40. Show that f is continuous on (-∞,∞). f(x)={sin⁡x if x⋖π/4, cos⁡x if x≥π/4

40. Show that f is continuous on (-∞,∞).

f(x)={sin⁡x if x⋖π/4, cos⁡x if x≥π/4

Calculus: Early Transcendentals
Chapter 2: Limits and Derivatives
Section 2.5: Continuity
Problem 40

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[jeangtech]

Thanks for the explanation of this question and the latter one.