Question

Prove or give a counterexample: If f is continuous on R and differentiable on R∖{0} with...

Prove or give a counterexample: If f is continuous on R and differentiable on R∖{0} with limx→0 f′(x) = L, then f is differentiable on R.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

Please right in comment box if doubt is still there.

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Prove or give a counter example: If f is continuous on R and differentiable on R...
Prove or give a counter example: If f is continuous on R and differentiable on R ∖ { 0 } with lim x → 0 f ′ ( x ) = L , then f is differentiable on R .
Prove or provide a counterexample Let f:R→R be a function. If f is T_U−T_C continuous, then...
Prove or provide a counterexample Let f:R→R be a function. If f is T_U−T_C continuous, then f is T_C−T_U continuous. T_U is the usual topology and T_C is the open half-line topology
if f: D - R be continuous, and D is close, then F(D) is closed. prove...
if f: D - R be continuous, and D is close, then F(D) is closed. prove or give counterexample
Let f : R → R be differentiable with derivative f'. Prove that f(x + h)...
Let f : R → R be differentiable with derivative f'. Prove that f(x + h) = f(x) + f'(x)h + o(h), as h → 0.
Let f be continuous on [ 0 , ∞ ) and differentiable on ( 0 ,...
Let f be continuous on [ 0 , ∞ ) and differentiable on ( 0 , ∞ ) . If f ( 0 ) = 0 and | f ′ ( x ) | ≤ | f ( x ) | for all x > 0 , then f ( x ) = 0 for all x ≥ 0 .
if the function f is differentiable at a, prove the function f is also continuous at...
if the function f is differentiable at a, prove the function f is also continuous at a.
Theorem 4 states “If f is differentiable at a, then f is continuous at a.” Is...
Theorem 4 states “If f is differentiable at a, then f is continuous at a.” Is the converse also true? Specifically, is the statement “If f is continuous at a, then f is differentiable at a” also true? Defend your reasoning and/or provide an example or counterexample (Hint: Can you find a graphical depiction in the text that shows a continuous function at a point that is not differentiable at that point?)
4a). Let g be continuous at x = 0. Show that f(x) = xg(x) is differentiable...
4a). Let g be continuous at x = 0. Show that f(x) = xg(x) is differentiable at x = 0 and f'(0) = g(0). 4b). Let f : (a,b) to R and p in (a,b). You may assume that f is differentiable on (a,b) and f ' is continuous at p. Show that f'(p) > 0 then there is delta > 0, such that f is strictly increasing on D(p,delta). Conclude that on D(p,delta) the function f has a differentiable...
NOTE- If it is true, you need to prove it and If it is false, give...
NOTE- If it is true, you need to prove it and If it is false, give a counterexample f : [a, b] → R is continuous and in the open interval (a,b) differentiable. a) f rises strictly monotonously ⇐ ∀x ∈ (a, b) : f ′(x) > 0. (TRUE or FALSE?) b) f is constant ⇐⇒ ∀x∈(a,b): f′(x)=0 (TRUE or FALSE?) c) If f is reversable, f has no critical point. (TRUE or FALSE?) d) If a is a “minimizer”...
let F : R to R be a continuous function a) prove that the set {x...
let F : R to R be a continuous function a) prove that the set {x in R:, f(x)>4} is open b) prove the set {f(x), 1<x<=5} is connected c) give an example of a function F that {x in r, f(x)>4} is disconnected
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT