For a continuous function (let's say f(x)) at a point x=c, is f(c) the limit of the function as x tends to c? Please explain.

Answer 1

Yes, by definition

One commonly used definition for a function #f# being continuous at a point #c# is that #f# is continuous at #c# if
#lim_(x->c)f(x) = f(c)#
(note that this definition implicitly requires #lim_(x->c)f(x)# and #f(c)# to exist)
As the question #f(x)# being continuous at #c# as a given, that means all necessary conditions for #f(x)# being continuous at #c# must be true, in particular, #lim_(x->c)f(x) = f(c)#.
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

Yes, for a continuous function f(x) at a point x=c, f(c) is indeed the limit of the function as x tends to c. This is known as the continuity property of functions. In simpler terms, if a function is continuous at a specific point, it means that the value of the function at that point is equal to the limit of the function as x approaches that point.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7