Using Different MethodsIn Exercises 47–50, find d w / d t (a) by using appropriate Chain Rule and (b) by converting w to a function of t before differentiating. w = sin x + y 2 z + 2 z , x = arcsin ( t − 1 ) , y = t 3 , z = 3
Using Different MethodsIn Exercises 47–50, find d w / d t (a) by using appropriate Chain Rule and (b) by converting w to a function of t before differentiating. w = sin x + y 2 z + 2 z , x = arcsin ( t − 1 ) , y = t 3 , z = 3
Solution Summary: The author explains how to calculate the derivative of w=mathrmsinx+y2z+2z with respect to t.
Using Different MethodsIn Exercises 47–50, find
d
w
/
d
t
(a) by using appropriate Chain Rule and (b) by converting
w
to a function of
t
before differentiating.
w
=
sin
x
+
y
2
z
+
2
z
,
x
=
arcsin
(
t
−
1
)
,
y
=
t
3
,
z
=
3
With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.
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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