Suppose that g: IR is differentiable at x = xo. Does the following limitg(xo +6h) - g(xo - 6h)12hexist? (Either prove your answer or give a counterexample).limh→0Is the converse true? That is suppose the limitlimh→0g(xo +6h)-g(xo - 6h)12h= Lexists, is g differentiable at x = xo? (Either prove your answer or give a coun-terexample).

Answered: Image /qna-images/answer/fe5df4d1-272c-4ab1-904f-e197a559ac6f.jpg

Answered: Suppose that g : I → R is…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

4. Suppose F: R" → R? is of the form F(r) = (f(x), g(x)), TE R". (i) Show that lim F(r) = (a,b) if and only if lim f(r) = a and lim g(x) = b. (ii) Show that F is continuous at ro if and only if f and g are both continuous at 1o-
A function f(r) is said to have a jump discontinuity at z= a if. 1. lim f(r) exists. 2. lim f(z) exists. エat 3. The left and right limits are not equal. Let f(z) = (7z-6, if z<7 if z 27 Show that f(1) has a jump discontinuity at z= 7 by calculating the limits from the left and right at r = 7. lim f(1) = lim f(1)= zラ74 Now, for fun, try to graph f(r).
Provide the General Solution of each differential equations. Box your Final Answer and show your solutions:
H. B. B. A. A show that EA=AE
4. Find the following limits or determine that they do not exist: 1+1/x a. lim,0 1+1/x? 1+1/x2 b. lim,→0 1+ 1/x 1+1/(x – 1) 2+1/(x – 1)2 c. lim→1
5. Let c e R and suppose f,g : R → R are functions such that lim→c ƒ(x) exists, and for some e > 0, |g(x)| < |f(x)| whenever |x – c| < e. Explain why lim [sin (x – c)g(x)] exists. State explicitly any theorem or result that you are using in your argument.
For which value of c, the limit lim f(x) exists? x→6 C = f(x) = 6x + c -4x+7 if x < 6 if x ≥ 6
Evaluate the limit of (d)
Given lim f(x)=L, Im fx)=L, and L, =L, 1. lim f(x)=L, II. lim f(x)=L, III. lim f(x) does not exist
5. Let f, 9: R → R. In each case, give a counterexample to show that the given statement is false. (a) If lim f(r) = o and lim g(r) = 0 then lim [f(r)g(x)] = 0. エ→ (b) If lim f(r) = and lim g(x) = 0 then lim [f(r)g(x)] = o0 エ→ (c) If lim f(r) = 00 and lim g(x) = 00 then lim f(x) = 1. g(x) = o then lim [f(x) – g(x)] = 0. (d) If lim f(r) = 00 and lim g(r)
Consider the following. = - {x²- -3 f(x) -2 - 2 -1 if x + 1 if x = 1 y -1 -3 1 2 X Use the graph to find the limit below (if it exists). (If an answer does not exist, enter DNE.) lim f(x) X→ 1
3. Evaluate lim f(x), given that: x→3 A • lim f(√x) = 4 x→9 the function f is continuous over (-∞0,00). Hint: If g(x)=√x, then lim f(√x) = lim f(g(x)) = 7-9 7-9

SEE MORE QUESTIONS

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS

Suppose that g : I → R is differentiable at x = xo. Does the following limit g(xo +6h) — g(xo – 6h) 12h exist? (Either prove your answer or give a counterexample). lim h→0 Is the converse true? That is suppose the limit lim h→0 g(xo +6h)-g(xo - 6h) 12h = L