Match each function in column A with the most appropriate rule to use for differentiating the function. [ 1 . 5 , 1 . 6 ] Column B a. Extended Power Rule b. Product Rule c. Sum Rule d. Different Rule e. Power Rule f. Quotient Rule g ( x ) = x + 9
Match each function in column A with the most appropriate rule to use for differentiating the function. [ 1 . 5 , 1 . 6 ] Column B a. Extended Power Rule b. Product Rule c. Sum Rule d. Different Rule e. Power Rule f. Quotient Rule g ( x ) = x + 9
Match each function in column A with the most appropriate rule to use for differentiating the function.
[
1
.
5
,
1
.
6
]
Column B
a. Extended Power Rule
b. Product Rule
c. Sum Rule
d. Different Rule
e. Power Rule
f. Quotient Rule
g
(
x
)
=
x
+
9
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.
A driver is traveling along a straight road when a buffalo runs into the street. This driver has a reaction time of 0.75 seconds. When the driver sees the buffalo he is traveling at 44 ft/s, his car can decelerate at 2 ft/s^2 when the brakes are applied. What is the stopping distance between when the driver first saw the buffalo, to when the car stops.
Topic 2
Evaluate S
x
dx, using u-substitution. Then find the integral using
1-x2
trigonometric substitution. Discuss the results!
Topic 3
Explain what an elementary anti-derivative is. Then consider the following
ex
integrals: fed dx
x
1
Sdx
In x
Joseph Liouville proved that the first integral does not have an elementary anti-
derivative Use this fact to prove that the second integral does not have an
elementary anti-derivative. (hint: use an appropriate u-substitution!)
1. Given the vector field F(x, y, z) = -xi, verify the relation
1
V.F(0,0,0) = lim
0+ volume inside Se
ff F• Nds
SE
where SE is the surface enclosing a cube centred at the origin and having edges of length 2€. Then,
determine if the origin is sink or source.
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