Question: Prove that if f: Rn Rm is differentiable at a Rn, then it is continuous at a.

Prove that if f: Rn → Rm is differentiable at a € Rn, then it is continuous at a.

Step by Step Solution

★★★★★

3.42 Rating (152 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

If is different... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Document Format (1 attachment)

Word file Icon

M-C-1.docx

120 KBs Word File

Students Have Also Explored These Related Calculus Questions!

Q:

Prove that if f and g are integrable on [a, b], then so are f g and f g (see Exercise 3.1.8).

Q:

Prove that if f is integrable on [0,1] and > 0, then for all a 1/n lim

Q:

Prove that if f is absolutely integrable on (l, ), then lime, f(x" ) dx=0.

Q:

4. Let f : Rn ---+ Rm be differentiable at a, and 9 : Rm ---+ R be differentiable at b = f(a). Prove that if g (b) is a local extremum of g, then '\1(g 0 f) (a) = O.

Q:

please solve #4 parts a - c asap ? 4. (18 points) In part (a), you do not need to justify your answer. a. (2 pts) Give an open cover of the set S = (1,3] that has no finite subcover. b. (8 pts)...

Q:

Suppose that f: Rn Rm is differentiable at a, and that g: Rm R is differentiable at b = f(a). Prove that if g(b) is a local extremum of g, then (g o f)(a) = 0.

Q:

4. [QUOTIENT RULE] Let f : Rn -> R be differentiable at a with f (a) f 0. (a) Show that for Ilhll sufficiently small, f(a+h) f 0. (b) Prove that D f(a)(h)/llhll is bounded for all h ERn \ {o}. (c)...

Q:

Suppose that a Rn that L Rm, and that f: Rn Rm. Prove that if f(x) L as x a, then there is an open set V containing a and a constant M > 0 such that ||f(x)||

Q:

Suppose f: Rn Rn is differentiable and has a differentiable inverse F -1: Rn Rn. Show that (f-1) I (a) = (fi (f-1(a)))-1.

Q:

im stuck here please solve this question Let f : Rn - Rm be given by f(x) = Ar + b where A is an m x n matrix and be Rm. Let S E Rm be convex. Prove that the set Q := {r ER" : f(x) ES} is convex

Q:

Marsfield Ltd and Ryde Ltd have provided the following information, which relates to the year ended 30 June 2021. Marsfield Ltd Ryde Ltd Industry Average Return on assets 12.31% 18.10% 15% Return on...

Q:

On July 31 ABC Company declared a $0.50 per share cash dividend to be paid on August 15 to shareholders of record on August 10. There were 100,000 shares of common stock authorized, 50,000 issued,...

Q:

which of the following js considered a performance obligation? A right of returnQuality assurance warranties on electronic productsUpfront registration feed for a gym membershipExtended warratnies on...

Q:

The acronym KPI relates to which of the following phrases? a. Key Profitability Indicator. b. Key Performance Indicator. c. Known Performance Increment. d. Known Profitability Increment.

Q:

What are the steps to solve this problem? Match the regression equation with the appropriate graph. Drag each graph given below to its corresponding regression equation to the right. 13. y= - 1.361x...

Q:

A company with n employees publishes an internal calendar, where each day lists the employees having a birthday that day. What is the probability that there is at least one day in the year when...

Q:

Formaldehyde is produced by the dehydrogenation of ethanol in a catalytic reactor. The following reaction takes place in the reactor: C H 3 O H HCHO + H 2 Methanol feed rate to the reactor is 5 0 kmo...