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MAT1512 Assignment 5 2021

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MAT1512 - Calculus A (MAT1512)
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UNISA MAT1512 Calculus A Assignment FIVE of 2021 solutions. Topics covered: Implicit differentiation. Equations of tangent lines. Equations of normal lines.

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MAT1512 ASSIGNMENT 5 2021


𝑑𝑦
𝑁𝑜𝑡𝑒 𝑡ℎ𝑎𝑡 = 𝑦′
𝑑𝑥
Question 1


𝑥 2 𝑦 2
( ) +( ) =1
𝑎 𝑏


𝑥2 𝑦2
+ =1
𝑎2 𝑏 2


1 𝑑 2 1 𝑑 2 𝑑
(𝑥 ) + (𝑦 ) = (1)
𝑎2 𝑑𝑥 𝑏 2 𝑑𝑥 𝑑𝑥


1 1
2
2𝑥 + 2 2𝑦 × 𝑦 ′ = 0
𝑎 𝑏


2𝑥 2𝑦 ′
+ 𝑦 =0
𝑎2 𝑏 2


2𝑦 ′ 2𝑥
2
𝑦 =− 2
𝑏 𝑎


𝑏 2 2𝑦 ′ 𝑏 2 2𝑥
× 2𝑦 = ×− 2
2𝑦 𝑏 2𝑦 𝑎



2𝑏 2 𝑥
𝑦′ = −
2𝑦𝑎2



𝑏2𝑥
𝑦′ = −
𝑎2 𝑦

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