Use Newton's Method to approximate the zero(s) of the function. Continue the iterations until two successive approximations differ by less than 0.001. Then find the zero(s) to three decimal places using a graphing utility and compare the results. f(x) = x − 2 x + 6

Step-by-step explanation:

The Newton's Method to approximate the zeros is useful, despite the fact that it might not work. The key point here is find tangent lines, and applying that formula again and again till it gets closer to the roots.

It fits for any polynomial equation even though it is much more used, to higher degree polynomial.

*For the function given, f(x)=x-2x+6,  since the root is an integer, 6, in few trials we'll find the root, all of them bigger than 0.001 so let's replace th

1) Check graph below.

2) Taking a closer look,  to f(x)=-x+6 we can see that the root is between x=5 and x=7, we already know is -6.

Let's try x=7

Call it

Plugging into the formula:

In this function, the root is an integer, all the approximations were integer numbers and  larger than 0.001.

On the other hand, if the function had irrational roots then we could easily show results lesser than 0.001.

add all the numbers and check the ones place.

the answer is 486. as the ones place is more than 4, the estimation will be the next 10 ie, 490

"it's not the heat, it's the humidity".   that's a partly valid phrase you may have heard in the summer, but it's actually both.   the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature.   this has important considerations for the human body's comfort.   when the body gets too hot, it begins to perspire or sweat to cool itself off.   if the perspiration is not able to evaporate, the body cannot regulate its temperature.   evaporation is a cooling process.   when perspiration is evaporated off the body, it effectively reduces the body's temperature.   when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases.   in other words, the human body feels warmer in humid conditions.   the opposite is true when the relative humidity decreases because the rate of perspiration increases.   the body actually feels cooler in arid conditions.   there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

step-by-step explanation: