(a) If the symbol 〚 〛 denotes the greatest integer function defined in Example I 0, evaluate (i) lim x → 2 + 〚 x 〛 (ii) lim x → − 2 〚 x 〛 (iii) lim x → 2.4 〚 x 〛 (b) If n is an integer, evaluate (i) lim x → n − 〚 x 〛 (ii) lim x → n + 〚 x 〛 (c) For what values of a does lim x → 0 〚 x 〛 exist?
(a) If the symbol 〚 〛 denotes the greatest integer function defined in Example I 0, evaluate (i) lim x → 2 + 〚 x 〛 (ii) lim x → − 2 〚 x 〛 (iii) lim x → 2.4 〚 x 〛 (b) If n is an integer, evaluate (i) lim x → n − 〚 x 〛 (ii) lim x → n + 〚 x 〛 (c) For what values of a does lim x → 0 〚 x 〛 exist?
Solution Summary: The author evaluates the limit of the greatest integer function as x approaches right-hand side of 2.
Use the properties of logarithms, given that In(2) = 0.6931 and In(3) = 1.0986, to approximate the logarithm. Use a calculator to confirm your approximations. (Round your answers to four decimal places.)
(a) In(0.75)
(b) In(24)
(c) In(18)
1
(d) In
≈
2
72
Find the indefinite integral. (Remember the constant of integration.)
√tan(8x)
tan(8x) sec²(8x) dx
Chapter 2 Solutions
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