Question

the limit represents the derivative of some function f at some number a. state f and a.
lim (sin(pai/2 + t)-1)/t
t->0

Answer 1

Since df/dx = lim(t->0) [f(x+t)-f(x)]/t

f(a+t) - f(a) = sin(pi/2 + t) - sin(pi/2)

Looks like we have f(x) = sin(x) and a = pi/2