filmov
tv
Limits & Continuity of Vector-Valued Functions Examples | Calculus 3 - JK Math
Показать описание
Examples For How to Evaluate Limits of Vector-Valued Functions & Determine Continuity (Calculus 3)
In this video we look at examples of evaluating limits of vector-valued functions and using them to determine intervals of continuity. Additionally, we look at examples of how to use the limit definition of continuity to determine if a vector-valued function is continuous at specific values of the parameter t.
This video series is designed to help students understand the concepts of Calculus 3 at a grounded level. No long, boring, and unnecessary explanations, just what you need to know at a reasonable and digestible pace, with the goal of each video being shorter than the average school lecture!
Calculus 3 requires a solid understanding of concepts from calculus 2, calculus 1, precalculus, and algebra. This includes limits, differentiation, advanced integration techniques, applications of derivatives and integrals, polar coordinates, parametric equations, trigonometric functions, logarithms, factoring, equation manipulation, graphing, and much more. If you are not familiar with these prerequisite topics, be sure to learn them first!
Video Chapters:
0:00 Example 1: Limit of 〈 t, t², t^3 〉 as t→4
2:42 Example 2: Limit of 〈 t+1, t^(1/3), 1/t 〉 as t→0
5:14 Example 3: Limit of 〈 sint/t, (1-cost)/t, 2t 〉 as t→0
9:01 Example 4: Limit of 〈 (t²-4)/(t-2), (t²+t-6)/(5t-10), 3/(t²-1) 〉 as t→2+
14:50 Example 5: Limit of 〈 √t, ln(t)/(t²-1), (e^(t-1)-1)/(t-1) 〉as t→1
19:04 Example 6: Limit of 〈 t/e^t, ln(t)/t, (1-e^-t)/(1+e^-t) 〉 as t→∞
25:19 Example 7: Limit of 〈 1/t^3, arctan(t), te^(3t) 〉 as t→-∞
31:41 Example 8: Intervals of Continuity for 〈 t^4, t^5, t^6 〉
33:31 Example 9: Intervals of Continuity for 〈 √t, √(t-1), √(t-2) 〉
36:16 Example 10: Intervals of Continuity for 〈 ln(t), arcsin(t), 7t 〉
39:36 Example 11: Checking Continuity at t=-1 for 〈 t, √(t+1), (t²+1) 〉
43:43 Example 12: Checking Continuity at t=-2 for 〈 e^t, ln(t), sin(t) 〉
⚡️Math Products I Recommend⚡️
⚡️Textbooks I Use⚡️
⚡️My Recording Equipment⚡️
(Commissions earned on qualifying purchases)
Follow me on Social Media!
Found this video to be helpful? Consider giving this video a like and subscribing to the channel!
Thanks for watching! Any questions? Feedback? Leave a comment!
- Josh from JK Mathematics
#calculus
Disclaimer: Please note that some of the links associated with the videos on my channel may generate affiliate commissions on my behalf. As an amazon associate, I earn from qualifying purchases that you may make through such affiliate links.
In this video we look at examples of evaluating limits of vector-valued functions and using them to determine intervals of continuity. Additionally, we look at examples of how to use the limit definition of continuity to determine if a vector-valued function is continuous at specific values of the parameter t.
This video series is designed to help students understand the concepts of Calculus 3 at a grounded level. No long, boring, and unnecessary explanations, just what you need to know at a reasonable and digestible pace, with the goal of each video being shorter than the average school lecture!
Calculus 3 requires a solid understanding of concepts from calculus 2, calculus 1, precalculus, and algebra. This includes limits, differentiation, advanced integration techniques, applications of derivatives and integrals, polar coordinates, parametric equations, trigonometric functions, logarithms, factoring, equation manipulation, graphing, and much more. If you are not familiar with these prerequisite topics, be sure to learn them first!
Video Chapters:
0:00 Example 1: Limit of 〈 t, t², t^3 〉 as t→4
2:42 Example 2: Limit of 〈 t+1, t^(1/3), 1/t 〉 as t→0
5:14 Example 3: Limit of 〈 sint/t, (1-cost)/t, 2t 〉 as t→0
9:01 Example 4: Limit of 〈 (t²-4)/(t-2), (t²+t-6)/(5t-10), 3/(t²-1) 〉 as t→2+
14:50 Example 5: Limit of 〈 √t, ln(t)/(t²-1), (e^(t-1)-1)/(t-1) 〉as t→1
19:04 Example 6: Limit of 〈 t/e^t, ln(t)/t, (1-e^-t)/(1+e^-t) 〉 as t→∞
25:19 Example 7: Limit of 〈 1/t^3, arctan(t), te^(3t) 〉 as t→-∞
31:41 Example 8: Intervals of Continuity for 〈 t^4, t^5, t^6 〉
33:31 Example 9: Intervals of Continuity for 〈 √t, √(t-1), √(t-2) 〉
36:16 Example 10: Intervals of Continuity for 〈 ln(t), arcsin(t), 7t 〉
39:36 Example 11: Checking Continuity at t=-1 for 〈 t, √(t+1), (t²+1) 〉
43:43 Example 12: Checking Continuity at t=-2 for 〈 e^t, ln(t), sin(t) 〉
⚡️Math Products I Recommend⚡️
⚡️Textbooks I Use⚡️
⚡️My Recording Equipment⚡️
(Commissions earned on qualifying purchases)
Follow me on Social Media!
Found this video to be helpful? Consider giving this video a like and subscribing to the channel!
Thanks for watching! Any questions? Feedback? Leave a comment!
- Josh from JK Mathematics
#calculus
Disclaimer: Please note that some of the links associated with the videos on my channel may generate affiliate commissions on my behalf. As an amazon associate, I earn from qualifying purchases that you may make through such affiliate links.
0:03:59
Limits and Continuity for Vector-Valued Functions
0:12:50
Limits and Continuity of Vector-Valued Functions (Calculus 3)
0:13:02
Limits and Continuity for Vector Valued Functions
0:07:37
Limits and Continuity for Vector-Valued Functions Examples
0:07:51
10 3a Vector Valued Functions Defined, Limits, and Continuity
0:05:39
Finding the Limit of a Vector Function
0:04:19
Limits and Continuity of Vector Valued Functions
0:05:58
Limit of the vector function (KristaKingMath)
0:12:27
CALCULUS 3 | Limits and Continuity of Vector-Valued Functions
0:20:36
Limits and Continuity of Vector Functions
0:34:15
Limits and Continuity for Vector-Valued Functions
0:19:19
Limits and Continuity
0:08:09
limits, continuity, derivatives for vector functions
0:37:04
Limits & Continuity of Vector-Valued Functions | Calculus 3 Lesson 25 - JK Math
0:10:59
4. Vector Calculus - Limit and Continuity of Vector Functions
0:04:26
Determine Limits of a Vector-Valued Function (Basic)
0:10:48
Continuity of a Vector Function
0:19:04
Limits of Multivariable Functions - Calculus 3
0:09:04
Definition of Continuity for Vector-Valued Functions
0:04:14
Continuity of vector functions
0:02:53
LO 52 Determine if a vector valued function is continuous at a point
0:02:33
12.01.07 Continuity of Vector Valued Functions
0:06:09
12.01.08 Continuity of Vector Valued Functions Examples
0:01:14
Limit of a Vector-Valued Function Example
Комментарии