Answer:
A. FALSE
B. TRUE
C. FALSE
D. NOT POSSIBLE TO DETERMINE
Step-by-step explanation:
(A) FALSE. since the power series ∑ has radius of convergence |-4|=4 ans 7> 4 which is beyond its radius of convergence. thus by the theorem of power series, the series diverges at 10.
(B)TRUE. since the radius of convergence of the power series ∑ must be at least |-4| = 4 and 3 lies within this radius, thus it converges at x=3
(C)FALSE the series does not diverge at x=1, since 1 is within its radius of convergence |-4| = 4
(D)NOT POSSIBLE TO DETERMINE
At x=6, it is beyond its radius of convergence but has not attain its divergence point. thus it is not possible to determine.
The value of f(g(2)) is 2.
<h3>What is function?</h3>
An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
The given table is
x f(x)
–6 1
–3 2
2 5
5 3
8 0
If the coordinates of a function f(x) is defined as (x,y)
then, the coordinates of inverse of f(x) is defined as (y,x).
f(g(y))= f(x) [ g(x)= (y,x)]
f(g(y))= y
So, If g(x) is the inverse of f(x), the f(g(y)) = y.
Also, we know g(x) is the inverse of f(x), then f(g(2)) = 2.
Learn more about this concept here:
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The slope is 2. Use the slope formula (Y2-Y1/X2-X1) to find it, or count the rise over run.
The lowest common denominator of 6 and 10 is 30.