Homework Answers
From the given data about y= f (x),
Ff'(0)=0, which implies that the curve is taking a turn, either increasing to decrease or decreasing to increase. And the value of f at x= 0, is 1 . The curvature at x=0 is equal to 1.
Therefore, the curve is intersecting y axis at 1, when x= 0, taking a turn up or down and the portion of the curve lies in a circle of radius 1.
A graph of this curve is herewith attached.
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23. What can you conclude about a curve of the form y- f(x) if you know that f(O) that the unsigned curvature is always equal to 1 on the domain in which it is . Use the back pls. f (0) 0 and defined...
EXERCISE 1.63. The unsigned curvature of a plane curve γ(t)-(x(t), v(t)) can be computed with Proposition 1.46 by considering it to have a vanishing third component function: γ(t) (x(t),y(t),0)....
EXERCISE 1.63. The unsigned curvature of a plane curve γ(t)-(x(t), v(t)) can be computed with Proposition 1.46 by considering it to have a vanishing third component function: γ(t) (x(t),y(t),0). Use this method to compute the curvature function of the parabola y(t) (t, t2). How can the signed curvature be determined from this approach?
EXERCISE 1.63. The unsigned curvature of a plane curve γ(t)-(x(t), v(t)) can be computed with Proposition 1.46 by considering it to have a vanishing third component function:...
Let f : [0, 1] x [0, 1] + R be defined by f(x, y) =...
Let f : [0, 1] x [0, 1] + R be defined by f(x, y) = {1 if y = 23, 0 if y + x2 Show that f is integrable on (0, 1] x [0, 1]. You may take the previous problem as given
Use the guidelines to sketch the curve y = 2x^2/x^2 - 1. The domain is {x...
Use the guidelines to sketch the curve y = 2x^2/x^2 - 1. The domain is {x | x^2 - 1 0} = {x | x plusminus 1} The x- and y-intercepts are both 0. Since f(-x) = f(x), the function f is. The curve is symmetric about the y-axis. Since the denominator is 0 when x = plusminus1, we compute the following limits: Therefore the lines x = 1 and x = are vertical asymptotes. This information about limits and...
4. Suppose you are given an equation of the form F(x, y,z) 0. Then we can say that each of the variables is defined implicitly as a function of the others. 2 a) If F and z(x, y) are both assumed to b...
4. Suppose you are given an equation of the form F(x, y,z) 0. Then we can say that each of the variables is defined implicitly as a function of the others. 2 a) If F and z(x, y) are both assumed to be differentiable, fnd in terms of partial derivatives of F. b) Under similar assumptions on the other variables, find
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QUESTION 1 The slope of the line V f(x). O How much y changes when x...
QUESTION 1 The slope of the line V f(x). O How much y changes when x changes by a large amount How much y changes when x changes by a small amount 0 The level of y for a given amount of x O It depends on the shape of f(x). QUESTION 2 The relationship between y and x is linear if Changing X by 1 always changes V by the same amount. There is no relationship between V and...
1. Consider the function y f(x) defined by Supposing that you are given x, write an...
1. Consider the function y f(x) defined by Supposing that you are given x, write an R expression for y using if state- ments Add your expression for y to the following program, then run it to plot the function f. # input x,values <-seq(-2, 2, by 0.1) # for each x calculate y n <- length(x.values) y.values <- rep(0, n) for (i in 1 :n) x <- x. values[i] # your expression for y goes here y.values ij <-...
1. Consider the function y f(x) defined by Supposing that you are given x, write an...
1. Consider the function y f(x) defined by Supposing that you are given x, write an R expression for y using if state- ments Add your expression for y to the following program, then run it to plot the function f. # input x,values <-seq(-2, 2, by 0.1) # for each x calculate y n <- length(x.values) y.values <- rep(0, n) for (i in 1 :n) x <- x. values[i] # your expression for y goes here y.values ij <-...
(1 point) The equation 3ry2r 2y2 (*) can be written in the form y f(y/x), ie.,...
(1 point) The equation 3ry2r 2y2 (*) can be written in the form y f(y/x), ie., it is homogeneous, so we can use the substitution u = y/x to obtain a separable equation with dependent variable uu(x. Introducing this substitution and using the fact that y' ru' u we can write () as y xu'w = f(u) where f(u) Separating variables we can write the equation in the form da np (n)6 where g(u) = An implicit general solution with...
4:L1-2 Consider the vector field F on Rgiven by () F(x, y) 0 and the curve...
4:L1-2 Consider the vector field F on Rgiven by () F(x, y) 0 and the curve c: (0,1) + R2 with 2++ + cos(t) Compute the line integral de) = ( Cand cele). \<F1ds>. { <F | do>- <insert a positive integer> Ono For partial credit, fill in the following. You can use sage-syntax, or simply write text. Note that not all ways of solving this problem depend on all fields below. Is the vector field conservative? Oyes If the...
Problem #2: Use the given graphs to sketch the parametric curve x =f(0, y=g(1). х=f(t) y=g(t)...
Problem #2: Use the given graphs to sketch the parametric curve x =f(0, y=g(1). х=f(t) y=g(t) A m KA (А) (В) о (D) у х 1 0 2 х E) (F) ТО -1 о 2 (Н) 2 -2 2 х Problem #2: Select
EXERCISE 1.63. The unsigned curvature of a plane curve γ(t)-(x(t), v(t)) can be computed with Proposition 1.46 by considering it to have a vanishing third component function: γ(t) (x(t),y(t),0). Use this method to compute the curvature function of the parabola y(t) (t, t2). How can the signed curvature be determined from this approach?
EXERCISE 1.63. The unsigned curvature of a plane curve γ(t)-(x(t), v(t)) can be computed with Proposition 1.46 by considering it to have a vanishing third component function:...
Let f : [0, 1] x [0, 1] + R be defined by f(x, y) = {1 if y = 23, 0 if y + x2 Show that f is integrable on (0, 1] x [0, 1]. You may take the previous problem as given
Use the guidelines to sketch the curve y = 2x^2/x^2 - 1. The domain is {x | x^2 - 1 0} = {x | x plusminus 1} The x- and y-intercepts are both 0. Since f(-x) = f(x), the function f is. The curve is symmetric about the y-axis. Since the denominator is 0 when x = plusminus1, we compute the following limits: Therefore the lines x = 1 and x = are vertical asymptotes. This information about limits and...
4. Suppose you are given an equation of the form F(x, y,z) 0. Then we can say that each of the variables is defined implicitly as a function of the others. 2 a) If F and z(x, y) are both assumed to be differentiable, fnd in terms of partial derivatives of F. b) Under similar assumptions on the other variables, find
4. Suppose you are given an equation of the form F(x, y,z) 0. Then we can say that each...
QUESTION 1 The slope of the line V f(x). O How much y changes when x changes by a large amount How much y changes when x changes by a small amount 0 The level of y for a given amount of x O It depends on the shape of f(x). QUESTION 2 The relationship between y and x is linear if Changing X by 1 always changes V by the same amount. There is no relationship between V and...
1. Consider the function y f(x) defined by Supposing that you are given x, write an R expression for y using if state- ments Add your expression for y to the following program, then run it to plot the function f. # input x,values <-seq(-2, 2, by 0.1) # for each x calculate y n <- length(x.values) y.values <- rep(0, n) for (i in 1 :n) x <- x. values[i] # your expression for y goes here y.values ij <-...
1. Consider the function y f(x) defined by Supposing that you are given x, write an R expression for y using if state- ments Add your expression for y to the following program, then run it to plot the function f. # input x,values <-seq(-2, 2, by 0.1) # for each x calculate y n <- length(x.values) y.values <- rep(0, n) for (i in 1 :n) x <- x. values[i] # your expression for y goes here y.values ij <-...
(1 point) The equation 3ry2r 2y2 (*) can be written in the form y f(y/x), ie., it is homogeneous, so we can use the substitution u = y/x to obtain a separable equation with dependent variable uu(x. Introducing this substitution and using the fact that y' ru' u we can write () as y xu'w = f(u) where f(u) Separating variables we can write the equation in the form da np (n)6 where g(u) = An implicit general solution with...
4:L1-2 Consider the vector field F on Rgiven by () F(x, y) 0 and the curve c: (0,1) + R2 with 2++ + cos(t) Compute the line integral de) = ( Cand cele). \<F1ds>. { <F | do>- <insert a positive integer> Ono For partial credit, fill in the following. You can use sage-syntax, or simply write text. Note that not all ways of solving this problem depend on all fields below. Is the vector field conservative? Oyes If the...
Problem #2: Use the given graphs to sketch the parametric curve x =f(0, y=g(1). х=f(t) y=g(t) A m KA (А) (В) о (D) у х 1 0 2 х E) (F) ТО -1 о 2 (Н) 2 -2 2 х Problem #2: Select
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