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Differentiable vector functions are continuous Show that if r(t) = ƒ(t)i + g(t)j + h(t)k is differentiable at t = t0, then it is continuous at t0 as well.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter6: Rates Of Change

Section6.1: Velocity

Problem 12SBE

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Concept explainers

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.

Question

Differentiable vector functions are continuous Show that if r(t) = ƒ(t)i + g(t)j + h(t)k is differentiable at t = t0, then it is continuous at t0 as well.

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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