Calculus
7th Edition
ISBN: 9781524916817
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 13, Problem 35SP
To determine
To find:The given line integral.
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1. Let ř(1) = . Find a vector and parametric equation of the line
tangent to F(1) at the point (- 3, 0, 2 In 2 ).
5. Let C be the portion of the parabola y = x², oriented from the starting
point (0, 0) towards the end point (3,9). Find the unit tangent vector T
and the unit normal vector n to C at the point (1, 1).
Chapter 13 Solutions
Calculus
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- 33. Define T: R³ → R³ by ED-L x - y + 2z T. 2x +3y- z x +2y - 2z a. Find all vectors in R that are mapped to the zero vector.arrow_forward5. Consider the force field F = (xy)i + (x −y)j and C, the straight line from the point (-1,2) to (3,3). (a) Find a parameterization of the straight line C. Show your process for this. Include the range of values of the parameter in your final answer. I (b) Express the work done by the field F along the line C as a line integral. Then convert that line integral into a single-variable integral.arrow_forward2. The temperature function on a circular plate R = {(x, y) |r² + y? < 36} is given by T(r, y) = 200 – 2² – y² in degrees Fahrenheit. (a) Sketch (by hand) the gradient field associated with this temperature function. Include level curves for reference, and several vectors. (b) Interpret the gradient field associated with this temperature function. Include ideas about temperature distribution on the plate, the magnitude if the gradient vectors, and changes in temperatures in the plate.arrow_forward
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