Question

Find the domain of the vector function r(t) = cos(t) i + ln(t) j + (1 / (t - 7)) k. Enter your answer using interval notation.

Answer 1

The domain of the vector function r(t) = cos(t) i + ln(t) j + (1 / (t - 7)) k is (0, 7) U (7, ∞).

Step-by-step explanation:

The domain of the vector function r(t) = cos(t) i + ln(t) j + (1 / (t - 7)) k consists of all values of t that make the function well-defined. The function is undefined when the natural logarithm term is not defined and when the denominator of the third component is zero.

Considering that the natural logarithm is only defined for positive real numbers, we have t > 0 as a restriction. Additionally, the denominator t - 7 cannot be equal to zero, so t ≠ 7. Therefore, the domain of the function is the interval (0, 7) U (7, ∞).