Calculus 6.1 day 1

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4.1 Antiderivatives and Indefinite
Integration (Part II)
Greg Kelly, Hanford High School, Richland,
Washington
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Objectives

• Write the general solution of a differential
  equation.
• Find a particular solution of a differential
  equation.

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General solution for various values of C for
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To find a particular solution, you need to know
the value of yF(x) for one value of x. This
information is called an initial condition.
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Find the particular curve that passes through the
point (2,4).
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Find the general solution of
Find the particular solution that satisfies the
initial condition F(1)0.
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A ball is thrown upward with an initial velocity
of 64 ft/sec from an initial height of 80 feet.
a.) Find the position function giving the height
as a function of the time t.
Using the formula
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A ball is thrown upward with an initial velocity
of 64 ft/sec from an initial height of 80 feet.
a.) Find the position function giving the height
as a function of the time t.
Without using the formula
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A ball is thrown upward with an initial velocity
of 64 ft/sec from an initial height of 80 feet.
When does the ball hit the ground?
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Examples
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Examples
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Homework

• 4.1 (page 250)
• 43-63 odd
• 67, 71-79 odd