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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.Show that |x2-4|<e , when 0<|x-2|<e(5+e)-1 and prove limx->2 x2=4 by using these inequalities.Which of the following statements aretrue, and which are false? If true, say why; if false, give a counterexample(that is, an example confirming the falsehood). If limx→c ƒ(x) exists but limx→c g(x) does not exist, thenlimx→c( ƒ(x) + g(x)) does not exist.
- If limxS1 ƒ(x) = 5, must ƒ be defined at x = 1? If it is, must ƒ(1) = 5? Can we conclude anything about the values of ƒ at x = 1? Explain.Which of the following statements aretrue, and which are false? If true, say why; if false, give a counterexample(that is, an example confirming the falsehood). If neither limx→c ƒ(x) nor limx→c g(x) exists, thenlimx→c ( ƒ(x) + g(x)) does not exist.→ Prove, using the formal definition, that limx→1 (sqrt(1-x))=0