Vector-valued functions and continuity: Given: r(t)=&lt;4t+2,sin⁡(πt),1t3&gt; what is the limr(t) as t⇒−1

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Vector-valued functions and continuity:  Given:  r(t)=&amp;lt;4t+2,sin⁡(πt),1t3&amp;gt;  what is the limr(t) as t⇒−1

Blanche McClain · Accepted Answer

Step 1 Given: A vector-valued function and continuity, r(t)=&amp;lt;4t+2,sin⁡(πt),1t3&amp;gt; To find: The limit of r(t), That is,limt⇒−1r(t) Step2 Formula used: limt⇒at=a andlimt⇒asin⁡(t)=sin⁡(a) Definition: A vector value function is a function where the domain is a subset of the real numbers and the range is a vector. In two dimensions r(t)=x(t)i+y(t)j In three dimensions r(t)=x(t)i+y(t)j+z(t)k  Step3 Here, r(t)=&amp;lt;4t+2,sin⁡(πt),1t3&amp;gt; limt⇒−1r(t)=limt⇒−1&amp;lt;4t+2,sin⁡(πt),1t3&amp;gt; limt⇒−1r(t)=&amp;lt;limt⇒−1(4t+2),limt⇒−1(sin⁡(πt),limt⇒−1(1(t3))&amp;gt; limt⇒−1r(t)=&amp;lt;4(−1)+2,−sin⁡(π(1)),1(−1)3&amp;gt; limt⇒−1r(t)=&amp;lt;−2,0,−1&amp;gt;

Vector-valued functions and continuity: Given: \r(t)=<4t+2,\sin(pi t),1/t^{3}> what is the \lim r(t) as

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