Let y be the curve with vector form r(t) = (1/(t +2), sin(sin(sin t)), e-t). (a) Determine whether the curve y passes through the point (1,0, 1). (b) Compute lim r(t), or show that this limit does not exist. t一→0 (c) Compute r(t) dt. -
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Given, is a curve with vector form
(a)
Claim: does not pass through (1,0,1).
Suppose that the curve passes through the point
Then there exists some such that all three are satisfied.
Solving them,
But t can't be 0 as well as -1 at the same time; which is a contradiction.
Hence, does not pass through (1,0,1).
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