Homework Statement
In my book, there is a formula that gives the amount (in grams) of Radium in a jar after t years (100 grams were initially stored):
R = 100⋅e-0.00043⋅t
The book asks me to sketch the graph of the equation. I decided to find a point where the time elapsed equals the...
Homework Statement
\lim\limits_{x \to 0} \left(\ln(1+x)\right)^x
Homework Equations
Maclaurin series:
\ln(1+x) = x - \frac{x^2}{2} + \frac{x^3}{3} + ... + (-1)^{r+1} \frac{x^r}{r} + ...
The Attempt at a Solution
We're considering vanishingly small x, so just taking the first term in the...
I've already completed the first question, but with number two, it's a different case. Here's my attempt:
\frac { d{ v }_{ y } }{ dt } \quad =\quad -g\quad -\quad \beta { v }_{ y }\\ \frac { d{ v }_{ y } }{ -g\quad -\quad \beta { v }_{ y } } \quad =\quad dt\\ \int { \frac { d{ v }_{ y } }{...
Homework Statement
f(x) = 1/ln (10-x) -- I would assume it to be a fairly simple equation, but I am screwing it up
Homework Equations
What is f'(x)?
The Attempt at a Solution
f'(x) = (ln (10-x))^-1
= -(ln (10-x))^-2 * -1 * 1/(10-x) -- 2 negatives cancel out
= 1/(10-x)...
Homework Statement
I posted a picture of it and my attempt it is number 3
Homework Equations
The Attempt at a Solution
I tried using log properties and I am not sure what went wrong and how to arrive at the correct answer.
Mod note: Messy, disorganized image deleted.
Homework Statement
By taking the natural logarithms of each side, that this equation can be linearized by making a semi logarithmic plot. Identify the variables and state what the slope , and y-intercept would represent.
Homework Equations
F=Fo*e^-(d/cτ)
The Attempt at a Solution
I tried...