Each of these limits correspond to the derivative of some function f(x) at a point x = a.
Recall the limit definition of a function f(x) :
f '(x) = lim [h → 0] ( f(x + h) - f(x) ) / h
Then if x = a, we get
f '(a) = lim [h → 0] ( f(a + h) - f(a) ) / h
From here, it's easy to identify what each function and point should be:
(a) f (a + h) = (1 + h)¹ʹ³ → f(x) = x ¹ʹ³ and a = 1
(that's a 1/3 in the exponent)
(b) f (a + h) = cos(π + h) → f(x) = cos(x) and a = π
(c) f (a + h) = 5 (4 + h)⁵ → f(x) = 5x ⁵ and a = 4
(d) f (a + h) = exp(4h) = exp(4 (0 + h)) → f(x) = exp(4x) and a = 0
(where exp(x) = eˣ )
