Homework Answers
clear all
t = linspace(-1,100);
x = sqrt(t.^3+1);
y = t.^3;
plot(x,y)
![Smooth function diftentiable is a hmation that is continuous and peiceswise te in the intervals [a, b]. and Zelt- of alt) – d](http://img.homeworklib.com/questions/9b1e9540-a0c2-11eb-b869-d1886b4e150a.png?x-oss-process=image/resize,w_560)
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3. Consider the vector-valued function: r(t) = Vt +1 i + pi a. State the domain...
A particle moves in the plane with position given by the vector valued function r(t)=cos^3(t)i+sin^3(t)j MA330...
A particle moves in the plane with position given by the
vector valued function r(t)=cos^3(t)i+sin^3(t)j
MA330 Homework #2 particle moves in the plane with position given by the vector-valued function The curve it generates is called an astrid and is plotted for you below. (a) Find the position att x/4 by evaluating r(x/4). Then draw this vector on the graph (b) Find the velocity vector vt)-r)-.Be sure to apply the power and (e) Find the velocity at t /4 by...
Suppose the vector-valued function rt-tht) is smooth on an interval containing the point t -to is the line parallel to the tangent vector r()that passes through ()().()).For the following functio...
Suppose the vector-valued function rt-tht) is smooth on an interval containing the point t -to is the line parallel to the tangent vector r()that passes through ()().()).For the following function, find the line tangent to the curve at t to the point to The line tangent to r(t) at r(t) (10 cos t,6 sin 16t,t), to Theline tangent to the curve at t:68COD
Suppose the vector-valued function rt-tht) is smooth on an interval containing the point t -to is the...
please make sure you solve problem throughly 1. Find the domain of the vector-valued function r(t)...
please make sure you solve problem throughly
1. Find the domain of the vector-valued function r(t) = 2ti + taj + In tk.
Using Mathematica Consider the vector-valued function r(t)=et cos t i+(sin t)/(t+4) j +t k. a) Plot...
Using Mathematica Consider the vector-valued function r(t)=et cos t i+(sin t)/(t+4) j +t k. a) Plot the curve with t going over the interval [-2, 2]. b) Plot the curve again over the same interval, but this time add the velocity vector in blue at (1, 0, 0) to the graph. c) Plot the curve again over the same interval, along with the blue velocity vector at (1, 0, 0), but this time add the acceleration vector in red at...
12.1 Given f(t) = 4tî - 1° +2+3 + vt +18 Find the domain of r(t)...
12.1 Given f(t) = 4tî - 1° +2+3 + vt +18 Find the domain of r(t) in interval notation. Find limi(t). t=0
The curvature of vector-valued functions theoretical Someone, please help! 2. The curvature of a vector-valued function r(t) is given by n(t) r (t) (a) If a circle of radius a is given by r(t) (a cos...
The curvature of vector-valued functions theoretical
Someone, please help!
2. The curvature of a vector-valued function r(t) is given by n(t) r (t) (a) If a circle of radius a is given by r(t) (a cos t, a sin t), show that the curvature is n(t) = (b) Recall that the tangent line to a curve at a point can be thought of as the best approx- imation of the curve by a line at that point. Similarly, we can...
Question 1. If C is a smooth curve given by a vector function r(t), a stsb,...
Question 1. If C is a smooth curve given by a vector function r(t), a stsb, show that Ser-dr = žlır(b)l2 – Ir(a)i?) Hint 1: Use the product rule and the fact that the dot product is commutative (this means a b = b.a for any two vectors a and b) to write: r(t).r' (t) Hint 2: Use FTC2 from first year calculus. 1 d 2 dt
Find the domain of the vector function r (t) = <sent, lnt, 1 / (x-2)> a....
Find the domain of the vector function r (t) = <sent, lnt, 1 / (x-2)> a. other answer b. (0, infinito) c. (0, 2) U (2, infinito) d. (-infinito, 2) U (2, infinito) e. (-infinito, infinito)
Sketch the space curve. Interval Vector-Valued Function r(t) = -ti + 5tj + 2tk [0, 1]...
Sketch the space curve. Interval Vector-Valued Function r(t) = -ti + 5tj + 2tk [0, 1] 6 2 2 6 6 22 7. 4 2 Find its length over the given interval. Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Maximize f(x, y) = 2x + 2xy + y Constraint: 2x + y = 200 file 40.80
Let C be the graph of y=1-x',-1sxsl. a) Write a vector-valued function r(t) that traces C....
Let C be the graph of y=1-x',-1sxsl. a) Write a vector-valued function r(t) that traces C. y b) Evaluate ca 11+4x2
A particle moves in the plane with position given by the
vector valued function r(t)=cos^3(t)i+sin^3(t)j
MA330 Homework #2 particle moves in the plane with position given by the vector-valued function The curve it generates is called an astrid and is plotted for you below. (a) Find the position att x/4 by evaluating r(x/4). Then draw this vector on the graph (b) Find the velocity vector vt)-r)-.Be sure to apply the power and (e) Find the velocity at t /4 by...
Suppose the vector-valued function rt-tht) is smooth on an interval containing the point t -to is the line parallel to the tangent vector r()that passes through ()().()).For the following function, find the line tangent to the curve at t to the point to The line tangent to r(t) at r(t) (10 cos t,6 sin 16t,t), to Theline tangent to the curve at t:68COD
Suppose the vector-valued function rt-tht) is smooth on an interval containing the point t -to is the...
please make sure you solve problem throughly
1. Find the domain of the vector-valued function r(t) = 2ti + taj + In tk.
12.1 Given f(t) = 4tî - 1° +2+3 + vt +18 Find the domain of r(t) in interval notation. Find limi(t). t=0
The curvature of vector-valued functions theoretical
Someone, please help!
2. The curvature of a vector-valued function r(t) is given by n(t) r (t) (a) If a circle of radius a is given by r(t) (a cos t, a sin t), show that the curvature is n(t) = (b) Recall that the tangent line to a curve at a point can be thought of as the best approx- imation of the curve by a line at that point. Similarly, we can...
Question 1. If C is a smooth curve given by a vector function r(t), a stsb, show that Ser-dr = žlır(b)l2 – Ir(a)i?) Hint 1: Use the product rule and the fact that the dot product is commutative (this means a b = b.a for any two vectors a and b) to write: r(t).r' (t) Hint 2: Use FTC2 from first year calculus. 1 d 2 dt
Sketch the space curve. Interval Vector-Valued Function r(t) = -ti + 5tj + 2tk [0, 1] 6 2 2 6 6 22 7. 4 2 Find its length over the given interval. Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Maximize f(x, y) = 2x + 2xy + y Constraint: 2x + y = 200 file 40.80
Let C be the graph of y=1-x',-1sxsl. a) Write a vector-valued function r(t) that traces C. y b) Evaluate ca 11+4x2
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