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- Decide if the following claims are true or false, and give shortjustifications for each conclusion. (c) If limx→a f(x) = L, then limx→a 3[f(x) − 2]2 = 3(L − 2)2.Evaluate the following limit, if it exists. Show your complete solution. 1.lim?→9 (9−?)/(√?−3) 2.lim?→? (tan?)/? 3. lim?→16 (4−√?)/(16?−?2) 4. lim?→3 (?2−9)/?2+2?−3The notation lim x→af(x)=L is read "the ____ of ___ as ____ approaches ___ equals the number ___."
- solve the following calculus problem evaluating the limitsProve the statement using the ?, ? definition of a limit. lim x→4 x2 − 2x − 8 x − 4 = 6 Given ? > 0, we need ? such that if 0 < |x − 4| < , then x2 − 2x − 8 x − 4 − 6 . We have x2 − 2x − 8 x − 4 − 6 < ? ⇔ (x − 4)(x + 2) x − 4 − 6 < ? ⇔ |x + 2 − 6| < ? [x ≠ 4] ⇔ |x − 4| < ?. Choose ? = . Then 0 < |x − 4| < ? ⇒ |x − 4| < ⇒ x2 − 2x − 8 x − 4 − 6 By the definition of a limit, lim x→4 x2 − 2x − 8 x − 4 = 6. View Picture of QuestionEvaluate the following limits. Show all pertinent solutions.