# tutorial6.pdf - MATH1013 Calculus IB Tutorial 6 Revision...

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Chapter 2 / Exercise 2
Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
Tan
Expert Verified
Wang Jingjing Page 1 Fall 2017 MATH1013 Calculus IB Tutorial 6 Revision Exercises for Midterm Exam 1) Evaluation of Composite Functions If ࠵? ࠵? = ࠵? , ࠵? ࠵? = ࠵? & − 2 , find the compostiions ࠵? ∘ ࠵?, ࠵? ∘ ࠵?, ࠵? ∘ ࠵? and ࠵? ∘ ࠵? . 2) Domain of a Function Find the Domain and Range of the following Functions : (a) ࠵? ࠵? = (࠵? / − 4) ࠵? + 5 (b) ࠵? ࠵? = (9 − ࠵? / ) 5 6 (c) ࠵? ࠵? = 89: (89/)(8;&) (d) ࠵? ࠵? = (2 − ࠵?) > ? 3) Suppose that ࠵? ࠵? = @ 6 ;@;/ @;/ ࠵? ≠ 2 4 ࠵? = 2 (a) Find ࠵?࠵?࠵? ࠵?→࠵? ࠵?(࠵?) . (b) Is ࠵?(࠵?) continuous at ࠵? = ࠵? ? (c) Is ࠵?(࠵?) differentiable at ࠵? = ࠵? ? 4) ࠵? ࠵? = @;:II @ ;:I (a) Find ࠵?࠵?࠵? ࠵?→࠵?࠵?࠵? L ࠵?(࠵?). (b) Find ࠵?࠵?࠵? ࠵?→࠵?࠵?࠵? O ࠵?(࠵?). (c) What is the value of ࠵?(࠵?࠵?࠵?) so that ࠵? ࠵? is continuous at ࠵? = ࠵?࠵?࠵? . Why? 5) Evaluate the Limits : (a) lim S→I & :T9&S 9U (b) lim S→I > VOW ; > V S (c) lim @→X (5 + YZ[ @ @ ) 6) If 7) Evaluate lim @→X ࠵? ࠵? and lim @→;X ࠵?(࠵?) for (a) ࠵? ࠵? = @ \ 9] > 5 [email protected] 6 9 [email protected] ? 9: (b) ࠵? ࠵? = 4࠵? 3࠵? − 9࠵? / + 1 8) ࠵?(࠵?) is definded by Determine values of the constants ࠵? and ࠵? for which ࠵? is continuous at ࠵? = ࠵? . 9) For what value of a for which ࠵?′(࠵?) exist ?
##### We have textbook solutions for you!
The document you are viewing contains questions related to this textbook.
The document you are viewing contains questions related to this textbook.
Chapter 2 / Exercise 2
Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
Tan
Expert Verified
Wang Jingjing Page 2 Fall 2017 10) Find ࠵?࠵? ࠵?࠵? , if : (a) ࠵? = ࠵? ࠵? ࠵? 9࠵? ࠵?࠵?࠵? ࠵? ࠵? (b) ࠵? = (࠵? + ࠵? ࠵?࠵?࠵? ࠵?) ࠵?࠵? (c) ࠵? = ࠵?࠵?࠵? ࠵? ࠵?࠵?࠵? ࠵? ࠵? (d) ࠵? = ࠵?࠵?࠵? ࠵? ࠵?࠵? (f) ࠵? = ࠵?࠵?࠵? ࠵? ࠵? ࠵?࠵?9࠵? (g) ࠵? = ࠵?࠵? ࠵? ࠵?࠵?࠵?࠵?࠵? + ࠵? ࠵? + ࠵? (h) ࠵? = ࠵? ࠵?࠵? ࠵? (i) ࠵? = (࠵?9࠵?) ࠵? ࠵? (࠵?;࠵?) ࠵? ࠵? (࠵?࠵?9࠵?) ࠵? ࠵? 11) Given that ࠵? ࠵? = ࠵?, ࠵? o ࠵? = ࠵? , ࠵? ࠵? = ࠵? , ࠵? o ࠵? = ࠵? , ࠵? ࠵? = ࠵? , ࠵? o ࠵? = ࠵? . (a) If ࠵? ࠵? = ࠵?(࠵?) ࠵?(࠵?)