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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Is pi/pi irrational

dedylja [7]

Answer:

No, $\frac{\pi}{\pi}$ is 1 which can be written as $\frac{1}{1}$ . The definition of rationals is any number that can be written as a ratio of an integer to an integer where the bottom integer is not 0.

Step-by-step explanation:

$\frac{\pi}{\pi}=1$ since $1(\pi)=\pi$ .

Rational numbers included anything that can be written as a fraction where the top and bottom are integers (bottom integer is not 0).

1 can be written many different ways. It can be written as $\frac{1}{1}$ .

Both the numerator and the denominator of the rewrite of one that I did are integers.

The integers include the following numbers:

{...,-4,-3,-2,-1,0,1,2,3,4,...}.

The integers are the whole numbers and the opposite of the whole numbers.

The whole numbers are {0,1,2,3,4,...}.

The opposite of the whole whole numbers are {...,-4,-3,-2,-1,0}.

3 0

4 years ago

Explain why (–4x)0 = 1, but –4x0 = –4.

hodyreva [135]

Any number raised to power of 0 is 1.
In (-4x)^0, because of the parenthesis, the whole number is being raided to 0, which gives 1.
But in -4x^0, only x is being raised to 0, thus -4x^0 = -4(1) = -4.

5 0

3 years ago

Find the distance between the two points in simplest radical form (4,6) and (-2,9)

MrRa [10]

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{4}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{9})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d = \sqrt{(-2-4)^2+(9-6)^2}\implies d = \sqrt{(-6)^2+3^2}\implies d = \sqrt{36+9} \\\\\\ d = \sqrt{45}\implies d = \sqrt{9\cdot 5}\implies d=\sqrt{3^2\cdot 5}\implies d = 3\sqrt{5}$

6 0

3 years ago

Jessica is going to a vegetable shop. She buys some lady fingers for $23, some potatoes for $30,

mario62 [17]

Answer:

$89

Step-by-step explanation:

add all the numbers together

6 0

3 years ago

If y=kx, where k is a constant, and y=24 when x=6, what is the value of y when x=5

Phoenix [80]

I hope this helps 24 = k * 6 4 = k y = kx y = 4x y = 4 * 5 y = 20

6 0

3 years ago