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Leto [7]
3 years ago
9

Use Newton's method to find all solutions of the equation correct to six decimal places. (Enter your answers as a comma-separate

d list.) ln(x) = 1 /x − 3

Mathematics
1 answer:
Nata [24]3 years ago
7 0

Answer:

  x ≈ {0.653059729092, 3.75570086464}

Step-by-step explanation:

A graphing calculator can tell you the roots of ...

  f(x) = ln(x) -1/(x -3)

are near 0.653 and 3.756. These values are sufficiently close that Newton's method iteration can find solutions to full calculator precision in a few iterations.

In the attachment, we use g(x) as the iteration function. Since its value is shown even as its argument is being typed, we can start typing with the graphical solution value, then simply copy the digits of the iterated value as they appear. After about 6 or 8 input digits, the output stops changing, so that is our solution.

Rounded to 6 decimal places, the solutions are {0.653060, 3.755701}.

_____

A similar method can be used on a calculator such as the TI-84. One function can be defined a.s f(x) is above. Another can be defined as g(x) is in the attachment, by making use of the calculator's derivative function. After the first g(0.653) value is found, for example, remaining iterations can be g(Ans) until the result stops changing,

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7. The graph shows the height, h, in feet, of water
MariettaO [177]

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4 0
2 years ago
How to find an equation for a line through two given points?​
xz_007 [3.2K]

Answer:

The equation of the line is: y = 0.6x + 0.6

Step-by-step explanation:

Equation of a line:

The equation of a line has the following format:

y = mx + b

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Two points:

We have these following two points in this exercise:

x = -6, y = -3, so (-6,-3)

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3 = 0.6*4 + b

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The equation of the line is: y = 0.6x + 0.6

4 0
3 years ago
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Ostrovityanka [42]

Answer:

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olga nikolaevna [1]

Answer:

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Step-by-step explanation:

quadrant

1st  (-,+)

2nd (+,+)

3rd (-,-)

4th (+,-)

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3 years ago
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3 0
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