Finding a Region In Exercises 11-14, the integrand of the definite integral is a difference of two functions. Sketch the graph of each function and shade the region whose area is represented by the integral. ∫ − 2 1 [ ( 2 − y ) − y 2 ] d y
Finding a Region In Exercises 11-14, the integrand of the definite integral is a difference of two functions. Sketch the graph of each function and shade the region whose area is represented by the integral. ∫ − 2 1 [ ( 2 − y ) − y 2 ] d y
Solution Summary: The author analyzes the graph of each given function displaystyle 'underset' and the region to be shaded.
Finding a Region In Exercises 11-14, the integrand of the definite integral is a difference of two functions. Sketch the graph of each function and shade the region whose area is represented by the integral.
∫
−
2
1
[
(
2
−
y
)
−
y
2
]
d
y
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
Can you answer this question and give step by step and why and how to get it. Can you write it (numerical method)
Can you answer this question and give step by step and why and how to get it. Can you write it (numerical method)
There are three options for investing $1150. The first earns 10% compounded annually, the second earns 10% compounded quarterly, and the third earns 10% compounded continuously. Find equations that model each investment growth and
use a graphing utility to graph each model in the same viewing window over a 20-year period. Use the graph to determine which investment yields the highest return after 20 years. What are the differences in earnings among the three
investment?
STEP 1: The formula for compound interest is
A =
nt
= P(1 + − − ) n²,
where n is the number of compoundings per year, t is the number of years, r is the interest rate, P is the principal, and A is the amount (balance) after t years. For continuous compounding, the formula reduces to
A = Pert
Find r and n for each model, and use these values to write A in terms of t for each case.
Annual Model
r=0.10
A = Y(t) = 1150 (1.10)*
n = 1
Quarterly Model
r = 0.10
n = 4
A = Q(t) = 1150(1.025) 4t
Continuous Model
r=0.10
A = C(t) =…
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