Answer to Question #228939 in Calculus for fouzi

Question #228939

 Find the domain of r(t) and the value of r(t0).4. r(t) = 2e−t ,sin−1 t, ln(1 − t); t0 = 0


1
Expert's answer
2021-09-01T11:41:33-0400


Let us find the domain of "r(t)", where

"r(t) = (2e^{\u2212t}, \\sin^{\u22121} t, \\ln(1 \u2212 t))."

Taking into account that the domain of the function "2e^{\u2212t}" is the set "\\R" of all real numbers, the domain of the function "\\sin^{\u22121} t" is the set "[-1,1]" and the domain of the function "\\ln(1 \u2212 t)" consists of all "t\\in\\R" such that "1-t>0," that is "t<1," we conclude that the domain of the vector-function "r(t)" is the set "[-1,1)."

Let us find the value of "r(t_0)" for "t_0=0:"

"r(t_0)=r(0)=(2e^{0}, \\sin^{\u22121} 0, \\ln(1 \u2212 0))=(2,0,0)."


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