Resolved: "Evaluate the vector-valued function at each given value..."

expeditiupc

Answered question

2021-12-10

Evaluate the vector-valued function at each given value of t.

r (t) = (2 t + 1) i + t^{2} j - \sqrt{t} + 2 k

(a)

r (0) (b) r {- 2) (c) r (c - 1)

(d)

r (1 + △ t) - r (1)

Serita Dewitt

Beginner2021-12-11Added 41 answers

Step2
Given -

r (t) = (2 t + 1) i + t^{2} j - (\sqrt{t + 2}) k

r (0) = (2 (0) + 1) i + {(0)}^{2} j - (\sqrt{0 + 2}) k = i - \sqrt{2} k

r (- 2) = (2 (- 2) + 1) i + {(- 2)}^{2} j - (\sqrt{- 2 + 2}} k = - 3 i + 4 j

Step3
c)

r (c - 1) = (2 (c - 1) + 1) i + {(c - 1)}^{2} j - (\sqrt{c - 1 + 2}) k + (2 c - 1) i + {(c - 1)}^{2} j + \sqrt{c + 1} k

r (1 + △ t) - r (1) = (2 (1 + △ t) + 1) i + {(1 + △ t)}^{2} j - (\sqrt{1 + △ t + 2}) k - ((2 (1) + 1) i + {(1)}^{2} j - (\sqrt{1 + 2} k)}

= 2 △ t i + (2 △ t + {(△ t)}^{2}) j - (\sqrt{3 + △ t} - \sqrt{3}) k

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