5) Differentiation Flashcards
1
Q
Describe the two special limits for exp(x)
A
2
Q
Describe the proof for
A
3
Q
What is the derivative of exp(x)
A
exp(x)
4
Q
Proof of derivative of exp(x)
A
5
Q
Are sin and cos even or odd functions
A
- sin(−α) = − sin(α) i.e. sin is an odd function
- cos(−α) = cos(α) i.e. cos is an even function
6
Q
What are some of the properties of sin and cos
A
7
Q
Describe the proof of the properties of sin and cos
A
8
Q
Describe the proof that sin and cos are continuous functions
A
9
Q
Describe a special limit for sin(x)
A
10
Q
Describe the proof of the speicial limit of sin(x)
A
Since both limx→0+ and limx→0− are equal to 1 we conclude the limit equals 1
10
Q
Describe the proof that sin(x) and cos(x) are differentiable
A