# Let f be a function so that (below). Which must be true? I. f is continuous at x=2 II. f is differentiable at x=2 III. The derivative of f is continuous at x=2 (A) I (B) II (C) I & II (D) I & III (E) II & III

##
#lim_(h->0)(f(2+h)-f(2))/h=5#

(C)

Now, looking at the statements:

I: True

Differentiability of a function at a point implies its continuity at that point.

II: True

III: False

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

(D) I & III

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

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.

- How do you evaluate the limit #w/(1/(-1+w)+1)# as w approaches #0#?
- How do you compute the limit of #cot(4x)/csc(3x)# as #x->0#?
- How do you find the limit of #(x ^ 3)(e ^ (-x ^ 2))# as x approaches infinity?
- What is an example l'hospital's rule?
- How do you evaluate the limit #(2tan^2x)/x^2# as x approaches #0#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7