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Lecture

# 157IQsol4.pdf

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School
Department
Mathematics
Course
MATH 157
Professor
Stephen Choi
Semester
Fall

Description
MATH 157 - D100A SSIGNMENT #4 Due date: Wednesday Feb 08, 2012 Instructor Questions accompanying paper Assignment # 4 Solution Directions: Print double sided, write your solutions to both questions directly on this page, place immediately after cover page and staple together! Marks: An answer without a detailed solution process will be awarded zero marks! 0 Q1: Use the four-step process to ﬁnd f (5) if a) f(x) = 4 x ▯ 3. Solution: p p Step 1. Compute f(5 + h) = (5 + h) ▯ 3 = 4 h + 2. p p ▯p p ▯ Step 2. The difference f(5 + h) ▯ f(5) = 4 h + 2 ▯ 4h + 2 ▯ 2 . Step 3. The Quotient ▯p p ▯ f(5 + h) ▯ f(5= 4 h + 2 ▯ 2 h h ▯p p ▯▯p p ▯ 4 h + 2 ▯ 2 h + 2 + 2 = h▯p h + 2 + 2▯ 4(h + 2 ▯ 2) = ▯p p ▯ h h + 2 + 2 4 = ▯p p ▯ h + 2 + 2 Step 4. Compute f(5 + h) ▯ f(5) 4 4 2 p f (5) = lim = lim▯p p ▯ = ▯p p ▯ = p = 2: h!0 h h!0 h + 2 + 2 0 + 2 + 2 2 DR. HO,PRIN2012 1 MATH 157 - D100A SSIGNMENT #4 b) f(x) = 4x ▯ 3. Solution: p p Step 1. Compute f(5 + h) 4(5 + h) ▯ 3 =4h + 17. p p Step 2. The difference f(5 + h) ▯ f4h + 17 ▯17. Step 3. The Quotient p p f(5 + h) ▯ f(5= 4h + 17 ▯ 17 h h ▯p p ▯▯p p ▯ = 4h + 1▯p▯ 17 4p + ▯7 + 17 h 4h + 17 + 17 (4h + 17 ▯ 17) = ▯p p ▯ h 4h + 17 + 17 4 = ▯p p ▯ 4h + 17 + 17 Step 4. Compute p f(5 + h) ▯ f(5) 4 4 2 2 17 f (5) = lim = lim▯p p ▯= ▯p p ▯ = p = : h!0 h h!0 4h + 17 + 17 4
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