Chapter 11: Q. 4 (page 859)

$Let r (t) = <x (t), y (t), z (t)> . What is the definition of \lim_{t \to c} r (t) ?$

Short Answer

Expert verified

$\lim_{t \to c} r (t) = \lim_{t \to c} x (t) i + \lim_{t \to c} y (t) j + \lim_{t \to c} z (t) k, which is a vector .$

Step by step solution

Step 1. Given information is

$r (t) = <x (t), y (t), z (t)>$

Step 2. Definition of limt→cr(t)

$The limit of r (t) as t approaches c, denoted by \lim_{t \to c} r (t), is defined by \lim_{t \to c} r (t) = \lim_{t \to c} <x (t), y (t), z (t)> = \lim_{t \to c} x (t) i + \lim_{t \to c} y (t) j + \lim_{t \to c} z (t) k, where \lim_{t \to c} x (t), \lim_{t \to c} y (t) and \lim_{t \to c} z (t) exists . Thus \lim_{t \to c} r (t) = \lim_{t \to c} x (t) i + \lim_{t \to c} y (t) j + \lim_{t \to c} z (t) k, which is a vector .$

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$Let r (t) = <x (t), y (t), z (t)> . What is the definition of \lim_{t \to c} r (t) ?$

Short Answer

Step by step solution

Step 1. Given information is

Step 2. Definition of limt→cr(t)

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Letr(t)=x(t),y(t),z(t).Whatisthedefinitionoflimt→cr(t)?

Short Answer

Step by step solution

Step 1. Given information is

Step 2. Definition of limt→cr(t)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

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$Let r (t) = <x (t), y (t), z (t)> . What is the definition of \lim_{t \to c} r (t) ?$