Let r(t) = (12,1 – 1,4t). Calculate the derivative of r(t)·a(t) at t = 2 assuming...

Question

Question

Let r(t) = (12,1 – 1,4t). Calculate the derivative of r(t)·a(t) at t = 2 assuming that a(2) = (8, -4,6) a (2) = (6,8,3) (Use

math calculus

Answer 1

Answer #1

Q 2 r(t) = (te, 1-t, ut a (2) = (8,-4, 6 a (2) = (6,8,37 di(t) = (2+, 1, 47 din (2)=(4,-1,97 if(put)alt))} = (24t) - a (t) +

Answer 2

Similar Homework Help Questions

1. Let T : P (R) Pn+1(R) be defined: T(p()) = (x + 1)p(x + 2)...

1. Let T : P (R) Pn+1(R) be defined: T(p()) = (x + 1)p(x + 2) (a) (2 marks) Show that T is a linear transformation. (b) (3 marks) Is T one-to-one? Describe ker(T). What is the rank of T? (c) (8 marks) Find a matrix representation for T with respect to the standard bases {1, 2, ..., 2"} for Pn and {1, 2, ..., xn+1} for Pn+1 if n = 4. (d) (5 marks) Let D : Pn+1(R) +...
1. Let T: Pn(R) + Pn+1(R) be defined: T(P(x)) = (x + 1)p(x + 2) (c)...

1. Let T: Pn(R) + Pn+1(R) be defined: T(P(x)) = (x + 1)p(x + 2) (c) (8 marks) Find a matrix representation for T with respect to the standard bases {1, 2, ...,2"} for Pn and {1, 2, ...,xN+1} for Pn+1 if n = 4. (d) (5 marks) Let D : Pn+1(R) + Pn(R) be the derivative operator. What is the rank of DoT? Justify your answer. Describe ker(DoT). Is DoT one-to-one? (e) (5 marks) What is the rank of...
2.- Let r(t) = (121,842/2, 31) and let (t) be the arc length function of r()...

2.- Let r(t) = (121,842/2, 31) and let (t) be the arc length function of r() based at t=0. Calculate 8(t) as an elementary formula in t. You may assume that t > 0.

8. DETAILS SCALCET8 2.8.502.XP. Find the derivative of the function using the definition of derivative. f(t)...

8. DETAILS SCALCET8 2.8.502.XP. Find the derivative of the function using the definition of derivative. f(t) = 3t - 862 f"(t) State the domain of the function. (Enter your answer using interval notation.) State the domain of its derivative. (Enter your answer using interval notation.)
1. Let T : Pn(R) + Pn+1(R) be defined: T(P(x)) = (x + 1)p(x + 2)...

1. Let T : Pn(R) + Pn+1(R) be defined: T(P(x)) = (x + 1)p(x + 2) bases {1, X, ..., (a) (2 marks) Show that T is a linear transformation. (b) (3 marks) Is T one-to-one? Describe ker(T). What is the rank of T? (c) (8 marks) Find a matrix representation for T with respect to the standard xn} for Pn and {1, 2, ..., xn+1} for Pn+1 if n = 4. (d) (5 marks) Let D : Pn+1(R) +...
Calculate the first AND second derivative dy/dx and d^2y/dx^2 for the curve given by: r(t) =...

Calculate the first AND second derivative dy/dx and d^2y/dx^2 for the curve given by: r(t) = t-t, y(t) = 3t - t

What's the solution of d and e 1. Let T : Pn(R) + Pn+1(R) be defined:...

What's the solution of d and e 1. Let T : Pn(R) + Pn+1(R) be defined: T(P(x)) = (x + 1)p(x + 2) bases {1, X, ..., (a) (2 marks) Show that T is a linear transformation. (b) (3 marks) Is T one-to-one? Describe ker(T). What is the rank of T? (c) (8 marks) Find a matrix representation for T with respect to the standard xn} for Pn and {1, 2, ..., xn+1} for Pn+1 if n = 4. (d)...
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...
Theorem 2. Let E be an open subset of R² and suppose that fe C'(E). Let...

Theorem 2. Let E be an open subset of R² and suppose that fe C'(E). Let y(t) be a periodic solution of (1) of period T. Then the derivative of the Poincaré map P(8) along a straight line normal to r = {x E R x = y(t) - (0),O SE ST} at x = 0 is given by T P(0) = exp V. f(y(t)) dt. 4. Show that the system • = -y + (1 – 22 - y2)2...

(d) (4 points) Let T : R² + Rº be the transformation that rotates any vector...

(d) (4 points) Let T : R² + Rº be the transformation that rotates any vector 90 degrees counterclockwise. Let A be the standard matrix for T. Is A diagonalizable over R? What about over C? (e) (3 points) Let T : R4 → R4 be given by T(x) = Ax, A = 3 -1 7 12 0 0 0 4 0 0 5 4 0 4 2 1 Is E Im(T)? 3 (f) (9 points) Let U be a...