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12 Σεπ 2019 · Calculus with Vector Functions – In this section here we discuss how to do basic calculus, i.e. limits, derivatives and integrals, with vector functions. Tangent, Normal and Binormal Vectors – In this section we will define the tangent, normal and binormal vectors.
- Improper Integrals
Here is a set of practice problems to accompany the Improper...
- Polar Coordinates
Here is a set of practice problems to accompany the Polar...
- Hydrostatic Pressure and Force
Here is a set of practice problems to accompany the...
- Absolute Convergence
Here is a set of practice problems to accompany the Absolute...
- Special Series
11.2 Vector Arithmetic; 11.3 Dot Product; 11.4 Cross...
- Integral Test
In this section we will discuss using the Integral Test to...
- Integration Strategy
The guidelines give here involve a mix of both Calculus I...
- Parametric Equations and Curves
Section 9.1 : Parametric Equations and Curves. To this point...
- Improper Integrals
16 Νοε 2022 · Here is a set of practice problems to accompany the Vectors chapter of the notes for Paul Dawkins Calculus II course at Lamar University.
Free practice questions for Calculus 2 - Vector Calculations. Includes full solutions and score reporting.
Vector Calculus Solutions to Sample Final Examination #1 1. Let f(x;y)=exysin(x+ y). (a) In what direction, starting at (0;ˇ=2), is fchanging the fastest? (b) In what directions starting at (0;ˇ=2) is fchanging at 50% of its maximum rate? (c) Let c(t) be a flow line of F = rfwith c(0) = (0;ˇ=2). Calculate d dt [f(c(t))] t=0: Solution
Problem 2.1: a) Find a unit vector parallel to ~x= ~u+ ~v+ 2w~if ~u= [ 1;0;1] and ~v= [1;1;0] and w~= [0;1;1]. b) Now nd a unit vector perpendicular to ~x. (there are many solutions). Problem 2.2: An Euler brick is a cuboid with side lengths a;b;csuch that all face diagonals are integers.
Vector problems 1. a) A river flows at 3 mph and a rower rows at 6 mph. What heading should the rower take to go straight across a river? b) Answer the same question if the river flows at 6 mph and the rower rows at 3 mph. 2. Find a unit vector in the direction of 2, 3 . 3.
Examples of using unit vectors in engineering analysis Example 3.1: A vector A in Figure 3.2(b) has its two components along the x- and y-axis with respective magnitudes of 6 units and 4 units.
