Question

U. I also
(B) Multiple Choice Questions
lim
lim
1. Let f(t) and g(t) be two vector functions such that f(t) = L and g(t) = M, then
t - to
t to
lim
[f(t) x g(t)] is
t to
(a) L
(b) M
(C) LM
(d)LxM​

Answer 1

Answer:

A vector function r(t)=⟨f(t),g(t),h(t)⟩ is a function of one variable—that is, there is only one "input'' value. What makes vector functions more complicated than the functions y=f(x) that we studied in the first part of this book is of course that the "output'' values are now three-dimensional vectors instead of simply numbers. It is natural to wonder if there is a corresponding notion of derivative for vector functions. In the simpler case of a function y=s(t), in which t represents time and s(t) is position on a line, we have seen that the derivative s′(t) represents velocity; we might hope that in a similar way the derivative of a vector function would tell us something about the velocity of an object moving in three dimensions.

One way to approach the question of the derivative for vector functions is to write down an expression that is analogous to the derivative we already understand, and see if we can make sense of it. This gives us

Step-by-step explanation: