11. Consider lim /x + 3.x→1(a) Show that |x +3 – 2| < |x – 1| if |x – 1| < 4. Hint: Multiplythe inequality by |/x +3+ 2| and observe that |/x +3+ 2| > 2.---(b) Find & > 0 such that |/x +3 – 2| < 10¬4 for |x – 1| < 8.--(c) Prove rigorously that the limit is equal to 2.

Answered: Image /qna-images/answer/4e9c6be0-aad3-4317-9146-900b8bb677fd.jpg

Answered: 11. Consider lim x + 3. x→1 (a) Show…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Similar questions

Suppose that lim x→0f(x)/x = 3. Thenlim x→−1f(x^2 + x)/(x^2 − x − 2) =(a) = −1 (b) = 1 (c) = 0 (d) does not exist (e) none of these
The limit as x approaches infinty of (x+3^x)/(x^2-3^x) Evaulate using L'Hospital's Rule providing a real solution
If (an) has limit −1 and (bn) tends to infinity, does it follow that only finitely many terms of (anbn) are positive?
Prove or disprove: If xn ≥ 0 for all n ∈ N and lim sup xn = 0, then xn → 0
Prove rigorously that lim (4 + 8x) = −4. x→−1
Is there a value of a for which limx1 3x^2+ax+a+3/x^2+x-2 exists? Enter the value of a if such a exist otherwise enter 0.
b) If (an) has limit−1 and (bn) tends to infinity, does it follow that only finitely many terms of (an bn) are positive?
Determine value for c so that lim f(x) x--> 3 exists f(x)= 1/3x+c For x<3 -x+8 For x>3
Consider the function f(x) = 1/x for x ∈ ℝ and 3 < x < 7. Prove that limx→5 f(x) = 1/5. using epsilon and delta method
Show that if xn ≤ yn ≤ zn for all n ∈ N, and if lim xn = lim zn = l, then lim yn = l as well.
1. Is it possible that f(2) = 5 but limx→2f(x) = 7? If so, what kind of function can satisfy this?
If f(x)=x2−9x−3 , what is limx→3+x2−9x−3 , limx→3−x2−9x−3, and f(3) ? Is f(x) continuous at 3?

SEE MORE QUESTIONS

Recommended textbooks for you

Calculus: Early Transcendentals

Calculus

ISBN:

9781285741550

Author:

James Stewart

Publisher:

Cengage Learning

Thomas' Calculus (14th Edition)

Calculus

ISBN:

9780134438986

Author:

Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher:

PEARSON

Calculus: Early Transcendentals (3rd Edition)

Calculus

ISBN:

9780134763644

Author:

William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher:

PEARSON

Calculus: Early Transcendentals

Calculus

ISBN:

9781285741550

Author:

James Stewart

Publisher:

Cengage Learning

Thomas' Calculus (14th Edition)

Calculus

ISBN:

9780134438986

Author:

Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher:

PEARSON

Calculus: Early Transcendentals (3rd Edition)

Calculus

ISBN:

9780134763644

Author:

William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher:

PEARSON

Calculus: Early Transcendentals

Calculus

ISBN:

9781319050740

Author:

Jon Rogawski, Colin Adams, Robert Franzosa

Publisher:

W. H. Freeman

Precalculus

Calculus

ISBN:

9780135189405

Author:

Michael Sullivan

Publisher:

PEARSON

Calculus: Early Transcendental Functions

Calculus

ISBN:

9781337552516

Author:

Ron Larson, Bruce H. Edwards

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS

11. Consider lim x + 3. x→1 (a) Show that |vx +3 – 2| < 51x – 1| if |x – 1| < 4. Hint: Multiply the inequality by |/x +3 + 2| and observe that |/x +3 + 2| > 2. - - (b) Find & > 0 such that |/x + 3 – 2| < 10¬4 for |x – 1| < 8. (c) Prove rigorously that the limit is equal to 2.