On the figure below, sketch the graph of a functionf that satisfies: • f is continuous, • lim f(z) = 2, • f(-1) = 0, • f"(x) <0 for z> 1, and f(r+h)-f(z) • lim h+0 < 0 for z < -3, f(z) dz <0

On the figure below, sketch the graph of a functionf that satisfies: • f is continuous, • lim f(z) = 2, • f(-1) = 0, • f"(x) <0 for z> 1, and f(r+h)-f(z) • lim h+0 < 0 for z < -3, f(z) dz <0

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

Question

On the figure below, sketch the graph of a function f that satisfies:
•f is continuous,
• lim f(z) = 2,
• f'(-1) = 0,
• f"(x) <0 for >1, and
f(z +h)- f(x)
• lim
h+0
< O for r < -3,
f(z) dr <0
h

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