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Maths Calculus 2

This document outlines the assignments for Calculus II. It includes 4 problems involving sketching curves defined by vector-valued functions and finding the derivatives and tangent lines. It also specifies revising linear algebra concepts and completing 2 exercises for additional practice. Students are directed to come to tutorials or office hours if they have any questions.

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Fäb Rice
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50 views1 page

Maths Calculus 2

This document outlines the assignments for Calculus II. It includes 4 problems involving sketching curves defined by vector-valued functions and finding the derivatives and tangent lines. It also specifies revising linear algebra concepts and completing 2 exercises for additional practice. Students are directed to come to tutorials or office hours if they have any questions.

Uploaded by

Fäb Rice
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Calculus II: Assignments 1

• Assignment numbers are the ones as provided in the lecture notes.


• If you have questions, problems or comments, please come to the walk-in tutorials,
or to the office hours.
(2.1.10) Sketch the curves defined by the following paths.
(a) r : R → R3 , r(t) = (2t − 1, t, t + 3) .
(b) r : [0, 1] → R2 , r(t) = (t, et ).
What is the relation of this path (and the curve which it defines) to the path:
c : [0, 1] → R2 , c(s) = ( 1 − s , e(1−s) ) ?
(c) r : R1 → R2 , r(t) = (sinh(t), cosh(t)) .
(d) r : R1 → R3 , r(t) = (sin(t), cos(t), cos(t)) .
(2.2.6) For each of the following vector-valued functions r(t)
- Sketch the curve
- Calculate r0 (t)
- Indicate r0 (t) on your graph at the point where t = 1.

(a) r(t) = cosh ti + sinh tj;


(b) r(t) = 3i + 5tj − tk
(c) r(t) = cos 2πti + sin 2πtj + tk

(2.3.3) Sketch the curves defined by the following paths.

(a) r : [− π4 , π4 ] → R2 , r(t) = (t, tan(t)).


How does this path (and the curve which it defines) compare to the path:
c : [0, π2 ] → R2 , c(s) = ( π/4 − s , tan(π/4 − s) ) ?
(b) r : R1 → R3 , r(t) = ( sin(t) , 5 cos(t) , cos(2t) ) .

(2.3.4) Compute r0 (0) for each of the paths in exercise (2.3.3). Hence compute, in each case, a
parametric equation of the tangent line to the curve at r(0).
(Appendix A) Revise some of the linear algebra in appendix A of the lecture notes/workbook. Also,
do exercises A.3.1 and A.3.2. for revision of that material.

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