Question: Prove that if (x) is continuous at x = a and g(y) is continuous at y = b, then F(x, y) = (x)g(y) is continuous

Prove that if ƒ(x) is continuous at x = a and g(y) is continuous at y = b, then F(x, y) = ƒ(x)g(y) is continuous at (a, b).

Step by Step Solution

★★★★★

3.42 Rating (158 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Given that fx is continuous at x a we know that lim fx fa xa and ... 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 Calculus 4th Questions!

Q:

Prove that if x is irrational, then 1/x is irrational.

Q:

If one attempted to dualize the notion of free module over a ring R (and called the object so defined "co-free") the definition would read: An R-module F is co-free on a set X if there exists a...

Q:

What are some examples of conventions, mores, and laws found in U.S. society?

Q:

[14 marks] Working with functions. In this question, we will explore various properties of functions. You may want to review the basic definitions and terminology introduced on pages 15-16 of the...

Q:

nitial value. Is function rule by using the rate of change (constant 1 . Given the following table, X 0 2. Given the following table, f (x) 1 1 1 3 2 4 1 3 4 0 3 x 9 27 81 g (x ) 4 12 20 28 36 Type...

Q:

10, p= d( x )= 300-6x2 x = # of thosands of consoles P = dollars Find average rate of change as demand goes from sooo to 7000 console's 1. f (x ) = $4xis if xEs Kx 2 if x 75 for what value of K will...

Q:

Help me with this legendre equation. THE QUESTION IS IN THE LAST PIC. QUESTION IS NOT INCOMPLETE JUST FOLLOW THE STEPS IN THE REFERENCE PICS. \fRecurrence formulas Differentiate the generating...

Q:

8 What does it mean that a function is continuous at a point x a Give definition and check whether the function f x is continuous at the points and x 0 x 1 if f x left begin array cl 2 x Y 3 text if...

Q:

Please help with the following question on Continuity I. (a) Given / (x) = + 2x-3 x- 1 (i) Determine the region where f (x) is continuous. Express your answer in interval notation. [2] (ii) Redefine...

Q:

Help please. Problems 17 -32, find the limits, if they exist, for the given piecewise-defined functions. x+3, x 17. lim f (x) x-2+ 21. lim f (x) 25. lim_g(x) 29. lim g (x) Problems 17 32, find the...

Q:

Prove the domination laws in Table 1 by showing that a) A U = U. b) A = .

Q:

Suppose that two players A and B are trying to throw a basketball through a hoop. The probability that player A will succeed on any given throw is p, and he throws until he has succeeded r times. The...

Q:

Which of the following cannot help reduce overfitting in decision trees: a . pruning ; b . make sure each terminal node has very few observations ( in training set ) ; c . restrict the depth of the...

Q:

=+Fines incurred (external failure cost) 1500 3000 Training in marine park regulations for new staff members 4500 2000 1000 Regular inspections to ensure that boat motors are not releasing oil into...

Q:

Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. If the sequence is...

Q:

Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. If the sequence is...

Q:

Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. If the sequence is...

Q:

Required information Problem 04-49 (LO 04-3) (Algo) [The following information applies to the questions displayed below.] Jacob is a member of WCC (an LLC taxed as a partnership). Jacob was allocated...

Q:

what is the value of gamma after thr following statements execute

Q:

Fatal Inc. manufactures parachutes. Fixed and variable manufacturing cost pools are allocated to each parachute using budgeted assembly hours. Budgeted assembly time is 4 hours per unit. The...