Answer:
Step-by-step explanation:
It's D.
A theorem is true by some sort of mathematical logic.
It is not a definition. Not C
It is not in the end true because of inductive reasoning (a theorem may lend itself to inductive reasoning, but it must be proved.) Not A
It certainly not assumed to be true without proof. Not B
Answer:
4/6 and 6/9 us simlar as 2/3
Answer:
b = (log(y^45))/log(1/y^9) + (2 i π n)/log(1/y^9) for n element Z
Step-by-step explanation:
Solve for b:
(1/y^9)^b = y^45
Take the logarithm base 1/y^9 of both sides:
Answer: b = (log(y^45))/log(1/y^9) + (2 i π n)/log(1/y^9) for n element Z
Answer:
The principle will be "40295.63". A further explanation is given below.
Step-by-step explanation:
The given values are:
Total amount,
A = 99,000
Rate of interest,
R = 3%
Time period,
T = 30 years
= 360 months
As we know,
⇒ 
On substituting the values, we get
⇒ 
⇒ 
⇒ 
⇒ 
Answer:

General Formulas and Concepts:
<u>Calculus</u>
Limits
Limit Rule [Constant]: 
Limit Rule [Variable Direct Substitution]: 
Limit Property [Addition/Subtraction]: ![\displaystyle \lim_{x \to c} [f(x) \pm g(x)] = \lim_{x \to c} f(x) \pm \lim_{x \to c} g(x)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%20%5Cto%20c%7D%20%5Bf%28x%29%20%5Cpm%20g%28x%29%5D%20%3D%20%20%5Clim_%7Bx%20%5Cto%20c%7D%20f%28x%29%20%5Cpm%20%5Clim_%7Bx%20%5Cto%20c%7D%20g%28x%29)
L'Hopital's Rule
Differentiation
- Derivatives
- Derivative Notation
Derivative Property [Addition/Subtraction]: ![\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28x%29%20%2B%20g%28x%29%5D%20%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28x%29%5D%20%2B%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bg%28x%29%5D)
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Step-by-step explanation:
We are given the following limit:

Let's substitute in <em>x</em> = -2 using the limit rule:

Evaluating this, we arrive at an indeterminate form:

Since we have an indeterminate form, let's use L'Hopital's Rule. Differentiate both the numerator and denominator respectively:

Substitute in <em>x</em> = -2 using the limit rule:

Evaluating this, we get:

And we have our answer.
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits