5. Let c ER and suppose f, g: R → R are functions such that limc f(x) exists, and for some > 0, g(x)| ≤ f(x) whenever |x- c < €. Explain why lim [sin²(x - c)g(x)] exists. State explicitly any theorem or result that you are using in your argument.
5. Let c ER and suppose f, g: R → R are functions such that limc f(x) exists, and for some > 0, g(x)| ≤ f(x) whenever |x- c < €. Explain why lim [sin²(x - c)g(x)] exists. State explicitly any theorem or result that you are using in your argument.
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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![5. Let c e R and suppose f,g : R → R are functions such that lim→c ƒ(x) exists, and for some e > 0,
|g(x)| < |f(x)| whenever |x – c| < e. Explain why
lim [sin (x – c)g(x)]
exists. State explicitly any theorem or result that you are using in your argument.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc3a15436-4919-49da-a36d-43760d876cb8%2Fcc1dacde-bc50-4970-a54e-51f6499d74d9%2Ftq0174o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:5. Let c e R and suppose f,g : R → R are functions such that lim→c ƒ(x) exists, and for some e > 0,
|g(x)| < |f(x)| whenever |x – c| < e. Explain why
lim [sin (x – c)g(x)]
exists. State explicitly any theorem or result that you are using in your argument.
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