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- Is there a value of a for which limx1 3x^2+ax+a+3/x^2+x-2 exists? Enter the value of a if such a exist otherwise enter 0.1. Is it possible that f(2) = 5 but limx→2f(x) = 7? If so, what kind of function can satisfy this?A. i. Using Arithmetic of Limits, find limn→∞ 2n / (3n + 5) . (2n devided 3n+5..ii. Working directly from the definition of limits, give a direct verification that your answer in (i) is correct. (Your answer should involve the letter ε.)
- Find the limit lim x-2 (3x-1)2/x+11.3 Evaluate the limit limz→2+i[(z-1)(3-2i)+1-3i] and use the definition of the limit (ε - δ) to verify this limit.Using the ε − N definition of a limit, prove that lim(n→∞)=(6n^3 −2n+1)/(2n^3+1)=3. The expert missed the first part of the question which asks for the ε − N definition.