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Let f be a function with domain R, let L be a real number, and let c be a positive real number. Prove that if lim f(x) = L, then lim 7f (cx² x) = 7L. You may not use any limit laws in x→0 x→0 this problem. Work directly from the definitions of these limits only.

Let f be a function with domain R, let L be a real number, and let c be a positive real number. Prove that if lim f(x) = L, then lim 7f (cx² x) = 7L. You may not use any limit laws in x→0 x→0 this problem. Work directly from the definitions of these limits only.

Algebra for College Students
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter9: Polynomial And Rational Functions
Section9.5: Graphing Rational Functions
Problem 36PS
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Let f be a function with domain R, let L be a real number, and let c be a positive real number. Prove that if lim f(x) = L, then lim 7f (cx² x) = 7L. You may not use any limit laws in x→0 x→0 this problem. Work directly from the definitions of these limits only.
Transcribed Image Text:Let f be a function with domain R, let L be a real number, and let c be a positive real number. Prove that if lim f(x) = L, then lim 7f (cx² x) = 7L. You may not use any limit laws in x→0 x→0 this problem. Work directly from the definitions of these limits only.
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