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- 3. What is limx→0sin xx?limx--->2^- f(x), where f(x)=2x-5 if x <2 x^2+2 if x is greater than or equal to 2(a) Estimate the value of ___________limx->-∞(√ x2 + x + 1 + x) by graphing the function . f(x) = limx->-∞(√ (x2 + x + 1 ) + x) (b) Use a table of values of f(x) to guess the value of thelimit.(c) Prove that your guess is correct.
- Determine limx→−2 6/x-2, if it existsUsing Arithmetic of Limits, find limn→∞ 2n / (3n + 5) .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.)you need the definition of lim sup. Also note that the definition of lim sup |Sn| is different from lim sup Sn. please show clear, thanks