Question

Evaluate the vector-valued function at each given value of t. (If an answer does not exist, enter DNE.) r(t) = (2+ + 1)i + taj - Vt+ 2k + (a) r(0) i- v2k (b) r(-2) -3i + 4j (c) r(C-1) (20 – 1)i+(c-1);-vc+1 k (d) r(1 + At) - r(1)

Answer 1

To evaluate a vector-valued function at given values of t, substitute the values into the function. For example, to evaluate r(0), substitute t = 0 into the function.

Step-by-step explanation:

To evaluate the vector-valued function r(t) = (2 + t)i + taj - Vt + 2k at the given values of t, substitute those values into the function.

(a) To evaluate r(0), substitute t = 0 into the function: r(0) = (2 + 0)i + 0aj - V(0) + 2k = 2i - V2k.

(b) To evaluate r(-2), substitute t = -2 into the function: r(-2) = (2 - 2)i + (-2)aj - V(-2) + 2k = -2i - V2k.

(c) To evaluate r(C-1), substitute t = C-1 into the function: r(C-1) = (2 + C - 1)i + (C - 1)aj - V(C - 1) + 2k = (1 + C)i + (C - 1)aj - V(C - 1) + 2k.

(d) To evaluate r(1 + At) - r(1), first evaluate r(1 + At) by substituting t = 1 + At into the function, and then subtract r(1) from it.