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.
Answer
A) one and three fourths
Step by step explanation
y = x^2 - x + 2
Here we have to use the formula.
The x coordinate of the vertex = -b/2a
Compare the given equation y = x^2 - x + 2 with the general form y = ax^2 + bx + c and identify the value of "a" and "b"
Here a = 1 and b = -1
Vertex of x coordinate = -b/2a, now plug in the value of a and b, we get
x = - (-1)/2(1)
x = 1/2
Now we have to find the y-coordinate of vertex.
Now plug in x = 1/2 in the given equation, we get
y = (1/2)^2 - 1/2 + 2
y = 1/4 - 1/2 + 2
y = 1 3/4
That is one and three fourths.
The answer is A) one and three fourths.
Thank you.
0.75^2 = 0.5625.....sq rt 0.5625 = 0.75
