Question

Lecture 3: Why is (cos(delta x) - 1) / (delta x) equal to 1-cos(theta) / theta ?

Answer 1

can you make your question clearer? (cos(delta x) - 1) / (delta x) is not the same as 1-cos(theta) / theta .

Answer 2

He is referring to the geometric proof that lim Δx -> 0 cos( Δx)-1/ Δx = 0 . In the lecture, during the geometric proof, what actually gets proven is lim θ ->0 1-cosθ/θ = 0. The professor then goes and explains that, 1 - cos θ/ θ = 0, then by multiplying both sides by -1, cos θ - 1 / θ is also zero.

Answer 3

Well, it is the same because the limit of the first term is 0, and the second term is simply the first term times -1, so it's no problem because -1 * 0 = 0

Answer 4

because -(cos(delta x) - 1) is exactly equal to (1-cos(delta x)). that makes no difference as -1*0 = 0