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.