A number m plus 4 is greater than it equal to 7
1 answer:
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Answer:
- 6
- 9
- 1/8
- -10/11
Step-by-step explanation:
You can rewrite the given log expressions to express them in terms of ln(a), ln(b), and ln(c). Then substituting the given values will produce the value of the expression.
Or, you can define the variables 'a', 'b', and 'c' and let your calculator compute these directly.
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<h3>1.</h3>
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The applicable rules of logarithms are ...
- ln(ab) = ln(a) +ln(b)
- ln(a/b) = ln(a) -ln(b)
- ln(a^b) = b·ln(a)
- ln(a) = b ⇔ a = e^b
Of course, a square root is the same as a 1/2 power.
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
.