Question: Find the value(s) of a that make the following function f continuous everywhere. Justify your answer using limits. 1 a if x > a x

Find the value(s) of a that make the following function f continuous everywhere. Justify your answer using limits. 1 a if x > a x - a x (x - a) f(x) = 1 if x sa V8 - 7x3

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!

The general ledger of Zips Storage at January 1, 2024, includes the following account balances: Accounts Debits Credits Cash $26,300 17,100 Accounts Receivable Prepaid Insurance Land 15,400 165,000...

Section 1.5 1. Find values of a and b so that the following function is continuous everywhere. [5p] ax2 + b for x 2. 2. Use the Intermediate Value Theorem to show that the following equation [6p] 23...

Consider the piecewise function y=f(x) given below:\ Find the value of a that makes the function f continuous everywhere. Enter your answer as a fraction, in lowest terms, of the form (c)/(d) ....

Problem #1: Consider the function whose graph is given below. Evaluate the following limits. (3) xiiljh+xll (*0 nusre (A)doesnotexist (3)1 ((3)3 (IDno (low (3% (9)2 (Hm Problem #1(a): T Part (a)...

Find the value of k that makes the function f continuous on Justify your answer Jkx if x 2 3 if x 2 f x

1. (1 point) Find the value of the constant c that makes the 5. (1 point) Find a value of the constant &, if possible, at following function continuous on (-,). which f(s ) = cs+9 ifse (-, 8] f (x )...

please show work/steps clearly Evaluate the given limits. Exercise 1. [1 mark] x - 7 lim x-7 X Exercise 2. [3 marks] 2x2 - x - 15 lim x-+3 x2 - 9 Exercise 3. [3 marks] 1+ - lim x--1 1+x-8- -6 ( - 2,...

Problem 8. (1 point) 1 is discontinuous and state the type of discontinuity: x _ Determine the point at which the function f{x) : removable, jump, innite, or none of these. )7 : .1. Choose the type...

Exercise 1 1. Expand the logarithm Vx2 + 1 log( 100(x2 - 1)3) 2. Solve logz (x2 - 3) = 2. 3. Solve each equation for x. (a) 27-5 = 3. (b) In(a) + In(x - 1) = 1. Exercise 2 1. Find cosh(In x) and sinh...

3) Consider the function 5x-8, x 4 In each case, evaluate the given quantity or show it does not exist. If it is a limit that is not a number, write -00, 09, or DNE, and justify your answer.. (a) lim...

--gf b o] 5 & o * e For Exercises 5 - 10, determine if the function is continuous at the given value of . If the function is not continuous at x = c, also state the condition in the definition of...

Generation Xers are those people born roughly between 1965and 1981. As employees, Generation Xers tend to be more challengedwhen they can carry out tasks independently. This makes GenerationXers the...

Joanna Wu manages the University Lab Testing department within the University Hospital. Lab Testing, a profit center, performs most of the standard medical tests (such as blood tests) for other...

Scenario: Millions of electronic payments, checks, and wire transfers are processed every day across the country. Businesses need to pay their suppliers, employees need to receive their wages, and...

Suppose the Shelly Group (from problem 1) has identied two possible demand levels for copies per month: COPIES (PER MONTH) PROBABILITY 5,000.......... 50% 10,000........... 50% What is the expected...

The balance sheet for Plasma Screens Corporation and additional information are provided below. Additional Information for 2012: 1. Net income is $69,000. 2. Sales on account are $1,520,000. 3. Cost...

You are the new CEO of Dualjet, a company that makes expensive premium kitchen stoves for home use. You must decide whether to assemble the stoves in-house or to have a Mexican company do it. The xed...

Thomas More Company incurred the following costs during the current year in connection with its research and development activities. Cost of equipment acquired that will have alternative uses in...

Jims Camera shop sells two high-end cameras, the Sky Eagle and Horizon. The demand for these two cameras are as follows: DS = demand for the Sky Eagle, PS is the selling price of the Sky Eagle, DH is...

gantt charts provide a standard format for displaying schedule informationbu listing activities with their corresponding start and finish dates with a calender. Discuss the variations of the Gantt...

9. What is meant by the statement, the context is only relevant to us if we understand what it is trying to say?

7. What does it mean when we say that the words we use to denote a situation set limits on the solutions we can create at a later point?

8. Give examples from your own everyday life that the reference point you use has significance for the actions you take.