Question: 1. Let f: R -> R be the function defined by f(x)= (xsin(1/ x)) if x # 0 if x=0 Show that whether fis differentiable

1. Let f: R -> R be the function defined by

1. Let f: R -> R be the function defined by f(x)= (xsin(1/ x)) if x # 0 if x=0 Show that whether fis differentiable at x = 0

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock 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

Students Have Also Explored These Related Mathematics Questions!

Q:

Let f : R - R be the function defined by f (2 ) = 2x - 1 if x 1. Show that f is differentiable at 1 and compute f'(1). As always, carefully justify your work

Q:

please help 5. For a function f : A - B and subsets E and F of B, prove f-'(E - F) = f-'(E) -f-'(F). 6. Let f : R - R be the function defined by f(x) = x2 + ax + b, where a, be R. Determine whether f...

Q:

Problem 2(*): Let f : R - R be a function defined as f (x) = if & E Q 4x -4 if x 2 Q. Prove, using the definition of the derivative, that f is differentiable at x = 2 and find f' (2)

Q:

Q-2: 14+4] a) Let f: R -> R be a function defined as f (x) = 3x3-4. Determine whether the function is one to one. b) Find the inverse of the following function g (x) = (x + 4)/(2x - 5)

Q:

5. Does the following equation specify a function with an independent variable x? If yes, find the domain of the function. If not, explain briefly. (a) y(x + y) = 4 (b) x(x + y) =4 (c) x3 - yz = 0...

Q:

1. Let f be a differentiable scalar-valued function defined on an open subset of R". Sup- pose 5: R + R" has the property that flo(t)) = c for all t for some constant c. Prove that (1) o(t)) is...

Q:

Question 2 (a) Letf be the function defined on (-co,co) by f(x)=Je *#0 Construct an argument to determine whether fis differentiable at 0. (6 marks) (b) x(x+1) Let y Find dy 2 + sin 2x in terms of x...

Q:

Please show steps on how to solve this question Problem #11: A real-valued function g(x, y, z) is called a harmonic function in a region D CR if it satisfies the Laplace [8 marks] Equation V-g = V.Vg...

Q:

3. Answer two of the following three questions: (a) Let f: R - R be a function defined by X f (x) = HE XA x2 + 1' Is f one-to-one? (b) If f: X - Y and g: Y - Z are functions and go f is one-to-one,...

Q:

5. Let f: [-1,1] R be a function which satisfies |f(x)| x for every x = [-1, 1]. Show that f is differentiable at 0 and find f'(0).

Q:

Admin Assist provides office services to tradesmen needing admin support, including: Live reception and messaging services Email and small marketing services (e.g. development of flyers or client...

Q:

How does an increase in the minimum wage impact employment levels, prices, and economic growth?

Q:

Fill in the blanks and write two pages about the Excel document. 0 Increase in Costs Scenario: Assumptions: Fixed operating costs in dollars $ 85,000,000 Growing at 10% per year over the life of the...

Q:

To prevent against losing all four of these important assets, compose a report. Malaysian legislation must be mentioned to substantiate each degree of protection. For each law, the text and how it...

Q:

4. I try to make them feel what I really mean (1 is related to the visionary, 2 to the logical, 3 to action and 4 to the emotional).

Q:

4. What is the goal of the others in the network?

Q:

2. What we can learn from the past