Consider the following function. (Let n be an arbitrary integer.) r(t)=tan⁡(t)i+j+k (a) Find the domain of r. (b) Determine the interval(s) on which the function is continuous.

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Consider the following function. (Let n be an arbitrary integer.)  r(t)=tan⁡(t)i+j+k  (a) Find the domain of r.  (b) Determine the interval(s) on which the function is continuous.

Sevensis1977 · Accepted Answer

Step 1 part a we have been given the vector-valued function r(t)=tan⁡(t)i+j+k we have to find the domain of the vector-valued function to find the domain we intersect the domain of each component is tan(+) first component is tan⁡(t) which can be written as tan⁡(t)=sin⁡(t)cos⁡(t), tan⁡(t) can take all the values of R but it can&#039;t take the values where cos⁡(t) is zero otherwise tan⁡(t) will become non-definable. And cos⁡(t) is zero at {2n+1}π2 hence the domain of tan⁡(t) is R−{2n+1}π2 second and third components are constant therefore the domain of r(t) is R−{2n+1}π2 or t≠{2n+1}π2 Step 2 part b now, we have to find the interval where r(t) is continuous the vector function is continuous for all values of R but tan⁡(t) is piecewise continuous on R tan⁡(t) is not continuous at {2n+1}π2 as it is undefinable here hence, t≠{2n+1}π2

Consider the following function. (Let n be an arbitrary integer.) r(t)=\tan(t)i+j+k (a)

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