Answer:
- g(2.95) ≈ -1.8; g(3.05) ≈ -0.2
- A) tangents are increasing in slope, so the tangent is below the curve, and estimates are too small.
Step-by-step explanation:
(a) The linear approximation of g(x) at x=b will be ...
g(x) ≈ g'(b)(x -b) +g(b)
Using the given relations, this is ...
g'(3) = 3² +7 = 16
g(x) ≈ 16(x -3) -1
Then the points of interest are ...
g(2.95) ≈ 16(2.95 -3) -1 = -1.8
g(3.05) ≈ 16(3.05 -3) -1 = -0.2
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(b) At x=3, the slope of the curve is increasing, so the tangent lies below the curve. The estimates are too small. (Matches description A.)
D. Distributive Property
The distributive property allow you to multiply a sum by multiplying each addend separately.
Answer:
He would save $4.75.
Step-by-step explanation:
Without the pass,
In a month, Arnold has to spend: $2.50 x 20 = $50
With the pass,
In a month, Arnold has to spend: $45.25
So, Arnold may save: $50 - $45.25 = $4.75 if he has a monthly pass.
Answer: 1/36
Step-by-step explanation: 2/9 x 1/8 =2/72 = 1/36