Homework Help With Calculus?

Question

Suppose: lim f((3+h) - f(3)) / h = 5
h 0
which of the following must be true? May be more than one correct answer. Please explain why?

a) lim f(x) =5
x 3

b) f is continuous at x=3

c) f'(3)=5

d) none of the above

Answer 1

b
since above lim =f '(3)
so if derevative of a function exists at a point then the function has to be continuous at that point.

Answer 2

The correct answer is b) , What you have above is the calculation of the derivative of f(x) from the definition an the point x = 3.Since this exists and is finite the function is continuous at that point

Answer 3

c

Your limit is that of a difference quotient, which is in fact the definition of a derivative. h acts as delta x and 3 acts as x in the equation.