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CALC1141 Calculus I Assignment 1
- Course
- CALC1141 (CALC1141)
- Institution
- Thompson River University (TRU )
Assignment 1 covering functions, sin, cos, inverse functions, graphing functions, intervals, ranges, domains (Chapter 1-3)
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Page |1CALC 1141 THOMPSON RIVERS UNIVERSITY
CALC 1141 – ASSIGNMENT 1
QUESTION 1:
𝒇(𝒙+𝒉)−𝒇(𝒙) 𝟐𝒙−𝟏
Find and simplify for 𝒇(𝒙) = 𝟐𝒙+𝟏.
𝒉
f(x + h) − f(x)
=
h
2(x + h) − 1 2x − 1
(2(x + h) + 1) − (2x + 1)
=
h
2x + 2h − 1 2x − 1
( )−( )
= 2x + 2h + 1 2x + 1
h
(2x + 2h − 1)(2x + 1) − (2x − 1)(2x + 2h + 1)
(2x + 2h + 1) (2x + 1)
=
h
(4x 2 + 2x + 4xh + 2h − 2x − 1) − (4x 2 + 4xh + 2x − 2x − 2h − 1)
(2x + 2h + 1)(2x + 1)
=
h
(4x 2 + 4xh + 2h − 1) − (4x 2 + 4xh − 2h − 1)
(2x + 2h + 1)(2x + 1)
=
h
(4x 2 + 4xh + 2h − 1) − 4x 2 − 4xh + 2h + 1
(2x + 2h + 1)(2x + 1)
=
h
4h
(2x + 2h + 1)(2x + 1)
=
h
4h
=
h(2x + 2h + 1)(2x + 1)
4
=
(2x + 2h + 1)(2x + 1)
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