Explanation Given: r → ( t ) = 〈 t 2 , t 3 〉 at t = 1 Formula used: N → ( t ) = v ( t ) r ' ' ( t ) − v ' ( t ) r ' ( t ) ‖ v ( t ) r ' ' ( t ) − v ' ( t ) r ' ( t ) ‖ r → ' ( t ) = d r → ( t ) d t v ( t ) = ‖ r → ' ( t ) ‖ r ' ' ( t ) = d 2 r → ( t ) d t 2 v ' ( t ) = d d t v → ( t ) Calculation: r → ( t ) = 〈 t 2 , t 3 〉 r → ' ( t ) = d d t r → ( t ) = d d t 〈 t 2 , t 3 〉 = 〈 d d t t 2 , d d t t 3 〉 = 〈 2 t , 3 t 2 〉 r → ' ( t ) = ( 2 t , 3 t 2 ) ⋯ ⋯ ( 1 ) v ( t ) = ‖ r → ' ( t ) ‖ = ( 2 t ) 2 + ( 3 t 2 ) 2 = 4 t 2 + 9 t 4 ⋯ ⋯ ( 2 ) r → ' ' ( t ) = d d t r → ' ( t ) = d d t 〈 2 t , 3 t 2 〉 = 〈 d d t 2 t , d d t 3 t 2 〉 = 〈 2 , 6 t 〉 = ( 2 , 6 t ) ⋯ ⋯ ( 3 ) v ' ( t ) = 1 2 4 t 2 + 9 t 4 × ( 8 t + 36 t 3 ) = 4 t + 18 t 3 4 t 2 + 9 t 4 ⋯ ⋯ ( 4 ) Now, Substitute t = 1 in equation ( 1 ) , ( 2 ) , ( 3 ) and ( 4 ) to find r → ' ( 1 ) , v → ( 1 ) , r → ' ' ( 1 ) , v → ' ( 1 ) r ' ( 1 ) = 〈 2 , 3 〉 v → ' ( 1 ) = 4 + 9 = 13 r ' ' ( 1 ) = 〈 2 , 6 〉 v → ' ( 1 ) = 4 + 18 4 + 9 = 22 13 Since, N ( t ) = v ( t ) r → ' ' ( t ) − v ' ( t ) r → ' ( t ) ‖ v ( t ) r → ' ' ( t ) − v ' ( t ) ...

4th Edition

ISBN: 9781319055844

Author: FRANZOSA

Publisher: VST

See similar textbooks

Concept explainers

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These…

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are…

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) ge…

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.

Videos

Question

Chapter 14.4, Problem 47E

To determine

To calculate:

Normal vector $(\vec{N})$ at the indicated point.

$〈 t^{2}, t^{3} 〉, t = 1$

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.4, Problem 46E

Chapter 14.4, Problem 48E

Students have asked these similar questions

Calculus lll May I please have numbers 1 and 2 explanations resolved? Thank you,

5:38 Video Message instructor Submit Question ||| D

8:38 *** TEMU TEMU -3 -2 7 B 2 1 & 5G. 61% 1 2 -1 Based on the graph above, determine the amplitude, period, midline, and equation of the function. Use f(x) as the output. Amplitude: 2 Period: 2 Midline: 2 ☑ syntax error: this is not an equation. Function: f(x) = −2 cos(πx + 2.5π) +2× Question Help: Worked Example 1 ☑ Message instructor Submit Question ||| <

Chapter 14 Solutions

EBK CALCULUS

Ch. 14.1 - Prob. 1PQ Ch. 14.1 - Prob. 2PQ Ch. 14.1 - Prob. 3PQ Ch. 14.1 - Prob. 4PQ Ch. 14.1 - Prob. 5PQ Ch. 14.1 - Prob. 6PQ Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Normal vector ( N → ) at the indicated point. 〈 t 2 , t 3 〉 , t = 1

Solution Summary: The author calculates the normal vector ( N ) at the indicated point for the given function.

Concept explainers

Videos

To calculate:

Normal vector $(\vec{N})$ at the indicated point.

$〈 t^{2}, t^{3} 〉, t = 1$

Want to see the full answer?

Chapter 14 Solutions

Normal vector ( N → ) at the indicated point. 〈 t 2 , t 3 〉 , t = 1

Solution Summary: The author calculates the normal vector ( N ) at the indicated point for the given function.

Concept explainers

Videos

To calculate: Normal vector (N→) at the indicated point. 〈t2,t3〉,t=1

Want to see the full answer?

Chapter 14 Solutions

To calculate:

Normal vector $(\vec{N})$ at the indicated point.

$〈 t^{2}, t^{3} 〉, t = 1$