1
Q
At a point on an open interval, define the derivative
A
2
Q
A
3
Q
Requirement for derivative (limits)
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4
Q
A
5
Q
A
6
Q
The set of all continuously differentiable functions on (a,b)
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7
Q
A
8
Q
A
9
Q
A
10
Q
A
11
Q
A
12
Q
A
13
Q
A
14
Q
A
15
Q
A
16
Q
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17
Q
A
18
Q
Right derivative of f at point x
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19
Q
The left derivative of f at point x
A
(The one to the right of ‘and’)
20
Q
Quotient rule
A
Where f and g are differentiable functions
21
Q
Corollary to Fermat’s theorem? Give example
A
F does not have to be differentiable at the point where it has a local extremum.
Eg:
f(x) = |x| attains (global) min at x=0
But f’(0) doesn’t exist
22
Q
Taylor expansion of exp(x)
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23
Q
Taylor expansion of sin(x)
A
24
Q
Taylor expansion of cos(x)
A
25
Taylor expansion of log(1+x)
26
Asymptotic expansion of f, a function defined in a neighbourhood of x_0 €**R**
27
Asymptotic expansion of (below) as x -> 0
28
Compute first 3 non trivial terms of Taylor expansion
29
Requirements for Taylor’s formula to be valid
f€cn(a,b) and x_0 must be in (a,b)
KCL Real Analysis
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