Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Let f be an increasing, continuous and differentiable function on R and let g(x) = f(x) = f(x - 1). Suppose that there is m> 0 such that f'(x) > m, for all a R. Show that g(n) diverge. Hint: Note that since f is increasing, then g(x) > 0. Let sn = g(1) + g(2) + ..+g(n). We need to show that sn +∞ as n → +∞. a. Show that Sn = f(n) - f(0). b. Apply Mean-Value Theorem to show that there is cn € (0, n) such that Sn = nf'(cn). c. Apply (b) to show that sn +∞o as n +∞.

Let f be an increasing, continuous and differentiable function on R and let g(x) = f(x) = f(x - 1). Suppose that there is m> 0 such that f'(x) > m, for all a R. Show that g(n) diverge. Hint: Note that since f is increasing, then g(x) > 0. Let sn = g(1) + g(2) + ..+g(n). We need to show that sn +∞ as n → +∞. a. Show that Sn = f(n) - f(0). b. Apply Mean-Value Theorem to show that there is cn € (0, n) such that Sn = nf'(cn). c. Apply (b) to show that sn +∞o as n +∞.

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
See similar textbooks
icon
Related questions
Question
Pls answer 1a,1b,1c. Let f be an increasing, continuous and differentiable function on R and let g(x) = f(x) = f(x - 1). Suppose that there is m> 0 such that f'(x) > m, for all x E R. Show that Eg(n) diverge. - Hint: Note that since f is increasing, then g(x) > 0. Let sn= g(1) + g(2) + ... + g(n). We need to show that s → +∞o as n → +∞o. a. Show that Sn = f(n) - f(0). b. Apply Mean-Value Theorem to show that there is cn E (0, n) such that Sn = n f'(cn). c. Apply (b) to show that sn→ +∞o as n → +∞.
Let f be an increasing, continuous and differentiable function on R and let g(x) = f(x) = f(x - 1). Suppose that there is m> 0 such that f'(x) > m, for all x E R. Show that Eg(n) diverge. - Hint: Note that since f is increasing, then g(x) > 0. Let sn= g(1) + g(2) + ... + g(n). We need to show that s → +∞ as n → +∞o. a. Show that Sn = : f(n) - f(0). b. Apply Mean-Value Theorem to show that there is cn E (0, n) such that Sn = n f'(cn). c. Apply (b) to show that sn→ +∞o as n → +∞.
Transcribed Image Text:Let f be an increasing, continuous and differentiable function on R and let g(x) = f(x) = f(x - 1). Suppose that there is m> 0 such that f'(x) > m, for all x E R. Show that Eg(n) diverge. - Hint: Note that since f is increasing, then g(x) > 0. Let sn= g(1) + g(2) + ... + g(n). We need to show that s → +∞ as n → +∞o. a. Show that Sn = : f(n) - f(0). b. Apply Mean-Value Theorem to show that there is cn E (0, n) such that Sn = n f'(cn). c. Apply (b) to show that sn→ +∞o as n → +∞.
Expert Solution
steps

Step by step

Solved in 4 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
SEE MORE TEXTBOOKS