Explanation:
The notation means we apply the dilation to some point (x,y) to move it to
. Each coordinate has been multiplied by 4 which is the scale factor. This only works when we center the dilation around the origin. The "O" in
refers to "origin". It's not the number zero.
So to go from preimage to image, we multiply by 4. To go in reverse, we divide by 4.
G' is at (-8,4). Divide each coordinate by 4 to get (-2,1) which is where point G is located.
The equation of the tangent line at x=1 can be written in point-slope form as
... L(x) = f'(1)(x -1) +f(1)
The derivative is ...
... f'(x) = 4x^3 +4x
so the slope of the tangent line is f'(1) = 4+4 = 8.
The value of the function at x=1 is
... f(1) = 1^4 +2·1^2 = 3
So, your linearization is ...
... L(x) = 8(x -1) +3
or
... L(x) = 8x -5
The sum of the first five terms is 11/2
<h3>How to determine the sum?</h3>The series is given as:
1/2, -1,2,-4…
Calculate the common ratio of the series using
r = -4/2
Evaluate
r = -2
The sum is then calculated as:
This gives
Evaluate
Evaluate
Hence, the sum of the first five terms is 11/2
Read more about series at:
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