  # 7Exercise 5: Calculate the following limits, using the 6-e definition of a limit (i.e., provide an e-8 proof for thefollowing limits)(a) lim |1 - 3x|()+2(b) lim 2 - 5xft auU :Pd(c) lim r3Ix 2(d) lim f(x) where(hAhoe)*f (x) =H 3,2x < 37,2x3, x >3x 3dalwboowloong ut

Question help_outlineImage Transcriptionclose7 Exercise 5: Calculate the following limits, using the 6-e definition of a limit (i.e., provide an e-8 proof for the following limits) (a) lim |1 - 3x| () +2 (b) lim 2 - 5x ft auU : Pd (c) lim r3 Ix 2 (d) lim f(x) where (h Ahoe)* f (x) = H 3 ,2 x < 3 7, 2x3, x >3 x 3 dalw boowloong u t fullscreen
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Hey, since there are multiple questions posted, we will answer first three sub parts question. If you want any specific question to be answered, then please submit that question only or specify the question number in your message.

Step 2 help_outlineImage TranscriptioncloseDefinition: Let fbe a real valued function defined of a subset I of the real numbers. Let c be a limit point of I and let L be real number. We say that lim f(x) L if every > 0 there exist a positive number 0 such thatf(x)-L
Step 3 help_outlineImage Transcriptionclose(b) Consider the given limit as lim (2- 5x) x-0 By guess the limit of the limit is lim(2-5.x)= 2. x0 Now, the limit can be prove using (e,8) as follows f(x)-L 2-5x-2 =5x 5x 5x- 0 f(x)2-5x and L 2) Choose S <& fullscreen

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