Question: Show that the function is continuous on (-, ). Jx* sin(1/x) ifx + 0 if x = 0 f(x) =

Show that the function

Jx* sin(1/x) ifx + 0 if x = 0 f(x) =


is continuous on (-∞, ∞).

Jx* sin(1/x) ifx + 0 if x = 0 f(x) =

Step by Step Solution

★★★★★

3.28 Rating (174 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

f x x 4 sin1x is continuous on 0 0 since it is the product of a ... 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

Students Have Also Explored These Related Precalculus Questions!

Q:

Show that the function is continuous for x 1, 2. Then compute the right- and left-hand limits at x = 1, 2, and determine whether f (x) is left-continuous, right-continuous, or continuous at these...

Q:

Show that the function f(x):= 1/x2 is uniformly continuous on A: = (1, ), but that it is not uniformly continuous on B: = (0, ).

Q:

If f is continuous on [a, b], show that

Q:

Value Theorem may Pa 9. lim f(x) = 1 10. lim f(x) = f(0) x-+0 alue 1 11. lim f(x) = 2 x-2 x - 2 + 12. lim f(x) = 3 1 /( ) 13. lim f(x) does not exist. 14. lim f(x) = 3 x- 5 In Exercises 15-20, refer...

Q:

(A). The following function is an example of a "not nice" function. Using your graphing calculator (e.g., TI 83 or 84) or if you have access to some other graphing tool, graph the following function:...

Q:

11. [-/6 Points] DETAILS Consider this function y = f(x) on the domain (-co, co). f ( x ) = x2 sin( >)+ 16 ifx # 0 16 if x = 0 (a) If x+ 0 , f '(x)= 2x sin x - 5 cos n X (b) Answer these multiple...

Q:

can i get help 5-6 The graph of a function f is given. (a) At what numbers a does lim x-a f(x) not exist? (b) At what numbers a is f not continuous? (c) At what numbers a does lim x-a f(x) exist but...

Q:

can i get help with this please 5-6 The graph of a function f is given. (a) At what numbers a does lim x-a f(x) not exist? (b) At what numbers a is f not continuous? (c) At what numbers a does lim...

Q:

These are the practice problems for the final exam, the answers are there, I just want to know how to solve them? So can you please show to me the solving steps for each question! MATH 1720/1760...

Q:

Use Theorems 14 to show that the function is continuous. THEOREM 1 Basic Laws of Continuity If f and g are continuous at x = c, then the following functions are also continuous at x = C: (i) f + g...

Q:

A hot-air balloon must support its own weight plus a person for a total weight of 1300 N. The balloon material has a mass of 60 g/m2. Ambient air is at 25°C and 1 atm. The hot air inside the...

Q:

Determine c ER so that the following is not a spanning set for RX2. Justify your answer! 2 {[13_1],[ 33 - C- -2 C- 1 22] [20- 2c3 c +2, 2c 2c + 2 C 2 1 +2] [- + } ] } -c +3 -3 -c-2

Q:

28.96

Q:

Define secondary air pollutants and give an example.

Q:

(a) Program a calculator or computer to use Euler's method to compute y(1) where y(x)is the solution of the initial-value problem dy/dx + 3x2y = 6x2 y(0) = 3 (i) h = 1 (ii) h = 0.1 (iii) h = 0.01...

Q:

The figure shows a circuit containing an electromotive force, a capacitor with a capacitance of C farads (F), and a resistor with a resistance of R ohms (). The voltage drop across the capacitor is...

Q:

Use the direction field labeled II (above) to sketch the graphs of the solutions that satisfy the given initial conditions. (a) y(0) = 1 (b) y(0) = 2 (c) y(0) = - 1

Q:

Marketing 19-26 In which stage of the creative selling process would the salesperson say. "what quantity would you like to order?" Which of the following is the best example of a direct channel? The...

Q:

How can Rupert hedge his dollar exposure with a currency futures contract? What is the difference between a futures contract and a forward contract? Does the currency futures contract need to be...

Q:

Question 5: If X0CHF/USD=1.17 and then one year later X1CHF/USD=0.97 by how many percent did the USD appreciate/depreciate relative to the CHF ? 5.63%2.30%17.09%12.80% Question 6 2 pts Question 6: If...