MCV4U Unit 4 Assignment TVO ILC.pdf - MCV4U Assignment Unit...

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MCV4U Assignment Unit 4 I don’t remember what marks I got for this. There were mistakes here. Check the math to make sure it's right. Your welcome for saving you time. PS CourseHero sucks. 1. a) Given: ? 0 lim ??? ?;? = ??? ? Find: ? 0 lim ??? ?; Solve: Whether approaches from left or right (negative or positive sides), ? = ??? ? the curve approaches value cos x=1. Therefore, there is a limit of the function and it equals to 1 at x=0. b) Given: Find: ? lim ?𝑖? ? Solve: As it is impossible to determine the function at the infinity since the graph of the function is an oscillating curve, therefore, does not exist. ? lim ?𝑖? ? 2. Find the Derivative a) Solve: ? = ?𝑖? ? 5 ?' = 5? 4 · ??? ? 5 ; b) Solve: ? = ?𝑖? 5 ?
?' = 5?𝑖? 4 ? · ??? ?; c) Solve: ? = ???(4? + 9) ?' = − 4?𝑖?(4? + 9); d) Solve: ? = ??? 2 (? 2 + 3) ?' = 2 · ???(? 2 + 3) · 2? · (− ?𝑖?(? 2 + 3)); ?' = − 2? · 2 · ???(? 2 + 3) · ?𝑖?(? 2 + 3); ?' =− 2? · ?𝑖?(2(? 2 + 3)). e) Solve: ? = ? 2 ?𝑖?(? 2 + 5) ; ?' = 2? · ?𝑖?(? 2 + 5) + ? 2 · ???(? 2 + 5) · 2? ; ?' = 2?[?𝑖?(? 2 + 5) + ? 2 ???(? 2 + 5)] f) Solve: ? = 5? ? ; ?' = 5? ? g) Solve: ? = ? 5? ; ?' = 5· ? 5? ; h) Solve: ? = ?? 3?+1 ?' = 1· ? 3?+1 + ?· ? 3?+1 · 3; ; ?' = ? 3?+1 (1 + 3?) i) Solve: ? = ??(? + 3); ; ?' = 1 ? + 3 j) Solve: ? = 5??(? 2 + 4); ?' = 5 · 1 ? 2 + 4 · 2?;
; ?' = 10 ? 2 + 4 k) Solve: ? = 5 ? ; ? = 5 ? · (?? 5) l) Solve: ? = (? 2 + 2) 2 (? 2 + 2? + 1) 3 Formula: 𝐹'(?) = ?(?)?'(?) + ?'(?)?(?); then ?(?) = (? 2 + 2) 2 , ?'(?) = 2(? 2 + 2)(2?); then ?(?) = (? 2 + 2? + 1) 3 , ?'(?) = 3(? 2 + 2? + 1) 2 (2? + 2); ?' = (? 2 + 2) 2 3(? 2 + 2? + 1) 2 (2? + 2) + 2(? 2 + 2)(2?)(? 2 + 2? + 1) 3 ; Simplifying: ?' =(? 2 + 2? + 1) 2 (? 2 + 2)[(? 2 + 2)3(2? + 2) + 4?(? + 2? + 1)]; ?' =(? 2 + 2? + 1) 2 (? 2 + 2)[(? 2 + 2)6(? + 1) + 4?(? + 1) 2 ]; ? = (? + 1) 5 (? 2 + 2)[(? 2 + 2)6 + 4?(? + 1)]; ? = (? + 1) 5 (? 2 + 2)(6? 2 + 12 + 4? 2 + 4); ? = (? + 1) 5 (? 2 + 2)(10? 2 + 16); m) Solve: ? = ??(?𝑖? ?) ?' = 1 ?𝑖? ? · ??? ? = ??? ?; n) Solve: ? = (? + ?? ?) 5 ; ?' = 5(? + ?? ?) 4 · (1 + 1 ? ) 3. Given: ? = (? + 3) 2 (? + 2) 5 (? + 4) 7 Find: The derivative using logarithmic differentiation.
Solve: ? = (? + 3) 2 (? + 2) 5 (? + 4) 7 ?? ? = ??(? + 3) 2 − ??(? + 2) 5 − ??(? + 4) 7 ; ?? ? = 2??(? + 3) − 5??(? + 2) − 7??(? + 4); 1 ? = 2 ? + 3 5 ? + 2 7 ? + 4 ; 1 ? = 2(? + 2) − 5(? + 3) (? + 3)(? + 2) 7 ? + 4 ; 1 ? = 2? − 5? + 4 − 15 (? + 3)(? + 2) 7 ? + 4 ; 1 ? = −3? − 11 (? + 3)(? + 2) 7 ? + 4 ; 1 ? = (−3? − 11)(? + 4)−7(? + 3)(? + 2) (? + 2)(? + 3)(? + 4) ; 1 ? = −3? 2 − 12? − 11? − 44 − 7? 2 − 35? − 42 (? + 2)(? + 3)(? + 4) ; 1 ? = −10? 2 − 58? − 86 (? + 2)(? + 3)(? + 4) ; ?' = ? −10? 2 − 58? − 86 (? + 2)(? + 3)(? + 4) ( ) ?' = 2(?+3) 2 (−5? 2 −29?−43) (? + 2) 6 (? + 4) 8 ; 4. Given: when . ? = ??(? 2 − 2), ? = 3 Find: Equation of the Tangent Solve: Step 1: Find Derivative: ?' = 1 ? 2 −2 · 2?; ?' = 2? ? 2 −2 ; Step 2: Find slope:
? = 2(3) 3 2 − 2 = 6 7 ; Step 3: Find the point: ? = ?? (3 2 − 2) = ?? (7) = 1. 9459... Step 4: Equation of the Tangent Formula: ; ? = ?(? − ? 1 ) + ? 1 ? = 6 7 (? − 3) + 1. 9459...; ? = 6 7 ? − 18 7 + 1. 9459...; ? = 6 7 ? − 0. 6255...; 5. Given: ? = ??? 2 ? Find: The Equation of the Tangent when ? = π 3 Solve: Step 1: Find Slope ? = ???

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