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Calculus for vector functions
- Intro Lesson: a6:20
- Intro Lesson: b2:51
- Intro Lesson: c10:06
- Lesson: 15:47
- Lesson: 27:34
- Lesson: 36:58
- Lesson: 46:35
- Lesson: 55:28
- Lesson: 68:25
Calculus for vector functions
Lessons
Now that we know about vector functions, let's apply calculus to these functions!
Limits with Vector Functions
Limits of a vector function works in this way:
t→alimr(t)=t→alim<f(t),g(t),h(t)>
=<t→alimf(t),t→alimg(t),t→alimh(t)>
=t→alimf(t)i+t→alimg(t)j+t→alimh(t)k
Derivatives with Vector Functions
Derivatives of a vector function are done in the following way:
r′(t)=<f′(t),g′(t),h′(t)>
=f′(t)i+g′(t)j+h′(t)k
Integrals with Vector Functions
Indefinite integrals of vector functions are done in this way:
∫r(t)dt=<∫f(t)dt,∫g(t)dt,∫h(t)dt>+C
=∫f(t)dti+∫g(t)dtj+∫h(t)dtk+C
Definite integrals of vector functions work like this:
∫abr(t)dt=<∫abf(t)dt,∫abg(t)dt,∫abh(t)dt>+C
=∫abf(t)dti+∫abg(t)dtj+∫abh(t)dtk+C
- IntroductionCalculus For Vector Functions Overview:a)Limits of Vector Functions
- Apply limits to all components
- Example of Limits
b)Derivative of Vector Functions- Apply derivative to all components
- Example of Derivatives
c)Integral of Vector Functions- Apply integral to all components
- Example of Definite Integral
- Example of Indefinite Integral
- 1.Finding Limits of Vector Functions
Compute the following limit:
t→3lim<e3−t,9−t2t−3,log3t>
- 2.Compute the following limit:
t→∞lim(t1i+e−2tjt2−2t+1t2+1k)
- 3.Finding Derivative of Vector Functions
Compute the derivative of the following vector function:
r(t)=<1+t2t2−1,sin2t,cos2t>
- 4.Compute the derivative of the following vector function:
r(t)=<ln(sint),et2+te,(t+1)3t2>
- 5.Finding Integrals of Vector Functions
Evaluate the integral of ∫01r(t)dt, where:
r(t)=<3,21e−2t,cost>
- 6.Evaluate the integral of ∫r(t)dt, where:
r(t)=t1i+tetj+t2−2t+12t−2k