differentiating exponentials and logarithms
DESCRIPTION
Differentiating exponentials and logarithms. A geometric approach to f(x)=e x. A geometric approach to f(x)=e x. A geometric approach to f(x)=e x. Do Q1, Q2, Q3, Q4, p.54. An algebraic approach to f(x)=e x. A definition for f(x)=e x. Calculating e. Integrating e x. Do Q5-Q11, p.54. - PowerPoint PPT PresentationTRANSCRIPT
Differentiating exponentials and logarithms
A geometric approach to f(x)=ex
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A geometric approach to f(x)=ex
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A geometric approach to f(x)=ex
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An algebraic approach to f(x)=ex
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Do Q1, Q2, Q3, Q4, p.54
A definition for f(x)=ex
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Do Q5-Q11, p.54
The natural logarithm
log ln , , 0.exp for xey e x x y y x y y
01ln
1ln e
nnen ln
Derivative of the natural logarithm
.1
ln ,0For x
xdx
dx
The proof is a consequence of the ‘mini-theorem’ outlined on p.55.
Do Exercise 4B, p.57
The reciprocal integral
.ln1
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x
This plugs a gap!!!
Do Exercise 4C, pp.58-59
Extending the reciprocal integral
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Do Q1, p.62Do Misc. Exercise 4, Q1-Q18, pp.62-64