If an initial amount A0 of money is invested at an interest rate i compounded times a year, the value of the investment after t years is If we let n = 8, that is referred to as the continuous compounding of interest. Use L' Hospital's Rule to show that if interest is compounded continuously, then the amount after years is A=A0eit
Answers
Answer:
Following are the solution to the given point:
Step-by-step explanation:
Please find the comp[lete question in the attached file.
Given:
[tex]\bold{ \lim_{n \to \ \infty} (1+ \frac{r}{n})^{nt} =e^{rt}}[/tex]
In point 1:
[tex]\to y = (1+ \frac{r}{n})^{nt}[/tex]
In point 2:
[tex]\to \ln (y)= nt \ln(1+ \frac{r}{n})[/tex]
In point 3:
Its key thing to understand, which would be that you consider the limit n to[tex]\infty[/tex], in which r and t were constants!
[tex]=lim_{n \to \ \infty} \ln (y) = lim_{n \to \ \infty} nt \ln(1+\frac{r}{n})\\\\= lim_{n \to \ \infty} \frac{\ln(1+\frac{r}{n})}{\frac{1}{nt}}\\\\= lim_{n \to \ \infty} \frac{\frac{-r}{\frac{n^2}{(1+\frac{r}{n})}}}{- \frac{1}{n^2t}}\\\\= lim_{n \to \ \infty} \frac{\frac{rn^2t}{n^2}}{(1+\frac{r}{n})}\\\\= lim_{n \to \ \infty} \frac{rt}{(1+\frac{r}{n})}\\\\= \frac{rt}{(1+\frac{r}{0})}\\\\=rt[/tex]
In point 4:
[tex]\to \lim_{n \to \ \infty} = (1+\frac{r}{n})^{nt}[/tex] and
[tex]\to \lim_{n \to \ \infty} = A_0e^{rt}[/tex]
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:.
It is a right angle. All right angles equal 90°. So the two angles add up to 90
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Answers
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Answers
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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Answer:
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♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
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The expression for the quadratic function will be y = -4x² + 24x - 32.
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a numerical or constant quantity placed before and multiplying the variable in an algebraic expression.
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Step-by-step explanation:
Free Brainlyest for who says bababoi first
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bababoi .. yay I did something
Answer:
bababoi
Step-by-step explanation:
bababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoivbababoibababoibababoibababoibababoibababoibababoibababoivbababoibababoibababoibababoibababoibababoibababoibababoioibababoibababoivbababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoi
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Step-by-step explanation:
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Step-by-step explanation:
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Answers
Answer:
x = 31.8
Step-by-step explanation:
From the picture attached,
By applying Pythagoras theorem in right ΔADC,
AC² = AD² + CD²
(22)² = AD² + (16)²
AD² = 484 - 256
AD = √228
= 2√57
Now we apply Pythagoras theorem in right ΔADB,
AB² = AD² + DB²
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altitude of the given triangle that has solid lines.
x is approximately 31.812
Reasons:
The figure shows a triangle with an altitude that forms two triangles inside
the main triangle.
By Pythagoras's theorem, we have;
For the right triangle on the left;
22² = h² + 16²
h² = 22² - 16² = 228
h² = 228
h = √228 = 2·√57
h = 2·√57
In the right triangle to the right, we have;
The length of the top base, b = 44 - 16 = 28
The square of the hypotenuse, x² = h² + b²
∴ x² = 228 + 28² = 1012
x = √(1012) = 2·√253
x = 2·√253 ≈ 31.812
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https://brainly.com/question/6241683
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Answers
Answer:
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Step-by-step explanation: