lim (cos(π/4 + h) - cos (π/4))
h->0 _________________________
h
Somehow I ended up with cos(1).
lim (cos(π/4 + h) - cos (π/4)) / h
h->0
A store bought a toy rocket at a cost of $40 and marked it up 25%. Ronnie bought it and paid 10% sales tax. What was his total cost?
To evaluate the limit expression, we can use the fundamental trigonometric limit:
lim (θ -> 0) (sin(θ) / θ) = 1.
Let's apply this limit to our expression.
First, let's rewrite the numerator:
cos(π/4 + h) - cos(π/4) = [cos(π/4)cos(h) - sin(π/4)sin(h)] - cos(π/4)
Now, rearranging the terms:
= cos(π/4)(cos(h) - 1) - sin(π/4)sin(h)
Next, let's simplify further:
= (1/√2)[cos(h) - 1] - (1/√2)sin(h)
Now, let's substitute h=0:
= (1/√2)[cos(0) - 1] - (1/√2)sin(0)
= (1/√2)(1 - 1) - (1/√2)(0)
= 0
Therefore, the limit of the expression as h approaches 0 is 0, not cos(1). It seems there might have been an error in your calculations.