{n} + \frac{1}{n + 1} + \dots + \frac{1}{2 n - 1} \geq \log (2) ?$

Lisa Cooper 2022-04-09

Use identities to simplify ${\log (a^{2} + b^{2})}^{2}$
Use logarithmic identities to simply the following:
${\log (a^{2} + b^{2})}^{2}$
I started with
${\log (a^{2} + b^{2})}^{2} = 2 \cdot \log (a^{2} + b^{2})$
I think it's not the final result, but I don't know how to proceed. Any hints would be helpful.

Jasiah Vincent 2022-04-09

Use complex variables to find the sum of the Fourier Series:
$\sin (θ) + \frac{\sin (2 θ)}{2^{2}} + \frac{\sin (3 θ)}{2^{3}} + \dots$
where $θ$ is a real variable.

wadiad6qxb 2022-04-09

Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places, $\log_{40.863}$

Quinn Dean 2022-04-08

Find the product of the complex numbers $z_{1} = 1 + i$ and $z_{2} = 2 + 2 i$ . Leave answers in polar form.

Deja Vaughn 2022-04-08

I'm in doubt on simplifying the expression: $\log_{2} 6 - \log_{4} 9$
Working on it I've got: $\log_{2} 6 - \frac{\log_{2} 9}{2}$
There's anyway to simplify it more ? I'm learning logarithms now so I'm not aware of all properties and tricks.
Thanks in advance

Ekwadorkadba3 2022-04-08

How to simplify this?
$\frac{n^{\log m}}{m^{\log n}}$

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