Explanation Given information: The expression, lim x → − 3 x 2 − 9 x 2 − x − 12 Formula used: lim x → c [ f ( x ) g ( x ) ] = lim x → c f ( x ) lim x → c g ( x ) provided that lim x → c g ( x ) ≠ 0 Calculation: Here the denominator is x 2 − x − 12 , lim x → − 3 x 2 − x − 12 − 12 = ( − 3 ) 2 − ( − 3 ) − 12 = 0 As the limit of denominator is zero, so the limit of quotient cannot be used. By factoring numerator and denominator, lim x → − 3 x 2 − 9 x 2 − x − 12 = lim x → − 3 ( ( x − 3 )

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ISBN: 9780135228982

Author: Sullivan

Publisher: PEARSON

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Chapter 14, Problem 8RE

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u, v and w are three coplanar vectors: ⚫ w has a magnitude of 10 and points along the positive x-axis ⚫ v has a magnitude of 3 and makes an angle of 58 degrees to the positive x- axis ⚫ u has a magnitude of 5 and makes an angle of 119 degrees to the positive x- axis ⚫ vector v is located in between u and w a) Draw a diagram of the three vectors placed tail-to-tail at the origin of an x-y plane. b) If possible, find w × (ū+v) Support your answer mathematically or a with a written explanation. c) If possible, find v. (ū⋅w) Support your answer mathematically or a with a written explanation. d) If possible, find u. (vxw) Support your answer mathematically or a with a written explanation. Note: in this question you can work with the vectors in geometric form or convert them to algebraic vectors.

Question 3 (6 points) u, v and w are three coplanar vectors: ⚫ w has a magnitude of 10 and points along the positive x-axis ⚫ v has a magnitude of 3 and makes an angle of 58 degrees to the positive x- axis ⚫ u has a magnitude of 5 and makes an angle of 119 degrees to the positive x- axis ⚫ vector v is located in between u and w a) Draw a diagram of the three vectors placed tail-to-tail at the origin of an x-y plane. b) If possible, find w × (u + v) Support your answer mathematically or a with a written explanation. c) If possible, find v. (ū⋅ w) Support your answer mathematically or a with a written explanation. d) If possible, find u (v × w) Support your answer mathematically or a with a written explanation. Note: in this question you can work with the vectors in geometric form or convert them to algebraic vectors.

Chapter 14 Solutions

EBK PRECALCULUS

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The value of lim x → − 3 x 2 − 9 x 2 − x − 12 .

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Chapter 14 Solutions