Theorem 1 in Section 2.4 states the following: If (f) and (g) are continuous functions, then (f+g)

Question:

Theorem 1 in Section 2.4 states the following: "If $f$ and $g$ are continuous functions, then $f+g$ is continuous." Does it follow logically that if $f$ and $g$ are not continuous, then $f+g$ is not continuous?

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For answer-question

Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

See More Books

Question Posted: Jan 28, 2024 12:02 AM

See More Questions

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...
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...
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...
A Norman window has the outline of a semicircle on top of a rectangle. Suppose there are 8 + feet of wood trim available. Discuss why a window designer might want to maximize the area of the window....
A man doing push-ups pauses in the position shown in Fig. 9-84. His mass m = 75-kg. Determine the normal force exerted by the floor (a) On each hand; (b) On each foot. 30 cm mg 95 cm + 40 cm-
Small frogs that are good jumpers are capable of remarkable $\mathrm{BIO}$ accelerations. One species reaches a takeoff speed of $3.7 \mathrm{~m} / \mathrm{s}$ in $60 \mathrm{~ms}$. What is the...
For several years, the Otis Capital USA Corp has been exploring for gold on its mining claims held on public lands near the Idaho-Montana border. Otis filed a proposal to expand its current...
Sally Medavoy will invest $8,000 a year for 20 years in a fund that will earn 12% annual interest. If the first payment into the fund occurs today, what amount will be in the fund in 20 years? If the...
Required: Compute the annual dollar changes and percent changes for each of the following items. Round percent change to 1 decimal place. Current Year Prior Year Dollar Change Percent Change Cash...
Write out a proof by contradiction for this fact: There is no smallest positive rational number. Base your proof on the fact that if $r>0$, then \(0
The inverse of $A \Rightarrow B$ is the implication $eg A \Rightarrow eg B$. State the inverse of the Pythagorean Theorem. Is it true?
For the standard normal distribution, what is the area within two standard deviations of the mean?
Identify obstacles to coordination in a supply chain.
Inventory held to satisfy demand that is higher than forecast is known as safety backlog. safety capacity. safety inventory. safety sales.
What information does a master production schedule provide that an aggregate plan does not? Expense information for the planning period Revenue information for the planning period Specific product...
As the number of order cycles per season increases, the leftover inventory increases, but at a decreasing marginal rate. the leftover inventory increases, and at an increasing marginal rate. the...
What measures can a company employ to raise operational performance when information is distorted within the supply chain?
Word Wizard is a publishing company with a number of different book lines. Each line has contracts with a number of different authors. The company also owns a printing operation called Quick Press....
Information graphics, also called infographics, are wildly popular, especially in online environments. Why do you think infographics continue to receive so much attention? How could infographics be...
Use any test to determine whether the series is absolutely convergent, conditionally convergent, or divergent.
A series o an is defined by the equations a 1 = 1 Determine whether o an converges or diverges. 2 + cos n an+1
A series o an is defined by the equations a 1 = 1 Determine whether o an converges or diverges. 2 + cos n an+1
b) Explain two weaknesses of the featured network. Note that it is not enough to write that a certain network parameter is bad. Please explain the impact of the weak point. c) Modify the network so...
2. Consider the well with tunnel-barrier shown in the figure below. Assume the energy E is less than the well height V. a. Find the r and t coefficients at the second boundary x = = b. b. Find a...
5. Three identical wheels all have four 1 kg masses attached to their spokes. Each wheel has the four masses attached at different positions as shown in the diagram. Equal lengths of string are...

Theorem 1 in Section 2.4 states the following: If (f) and (g) are continuous functions, then (f+g)

Question:

Step by Step Answer:

No it does not logically follow that if f and g are not continuous then fg is not continuous The ...View the full answer

Calculus

Students also viewed these Mathematics questions