Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Consider the vector function: (see attached) a) Find the domain of r. b) Find the limit as t -> 0 of lim r(t). (see attached) c) Find the parametric equations for the line tangent to the space curve described by the vector function at t = 1.

Consider the vector function: (see attached) a) Find the domain of r. b) Find the limit as t -> 0 of lim r(t). (see attached) c) Find the parametric equations for the line tangent to the space curve described by the vector function at t = 1.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.5: Applications
Problem 2EQ
See similar textbooks
icon
Related questions
Question

Consider the vector function: (see attached)

a) Find the domain of r.

b) Find the limit as t -> 0 of lim r(t). (see attached)

c) Find the parametric equations for the line tangent to the space curve described by the vector function at t = 1.

F(t) = (t In(2 – t), VE + 3, 1)
Transcribed Image Text:F(t) = (t In(2 – t), VE + 3, 1)
Find the limit lim 7(t)
Transcribed Image Text:Find the limit lim 7(t)
Expert Solution
Step 1

Given:

rt=tln2-t,t+3,et-1t

a) Since logx is defined for x>0

So, ln2-t is defined for 2-t>0⇒t<2

Also t+3 is defined for 

t+3≥0⇒t≥-3

and et-1t is defined for t≠0

Takin intersection of all the three, we get 

t∈[-3,2)-0

So, domain of r is [-3,2)-{0}

Step 2

b) As t→0, tln2-t→0 , t+3→3

Also, 

limt→0et-1t=limt→0et1=1 ( Using l' Hopital Rule )

So, limt→0rt=limt→0tln2-t,t+3,et-1t         =lim t→0tln2-t,lim t→0 t+3,limt→0  et-1t          0,3,1

       

steps

Step by step

Solved in 4 steps

Blurred answer
Knowledge Booster
Vector Space
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS