Rewrite 6 as a decimal number.
2 answers:
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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.)
The effective rate is calculated in the following way:
where r is the effective annual rate, i the interest rate, and n the number of compounding periods per year (for example, 12 for monthly compounding).
our compounding period is 2 since the bank pays us semiannually(two times per year) and our interest rate is 8%
so lets plug in numbers:
where r is the effective annual rate, i the interest rate, and n the number of compounding periods per year (for example, 12 for monthly compounding).
our compounding period is 2 since the bank pays us semiannually(two times per year) and our interest rate is 8%
so lets plug in numbers: