1.1A Preview of Calculus What is Calculus? Calculus is the mathematics of CHANGE Calculus is a more...
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Transcript of 1.1A Preview of Calculus What is Calculus? Calculus is the mathematics of CHANGE Calculus is a more...
1.1 A Preview of Calculus
What is Calculus?
• Calculus is the mathematics of CHANGE
• Calculus is a more dynamic version of pre-calculus – more complex and applicable to real world situations – multidimensional
• Calculus is not a different math, it is a continuation of what you have already learned with applications to actual real world situations
1.1 A Preview of Calculus
Example 1
1.1 A Preview of Calculus
Example 2
1.1 A Preview of Calculus
Example 3
1.1 A Preview of Calculus
Example 4
1.1 A Preview of Calculus
Example 5
1.1 A Preview of Calculus
The 3 Main Ideas
• Limits – detailed curve sketching
• Derivatives – rates of change/slope of tangent lines
• Anti-Derivatives – area and volume of any shape or solid
1.1 A Preview of Calculus
Tangent Line Problem
1.1 A Preview of Calculus .1at 215 toline tangent theFind .1 2 xxxf
1.1 A Preview of Calculus .1at 215 toline tangent theFind .1 2 xxxf
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1
x
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215 2
x
x 13
1
22 2
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x
x mPQ
25.1
1.1
01.1
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65
2.4
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9.0
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999.0
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8.3
98.3998.3
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1.1 A Preview of Calculus
Area Problem
1.1 A Preview of Calculus
1.1 A Preview of Calculus
Pg. 46, 1.1 #1-11