please make sure you solve problem throughly 1. Find the domain of the vector-valued function r(t)...
3. Consider the vector-valued function: r(t) = Vt +1 i + pi a. State the domain of this function (using interval notation). b. Find the open intervals on which the curve traced out by this vector-valued function is smooth. Show all work, including r 't), the domain of r', and the other required steps. c. Provide a careful sketch of the path traced out by this function below. Include at least 3 points on the graph of this function. Assume...
Find a vector function r that satisfies the following conditions. r"(t) = 7 cos 2ti + 5 sin 9tj + t?k, r(0) = i + k, r'(O) = i +j+k
Tx N, for the vector-valued Find the vectors T and N, and the unit binomial vector B function r(t) and the given value of t. k, 3 to= 1 + Tx N, for the vector-valued Find the vectors T and N, and the unit binomial vector B function r(t) and the given value of t. k, 3 to= 1 +
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...
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)
PLEASE ANSWER THIS QUESTION CORRECTLY AND ASAP!!! What is the domain of the vector function r(t) = <2t+2, V3 –t, In (t) >. O a) {t]–3<t<0} b) {t|0<t<3} c) {t\t<3) d) {t|0<t <3} e) {t-3 <t<0}
Sketching a Curve In Exercises 9-12, sketch the curve represented by the vector-valued function and give the orientation of the curve. 2 9. r(t) = (n cost, i sin ) 10. r(t) = (1 + 2.12 - 1) 11. r(t) = (1 + 1)i + (31 - 1)j + 2tk 12. r(t) = 2 cos ti + tj + 2 sin tk 29 12. r(t) = 2 cos ti + tj + 2 sin tk
Sketch the space curve represented by the vector-valued function and give the orientation of the curve. r(t) = 5 cos(t)i + 5 sin(t)j + tk o op Tul Tul V - 5 y - 5
Solve the initial value problem for r as a vector function of t. dr Differential equation: = -32k . = 21 + 2] Initial conditions: r(0) = 60k and r(t) = (i+1+OK
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...