How do you use the limit definition of the derivative to find the derivative of f(x)=1/x?

1 answer:

6 0

Example 1. Let us start with the functionf(x) = x2. We have

So

which means f '(a) = 2a.

What about the derivative of f(x) = xn. Similar calculations, using the binomial expansion for (x+y)n (Pascal's Triangle), yield

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A survey of 1,000 men and women asked, "Do you earn over $50,000 per year?" The table below shows the responses for males and fe

Ierofanga [76]

Given:
Do you earn over $50,000 per year?

Male Female Total
Income over 50,000 475 375 850
Income below 50,000 75 75 150
Total 550 450 1,000

Yes, "being female" and "earning over 50,000" are independent events. Independents events are events that happen where the probability of one event happening is not affected by the happening of the other event.

In this case, regardless if you are male or female, you can earn over 50,000.
Also if you are female, you either earn under or over 50,000

6 0

4 years ago

Read 2 more answers

Gonzalez Manufacturing borrowed $. Part of the money was borrowed at %, part at %, and part at %. The annual interest was $

Pavel [41]

Answer:

The answer is "rate 12%, 14%, 16% and value 4000, 10000, and 7000".

Step-by-step explanation:

Let the value is x, y, and z. so,

The value of x amount will be borrowed at 12% $= \frac{12}{100} \times x= 0.12x$

The value of y amount will be borrowed at 14% $= \frac{14}{100} \times x= 0.14x$

The value of z amount will be borrowed at 16% $= \frac{16}{100} \times x= 0.16x$

If the total amount= 21000

$\to x+y+z=21000$

If the total interest= 3000

calculating the total interest:

$\to 0.12x +0.14y +0.16z = 3000$

The overall amount borrowing at 12% and 14% was half as much as the amount borrowed at 16%.

$\to x + y = 2z\\\\\to x + y - 2z = 0$

by calculating the value we have 3 equations that are:

$\to x+y+z=21000\\\\\to 0.12.x +0.14.y +0.16z = 3000\\\\\to x + y - 2z= 0\\$

calculate the matrix by above-given value:

$\left[\begin{array}{ccc}1&1&1\\0.12&0.14&0.16\\1&1&-2\end{array}\right]$ $\left[\begin{array}{c}x&y&z\\ \end{array}\right] =\left[\begin{array}{c}21000&3000&0\\ \end{array}\right]$