All categories

3 years ago

Find the linear approximation of f(x)=lnx at x=1 and use it to estimate ln(1.38).

1 answer:

5 0

$\bf f(x)=y=ln(x)\qquad 
\begin{cases}
x=1\\
y=ln(1)\to y=0
\end{cases}\\\\
-----------------------------\\\\
\left. \cfrac{dy}{dx}=\cfrac{1}{x} \right|_{x=1}\implies 1\impliedby m
\\\\\\
\textit{now, we know that }
\begin{cases}
x=1\\
y=0\\
m=1
\end{cases}\implies y-0=1(x-1)\implies y=x-1$

now, you're asked to use it when ln(1.38), which is just another way of saying x = 1.38

so set x = 1.38 and see what "y" is

You might be interested in

A consumer looking to buy a used red Miata car will call dealerships until she finds a dealership that carries the car. She esti

Alona [7]

Answer:

(a) <em>X</em> = number of dealerships the customer needs to call before she finds a used red Miata car.

(b) <em>X</em> = 1, 2, 3, 4,...

(d) The expected number of dealerships would we expect her to call until she finds one that has the car is 3.57.

(e) The probability that she must call at most 4 dealerships is 0.7313.

(f) The probability that she must call 3 or 4 dealerships is 0.2497.

Step-by-step explanation:

(a)

The random variable <em>X</em> can be defined as the number of dealerships the customer needs to call before she finds a used red Miata car.

(b)

The values that the random variable <em>X</em> can assume are:

<em>X</em> = 1, 2, 3, 4,...

(c)

The random variable <em>X</em> is defined as the number of trials before the first success. Each trial is independent of the others. And each trial has a similar probability of success.

This implies that the random variable <em>X</em> follows a Geometric distribution.

The probability of success, i.e. the probability that any independent dealership will have the car is <em>p</em> = 0.28.

Thus, the distribution of <em>X</em> is, $X\sim Geometric\ (p=0.28)$ .

(d)

The expected value of a Geometric distribution is:

$E(X)=\frac{1}{p}$

Compute the expected number of dealerships would we expect her to call until she finds one that has the car as follows:

$E(X)=\frac{1}{p}$

$=\frac{1}{0.28}\\$

$=3.57$

Thus, the expected number of dealerships would we expect her to call until she finds one that has the car is 3.57.

(e)

Compute the probability that she must call at most 4 dealerships as follows:

P (X ≤ 4) = P (X = 1) + P (X = 2) + P (X = 3) + P (X = 4)

$=\sum\limits^{4}_{x=1}{(1-0.28)^{x-1}\times 0.28}\\=0.28+0.2016+0.1452+0.1045\\=0.7313$

Thus, the probability that she must call at most 4 dealerships is 0.7313.

(f)

Compute the probability that she must call 3 or 4 dealerships as follows:

P (X = 3 or X = 4) = P (X = 3) + P (X = 4)

$=[(1-0.28)^{2-1}\times 0.28]+[(1-0.28)^{4-1}\times 0.28]\\=0.14515+0.10451\\=0.24966\\\approx0.2497$

Thus, the probability that she must call 3 or 4 dealerships is 0.2497.

6 0

3 years ago

Help I don’t get this

Gekata [30.6K]

Answer:

2.)4n>(n/2)^2

3. (The problem isn't clear)

4.)n^2+2n-3=129

5.)n-5=171

Step-by-step explanation:

2.)

4n(four times the number) >(larger than) (n/2)^2 (half the number squared)

4.)

Sum=addition

n^2 (number squared) +2n (twice the number)-3=129

5.)

N(unknown number of pages) -5(amount of pages already read)= 171(the number of pages it took her to finish)

8 0

2 years ago

The graph of the parent function f(x) = x3 is transformed such that g(x) = f(–2x). How does the graph of g(x) compare to the gra

Gnoma [55]

Every x value is multiplied by 3, expanding the graph

4 0

3 years ago

1. What should be done to these equations to solve the system of equations by elimination? 2+y=12 5x - 3y = -3

atroni [7]

<h3>Answer:</h3><h3>Multiply the first equation by 3</h3>

<h3>explanation</h3>

To solve a simultaneous equation using elimination method, you eliminate one variable first.

Before you can do that, the coefficient of one of the variable in the two equations must be same.

From the questions, for the coefficient of one variable in the two equations to be thesame, we multiply the first equation by 3.

If we do this, the coefficient of Y in the two equations will now be 3.

So that the correct option is

<h2>Multiply the first equation by 3</h2>

3 0

2 years ago

The points shown on the graph represent the numbers in

dedylja [7]

Answer: 3

Step-by-step explanation:

cause I said so :) mark brainliest pls

6 0

2 years ago