Use Theorems 14 to show that the function is continuous. (x) = x sin x THEOREM 1

Question:

Use Theorems 1–4 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

THEOREM 2 Continuity of Polynomial and Rational Functions Let P and Q be polynomials. Then: P and Q are

THEOREM 3 Continuity of Some Basic Functions y = x/" is continuous on its domain for n a natural number. sin

THEOREM 4 Continuity of Composite Functions If g is continuous at x = c, and f is continuous at x = g(c),

ƒ(x) = x sin x

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

Step by Step Answer:

Related Book For book-img-for-question

Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

See More Books

Question Posted: Oct 28, 2023 04:58 AM

See More Questions

Use Theorems 14 to show that the function is continuous. (x) = x + sin x THEOREM 1 Basic Laws of Continuity If f and g are continuous at x = c, then the following functions are also continuous at x =...
Use the Laws of Continuity and Theorems 2 and 3 to show that the function is continuous. 7. f(x) = x + sin x 9. f(x) = 3x + sin x 11. f(x) = 1 / x2 + 1
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...
How will you sort 1 PB numbers? 1 PB = 1000 TB.
1. Ignore the problem. Jacobss contributions to new product development are too valuable to risk losing him, and the problems over the past 10 years have always worked themselves out anyway. No sense...
Pullman Corp issued 10-year bonds four years ago with a coupon rate of 9.375 percent. At the time of issue, the bonds sold at par. Today bonds of similar risk and maturity must pay an annual coupon...
What are some strengths and weaknesses of ERP studies?
Jason and Kerri Consalvo, both in their 50s, have $50,000 to invest and plan to retire in 10 years. They are considering two investments. The first is a utility company common stock that costs $50...
calculate a Break even level of sales. Total sales revenue $ 4,350,000 Variable Costs cost of sales $ 2,233,000 Bank charges $ 8,950 Direct wages $ 653,000 Electricity $ 82,000 Freight $ 45,333 Sales...
Evaluate the limit using the Basic Limit Laws and the limits (t + 2)/2 lim 1-7 (t + 1)2/3
Suppose that Show that exists and equals 4. lim tg(t) = 12. 1-3
Some economists call for predetermined rules to guide the actions of government policy makers. What are two contrasting rationales that have been given for such rules?
Sravani Bought an audio CD containing 1 0 0 audio files , 1 0 of which are by S . P . Balasubrahmanyam . Assume the shuffle option is enabled to play the songs in random order. What is the...
Kroger Co. is one of the largest retail food companies in the United States as measured by total annual sales. The Kroger Co. operates supermarkets, convenience stores, and manufactures and processes...
time complexity of the following algorithm forn-1 to n-1 do for je +1 to n do Print & for Kn-3 to n+4 do print k
There are various compounds and epoxies that have been used to "final bed" rifle stocks. In your opinion, which is the best and why? Does this depend on the material of the stock? If so, why? Conduct...
Taylor Series: Problem 3 Previous Problem Problem List Next Problem 8 (5 points) Write the Taylor series for f(x) = x about x = 2 as C, (x 2)". Find the first five coefficients. n=0 - Co= C1= C2= C3=...
Briefly explain Fiedler's LPC contingency model.
Show that the peak of the black body spectrum as a function of ? is given by eq. (22.14) kg T Wmax = 2.82
Until the mid-eighteenth century when spinning became mechanized, cotton was an expensive and relatively unimportant textile (Virginia Postrel, What Separates Rich Nations from Poor Nations? New York...
During recessions, U.S. firm lay off a larger proportion of their workers than Japanese firm do. (It has been claimed that Japanese firms continues to produce at high levels and store the output or...
Many corporations allow CEOs to use the firms corporate jet for personal travel (see the Mini- Case Company Jets in Chapter 7 for more details). The Internal Revenue Service (IRS) requires that the...
The equity section of Cyril Corporation's balance sheet shows the following: $ 250,000 Preferred stock6% cumulative, $25 par value, 10,000 shares issued and outstanding ......... Common stock-$8 par...
1-3. Complete the t-accounts below using the transactions listed (1.5 pts). 4. Calculate the ending balance of each account (.5 pts). styx. issues a $1,000 bond in order to raise cash styx. issues...
Please Help with part " B " Concord Corporation makes backpacks, with a specialty line for baseball players. This backpack has a spot for everything - helmet, spikes, glove, and bats - and it comes...

Use Theorems 14 to show that the function is continuous. (x) = x sin x THEOREM 1

Question:

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 and f-g (iii) fg (ii) kf for any constant k (iv) f/g if g(c) #0

Step by Step Answer:

The polynomial function x is continuous by Theorem 2 and th...View the full answer

Calculus

Students also viewed these Mathematics questions