Answer:
Here we just want to find the Taylor series for f(x) = ln(x), centered at the value of a (which we do not know).
Remember that the general Taylor expansion is:
for our function we have:
f'(x) = 1/x
f''(x) = -1/x^2
f'''(x) = (1/2)*(1/x^3)
this is enough, now just let's write the series:
This is the Taylor series to 3rd degree, you just need to change the value of a for the required value.
<u><em>Answer</em></u>
<u><em>Explanation</em></u>
Based on the given conditions, formulate::
Substitute into
::
Rearrange variables to the left side of the equation:
Calculate the sum or difference:
Divide both sides of the equation by the coefficient of variable:
Cross out the common factor:
Let be the length of the two sides that are the same.
Then the third side would be .
The perimeter of the triangle will come from adding all of the sides together and setting it equal to the value given, .
That is,
As for the answer, the question was cut short, but with ,
the length of each of the common sides is , making the third side
, to get a total perimeter of
.
The hypotenuse of a right-angled triangle is its longest side, the base is its lower side, and the perpendicular, which stands next to the right angle, is its standing line.
You may determine the sides of a right-angled triangle using a number of techniques, such as the Pythagoras theorem or the triangle's perimeter.
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