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Find the equation of the tangent to: a y = p2x + 1 at x = 4 b y = 1 2 x at x = 1 c f(x)

Mathematics for the International Student: Mathematics SL | 3rd Edition | ISBN: 9781921972089 | Authors: Sandra Haese, Michael Haese, Robert Haese, Mark Humphries, Marjut Maenpaa ISBN: 9781921972089 446

Solution for problem 4 Chapter 16

Mathematics for the International Student: Mathematics SL | 3rd Edition

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Mathematics for the International Student: Mathematics SL | 3rd Edition | ISBN: 9781921972089 | Authors: Sandra Haese, Michael Haese, Robert Haese, Mark Humphries, Marjut Maenpaa

Mathematics for the International Student: Mathematics SL | 3rd Edition

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Problem 4

Find the equation of the tangent to: a y = p2x + 1 at x = 4 b y = 1 2 x at x = 1 c f(x) = x 1 3x at (1, 1 4 ) d f(x) = x2 1 x at (2, 4).

Step-by-Step Solution:
Step 1 of 3

6.2 Trigonometric integrals and Substitutions Trig Identities: si n θ+cos θ=1 Section A: Trig tan θ+1=sec θ2 Integrals Example 1: 1+cot θ=csc θ2 3 2 ∫ sin xcos xdx 2 1 co s θ= 2 [+co2 (θ 2] Step1:breakupthe factor= ∫in xcos xsinx dx 2 1 si n θ= [1−cos (θ ] x 2 x u = cosx 1−cos ¿cos xsin x dx du = - sin x dx  -du = sin x dx ¿ ¿ Step2:changesin ¿somethingwekow= ¿ ∫ Step3:U− ¿ 1−u 2)u (−du) Step4: foil out¿get a polynomial=∫ (u −u 4du u3 u5 Step5:Takeintegral=− − [3] 5 Example 2: ∫ cos xdx Page 1 of 2 6.2 Trigonometric integrals and Substitutions f

Step 2 of 3

Chapter 16, Problem 4 is Solved
Step 3 of 3

Textbook: Mathematics for the International Student: Mathematics SL
Edition: 3
Author: Sandra Haese, Michael Haese, Robert Haese, Mark Humphries, Marjut Maenpaa
ISBN: 9781921972089

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Find the equation of the tangent to: a y = p2x + 1 at x = 4 b y = 1 2 x at x = 1 c f(x)