Questions

MAT135H5_F25_ALL SECTIONS 2.3 Preparation Check

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Which of the following statements must be true, and which are false? Note: each part is independent from the others. a) If 𝑓 ( 𝑥 ) is a polynomial, then lim 𝑥 → 5 𝑓 ( 𝑥 ) can be evaluated by computing 𝑓 ( 5 ) . [ Select ] False True b) If 𝑅 ( 𝑥 ) is a rational function, then lim 𝑥 → 7 𝑅 ( 𝑥 ) can be evaluated by computing 𝑅 ( 7 ) . [ Select ] False True c) If 𝑝 ( 𝑥 ) is a polynomial, then lim 𝑥 → 5 + 𝑝 ( 𝑥 ) can be evaluated by computing 𝑝 ( 5 ) . [ Select ] True False d) If 𝑓 ( 2 ) = 4 then lim 𝑥 → 2 [ 𝑓 ( 𝑥 ) ] 2 = 16 [ Select ] False True e) If lim 𝑥 → 4 ( 5 𝑓 ( 𝑥 ) ) = 15 , then lim 𝑥 → 4 𝑓 ( 𝑥 ) = 3 . [ Select ] True False f) If lim 𝑥 → 4 ( 𝑥 𝑓 ( 𝑥 ) ) = 8 , then lim 𝑥 → 4 𝑓 ( 𝑥 ) = 2 . [ Select ] False True

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Step-by-Step Analysis

Here we go through each statement a–f and assess its truth value, keeping in mind basic limits rules for polynomials, rational functions, and general limit algebra. a) 'If f(x) is a polynomial, then lim_{x->5} f(x) can be evaluated by computing f(5).' - A polynomial is continuous at every real number, so the limit as x approaches 5 equals the function value at 5. In short, lim_{x->5} f(x) = f(5). This makes the statement true. b) 'If R(x) is a rational function,......Login to view full explanation

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