5) Differentiation

Question 1

Describe the two special limits for exp(x)

Answer 1

Question 2

Describe the proof for

Answer 2

Question 3

What is the derivative of exp(x)

Answer 3

exp(x)

Question 4

Proof of derivative of exp(x)

Answer 4

Question 5

Are sin and cos even or odd functions

Answer 5

• sin(−α) = − sin(α) i.e. sin is an odd function
• cos(−α) = cos(α) i.e. cos is an even function

Question 6

What are some of the properties of sin and cos

Answer 6

Question 7

Describe the proof of the properties of sin and cos

Answer 7

Question 8

Describe the proof that sin and cos are continuous functions

Answer 8

Question 9

Describe a special limit for sin(x)

Answer 9

Question 10

Describe the proof of the speicial limit of sin(x)

Answer 10

Since both limx→0+ and limx→0− are equal to 1 we conclude the limit equals 1

Question 10

Describe the proof that sin(x) and cos(x) are differentiable

Answer 10