Whats the answer to number
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Whats the answer to number
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1. Let r(t) = -i-e2t j + (t? + 2t)k...
what is the answer for number 4 1. Let r(t) = -i-e2t j + (t? +...
what is the answer for number
4
1. Let r(t) = -i-e2t j + (t? + 2t)k be the position of a particle moving in space. a. Find the particle's velocity, speed and direction at t = 0. Write the velocity as a product of speed and direction at this time. b. Find the parametric equation of the line tangent to the path of the particle at t = 0. 2. Find the integrals: a. S (tezi - 3sin(2t)j +...
(I point) Let F=21+(z + y) j + (z _ y + z) k. (1+4t). y = 4 + 2t, z = _ (1+t). Let the line l be ...
(I point) Let F=21+(z + y) j + (z _ y + z) k. (1+4t). y = 4 + 2t, z = _ (1+t). Let the line l be x =- (a) Find a point P-(zo, 30, zo) where F is parallel to 1. Find a point Q (which F and I are perpendicular. Q= and l are perpendicular Give an equation for the set of all points at which F and l are perpendicular. equation:
(I point) Let F=21+(z...
Let u(t) =t^3 i + ln(t) j + e^2t k and v(t) = 1/t^3 i +...
Let u(t) =t^3 i + ln(t) j + e^2t k and v(t) = 1/t^3 i + 2 j +
t k
2. Let u(t) - ti+In(t)j+ et k and Compute the derivative of the dot product f u(t)v() in two ways and confirm they agree: Compute the dot product u(t) v(t) first and then differentiate the result. . Alternatively, use the following "Dot Product Rule" u(t) v(t)] u'(t) v(t)+ u(t) v'(t) Aside: It's worth noting that there are other forms...
3. [3 marks] Show that for a plane curve described by r = c(t)i + y(t)j,...
3. [3 marks] Show that for a plane curve described by r = c(t)i + y(t)j, the curvature k(t) is I'Y' - YX| (x2 + y2)3/27 where a prime denotes differentiation with respect to t. 4. [2 marks] Let f(x, y) = xy +3. Find (a) f(x + y, x - y); (b) f(xy, 3.22y).
DUE DATE: 23 MARCH 2020 1 1. Let f(x,y) = (x, y) + (0,0) 0. (x,...
DUE DATE: 23 MARCH 2020 1 1. Let f(x,y) = (x, y) + (0,0) 0. (x, y) = (0,0) evaluate lim(x,y)=(4,3) [5] 2r + 8y 2. Show that lim does not exist. [10] (*.w)-(2,-1) 2.ry + 2 3. Find the first and second partial derivatives of f(x,y) = tan-'(x + 2y). [16] 4. If z is implicitly defined as a function of x and y by I?+y2 + 2 = 1, show az Əz that +y=z [14] ar ду 5....
Problem 1: Let y()- r(t+2)-r(t+1)+r(t)-r(t-1)-u(t-1)-r(t-2)+r(t-3), where r(t) is the ramp function. a) plot y(t) b) plot...
Problem 1: Let y()- r(t+2)-r(t+1)+r(t)-r(t-1)-u(t-1)-r(t-2)+r(t-3), where r(t) is the ramp function. a) plot y(t) b) plot y'() c) Plot y(2t-3) d) calculate the energy of y(t) note: r(t) = t for t 0 and 0 for t < 0 Problem 2: Let x(t)s u(t)-u(t-2) and y(t) = t[u(t)-u(t-1)] a) b) plot x(t) and y(t) evaluate graphically and plot z(t) = x(t) * y(t) Problem 3: An LTI system has the impulse response h(t) = 5e-tu(t)-16e-2tu(t) + 13e-3t u(t) The input...
a. Use the Chain Rule to find the indicated partial derivatives. z = x4 + x2y, x...
a. Use the Chain Rule to find the indicated partial derivatives. z = x4 + x2y, x = s + 2t − u, y = stu2; ∂z ∂s ∂z ∂t ∂z ∂u when s = 1, t = 2, u = 3 b. Use the Chain Rule to find the indicated partial derivatives. w = xy + yz + zx, x = r cos(θ), y = r sin(θ), z = rθ; ∂w ∂r ∂w ∂θ when r = 8, θ = pi/2 c. Use the...
1 a) Find the domain of r(t) = (2-Int ) and the value of r(to) for...
1 a) Find the domain of r(t) = (2-Int ) and the value of r(to) for to = 1. b) Sketch (neatly) the line segment represented by the vector equation: r=2 i+tj; -1 <t<l. c) Show that the graph of r(t) = tsin(t) i + tcos(t) j + t?k, t> 0 lies on the paraboloid: z= x2 + y². 2. a) Find r'(t) where r(t) = eti - 2cos(31) j b) Find the parametric equation of the line tangent to...
Consider the function Let where f(t) is differentiable for all t ∈ R. Show that z satisfies the ...
Consider the function Let where f(t) is differentiable for all t ∈ R. Show that z satisfies the partial differential equation (x2 − y2 ) ∂z/∂x + xy ∂z/∂y = xyz for all (x, y) ∈ R2 \ { (t, 0)|t ∈ R }.
Problem 1: Let F(, y,) be a function given by F(, y, z) (r2+y)e. Let S be the surface in R given ...
Problem 1: Let F(, y,) be a function given by F(, y, z) (r2+y)e. Let S be the surface in R given by the equation Fr, y, 2) 2. (a) Find an equation of the tangent plane to the surface S at the point p(-1,1,0) (b)Find the directional derivative -1,1,0) of F(,y,2) in the direction of the unit vector u = (ui, t», t's) at the point p(-1,1,0) - In what direction is this derivative maximal? In what direction is...
what is the answer for number
4
1. Let r(t) = -i-e2t j + (t? + 2t)k be the position of a particle moving in space. a. Find the particle's velocity, speed and direction at t = 0. Write the velocity as a product of speed and direction at this time. b. Find the parametric equation of the line tangent to the path of the particle at t = 0. 2. Find the integrals: a. S (tezi - 3sin(2t)j +...
(I point) Let F=21+(z + y) j + (z _ y + z) k. (1+4t). y = 4 + 2t, z = _ (1+t). Let the line l be x =- (a) Find a point P-(zo, 30, zo) where F is parallel to 1. Find a point Q (which F and I are perpendicular. Q= and l are perpendicular Give an equation for the set of all points at which F and l are perpendicular. equation:
(I point) Let F=21+(z...
Let u(t) =t^3 i + ln(t) j + e^2t k and v(t) = 1/t^3 i + 2 j +
t k
2. Let u(t) - ti+In(t)j+ et k and Compute the derivative of the dot product f u(t)v() in two ways and confirm they agree: Compute the dot product u(t) v(t) first and then differentiate the result. . Alternatively, use the following "Dot Product Rule" u(t) v(t)] u'(t) v(t)+ u(t) v'(t) Aside: It's worth noting that there are other forms...
3. [3 marks] Show that for a plane curve described by r = c(t)i + y(t)j, the curvature k(t) is I'Y' - YX| (x2 + y2)3/27 where a prime denotes differentiation with respect to t. 4. [2 marks] Let f(x, y) = xy +3. Find (a) f(x + y, x - y); (b) f(xy, 3.22y).
DUE DATE: 23 MARCH 2020 1 1. Let f(x,y) = (x, y) + (0,0) 0. (x, y) = (0,0) evaluate lim(x,y)=(4,3) [5] 2r + 8y 2. Show that lim does not exist. [10] (*.w)-(2,-1) 2.ry + 2 3. Find the first and second partial derivatives of f(x,y) = tan-'(x + 2y). [16] 4. If z is implicitly defined as a function of x and y by I?+y2 + 2 = 1, show az Əz that +y=z [14] ar ду 5....
Problem 1: Let y()- r(t+2)-r(t+1)+r(t)-r(t-1)-u(t-1)-r(t-2)+r(t-3), where r(t) is the ramp function. a) plot y(t) b) plot y'() c) Plot y(2t-3) d) calculate the energy of y(t) note: r(t) = t for t 0 and 0 for t < 0 Problem 2: Let x(t)s u(t)-u(t-2) and y(t) = t[u(t)-u(t-1)] a) b) plot x(t) and y(t) evaluate graphically and plot z(t) = x(t) * y(t) Problem 3: An LTI system has the impulse response h(t) = 5e-tu(t)-16e-2tu(t) + 13e-3t u(t) The input...
1 a) Find the domain of r(t) = (2-Int ) and the value of r(to) for to = 1. b) Sketch (neatly) the line segment represented by the vector equation: r=2 i+tj; -1 <t<l. c) Show that the graph of r(t) = tsin(t) i + tcos(t) j + t?k, t> 0 lies on the paraboloid: z= x2 + y². 2. a) Find r'(t) where r(t) = eti - 2cos(31) j b) Find the parametric equation of the line tangent to...
Problem 1: Let F(, y,) be a function given by F(, y, z) (r2+y)e. Let S be the surface in R given by the equation Fr, y, 2) 2. (a) Find an equation of the tangent plane to the surface S at the point p(-1,1,0) (b)Find the directional derivative -1,1,0) of F(,y,2) in the direction of the unit vector u = (ui, t», t's) at the point p(-1,1,0) - In what direction is this derivative maximal? In what direction is...
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