Lim ((sin(pi(cosx)))/(x^2)) as x->0

Both the numerator and denominator approach 0, so by L'Hopital's rule

Using the fact that

we find

as , and , so the limit is π/2.

(I'm wondering if there's a way to do this without L'Hopital's rule, in case you haven't learned it yet...)

25/4

step-by-step explanation:

call segment cd's length x. because dc and ab are parallel, angle acd and cab, so triangles adc and abc are similar and we can set up the equation x / ac = ac / ab, or x / 5 = 5 / 4 and x = 25/4.