Consider the two functions f(x) and g(x), where f(x) = 2x and g(x) is graphed below. Graph of g(x)

Compare the rate of change of the two functions on the interval 2 ≤ x ≤ 3.

The rate of change of the function g(x) is greater than f(x).
The rate of change of the function f(x) is greater than g(x).
The rate of change of the function f(x) and g(x) are the same.

The slope of the graph is 2 .

So the rate of change of g(x) is 2, just like f(x).

In fact, g(x) is also = 2x, just like f(x) .

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step-by-step explanation:

ik this stuph and i am smart donkey

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}