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Consider the following function x>0 h(x) = x≤0 (a) Sketch the function and mark its salient features. (b) Find the derivative h'(x), its limit as a → +∞o, and sketch this derivative. (c) Show that h and h' are both continuous functions. (d) Show h(r) is strictly increasing for x > 0.

Consider the following function x>0 h(x) = x≤0 (a) Sketch the function and mark its salient features. (b) Find the derivative h'(x), its limit as a → +∞o, and sketch this derivative. (c) Show that h and h' are both continuous functions. (d) Show h(r) is strictly increasing for x > 0.

Advanced Engineering Mathematics
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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Consider the following function h(x) = Se-1/² x > 0 +) = {5¹/² I≤0 (a) Sketch the function and mark its salient features. (b) Find the derivative h'(x), its limit as x→ +∞, and sketch this derivative. (c) Show that h and h' are both continuous functions. (d) Show h(r) is strictly increasing for x > 0.
Transcribed Image Text:Consider the following function h(x) = Se-1/² x > 0 +) = {5¹/² I≤0 (a) Sketch the function and mark its salient features. (b) Find the derivative h'(x), its limit as x→ +∞, and sketch this derivative. (c) Show that h and h' are both continuous functions. (d) Show h(r) is strictly increasing for x > 0.
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