Find the values of x for which the series converges. (enter your answer using interval notation.) [infinity] (x + 7)n n = 1

x belongs to (-8,-6)

Step-by-step explanation:

Given is a series in x as

we find that first term is x+7 and each successive term is multiplied by x+7

In other words this is a geometric series with common ratio as

An infinite geometric series converges only for

|r|<1

Hence here we have if series converges,

For all values of x lying in the open interval (-8,-6) the series converges.

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation:

he answer is x=1x3 because x=1 to x=3