# Mat1330 sample final 1 of 2

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Winter 2023 Instructeur: Punisher sample final review Instructions This is a Closed Book Exam of 80 minutes. The only calculators allowed are the ones approved by Faculty: Texas Instruments TI-30, Texas Instruments TI-34, Casio fx-260, Casio fx-300 . There are 16 pages including 16 for rough work. The points are indicated for each question. Read carefully each question. Questions 1-4 are multiple choice . Write your answer (choice) in the box. No work required. Questions 5-8 are long answer . You must show full and all work. May use the backs of pages and page 16 is for rough work. Do not detach the last page with rough work. Cellular phones, unauthorized electronic devices or course notes are not allowed during this exam. Phones and devices must be turned off and put away in your bag. Do not keep them in your possession, such as in your pockets. If caught with such a device or document, the following may occur: you will be asked to immediately leave the exam and academic fraud allegations will be filed, which may result in you obtaining a 0 (zero) for the exam. By signing below, you acknowledge that you have ensured that you are complying with the above statement. Last name: Student ID: First name: Signature: Goood Luck! page 1 of 16
MC 1 2 3 4 5 6 7 8 Maximum 2 2 2 2 2 2 2 2 Note 9 10 11 12 13 14 15 16 Total bonus! 3 3 4 7 7 3 7 3 50+3 Multiple choice Questions 1 to 8 are multiple choice and each is worth 2 points. No need for justification in Multiple choice. Question 1. The domain of f ( x ) = r x x 2 4 is: A. ( −∞ , 2) (0 , 1] B. ( −∞ , 2] [0 , 1] C. ( 2 , 0] (2 , ) D. ( −∞ , 2) E. [ 2 , 0) [2 , ) F. (2 , ). Answer: Answer: C Note that the denominator MUST not be zero: x 2 4 ̸ = 0 or ( x 2)( x + 2) ̸ = 0, so x ̸ = 2 and x ̸ = 2. NEXT: Case 1. x 0 and x 2 4 = ( x 2)( x + 2) > 0, hence x [0 , ) and x ( −∞ , 2) (2 , ). INTERSECT (see word AND) and we get: x (2 , ). Case 2. x 0 and x 2 4 = ( x 2)( x + 2) < 0, hence x [ −∞ , 0] and x ( 2 , 2). INTERSECT and we get: x ( 2 , 0]. Union of the two cases gives C. Happy? HS stuff as u can see.
Question 2. The table gives info on f ( x ), g ( x ), f ( x ) and g ( x ) for some x . Consider h ( x ) = ( f g )( x ). x 1 2 3 4 f ( x ) 1 4 2 3 g ( x ) 3 2 4 1 f ( x ) 2 3 1 4 g ( x ) 4 4 3 2 Find the correct answer: A. h (2) = 1 , h (2) = 12. B. h (2) = 8 , h (2) = 9 C. h (2) = 1 , h (2) = 6 D. h (2) = 8 , h (2) = 6. E. h (2) = 8 , h (2) = 1. F. h (2) = 4, h (2) = 12. Answer: Chain rule says: h (2) = f ( g (2)) g (2) = f (2) × 4 = 3 × 4 = 12. Note h (2) = f ( g (2)) = f (2) = 4, hiha SO: Answer: F That s the full solution. But if u do not know the chain rule, no way we can finish this exercise... Question 3. Find the derivative of f ( x ) = ln 2 x sin(2 x ) ( x + 1) 5 e x 2 : A. ln(2) + 2 cot(2 x ) B. 2 x + 2 cot(2 x ) 1 ( x + 1) 5 2 x C. ln(2) + 2 cos(2 x ) D. ln(2) 2 cot(2 x ) + 2 x 5 x + 1 E. ln(2) + 2 cot(2 x ) 2 x 5 x + 1 F. 2 x 2 cos(2 x ) 5 x + 1 2 x Answer: Answer: What U need here (except an infinite love for Cal 1) is LOG LAWS: WE MUST rewrite: f ( x ) = ln(2 x ) + ln(sin(2 x )) ln( x + 1) 5 ln( e x 2 ), WHICH it is in fact giving: f ( x ) = ln(2) + cos(2 x ) sin(2 x ) 2 5 x + 1 2 x . DONE E page 3 of 16