ILL MAKE MOST BRAINLIEST PLZ HELP!!!
2 answers:
Step-by-step explanation:
The slope would be 4 (because in y=mx+b form, m = slope)
The y-intercept would be zero (0,0) since b = y-intercept, and there is no b in this equation.
From (0,0) you would rise four to get (0,4) and go over to the right one (1,4)
To make another point, you could go down 4 from (0,0) to get (0,-4) and to the left one to get (-1,-4)
Hope this helps.
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Answer:
The Taylor series is .
The radius of convergence is .
Step-by-step explanation:
<em>The Taylor expansion.</em>
Recall that as we want the Taylor series centered at its expression is given in powers of
. With this in mind we need to do some transformations with the goal to obtain the asked Taylor series from the Taylor expansion of
.
Then,
Now, in order to make a more compact notation write . Thus, the above expression becomes
Notice that, if x is very close from 3, then y is very close from 0. Then, we can use the Taylor expansion of the logarithm. Hence,
Now, substitute in the previous equality. Thus,
<em>Radius of convergence.</em>
We find the radius of convergence with the Cauchy-Hadamard formula:
Where stands for the coefficients of the Taylor series and
for the radius of convergence.
In this case the coefficients of the Taylor series are
and in consequence . Then,
Applying the properties of roots
Hence,
Recall that
So, as we get that
.