Determine where the vector function r(t) = (14)i + (147) j is continuous. (Use symbolic notation and fractions where nee
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Determine where the vector function r(t) = (14)i + (147) j is continuous. (Use symbolic notation and fractions where nee
The position of an object at time t is r(t) = (7 + t)i + e¹j. Eliminate the parameter t to find y as a function of x. (Express numbers in exact form. Use symbolic notation and fractions where needed.) y =
Find the domain of the vector function r(t) = 8√ſti + 6 lntj+7tk. (Use symbolic notation and fractions where needed. Give your answers as intervals in the form (*, *). Use the symbol ∞ for infinity, U for combining intervals, and an appropriate type of parenthesis "(", ")", "[" or "]" depending on whether the interval is open or closed. Enter Ø if the interval is empty.) D(r(t)) = =
Let u(t) = tºi – t³j + 8tk and v(t) = 7ti − t³j + tºk. Find d[u(t) · v(t)] and [u(t) × v(t)]. (Express numbers in exact form. Use symbolic notation and fractions where needed.) -[u(t) · v(t)] = dt (Give your answer using component form or standard basis vectors. Express numbers in exact form. Use symbolic notation and fractions where needed.) d -[u(t) x v(t)] = dt
Find the angle between the tangent vectors to the curves traced out by r₁ (t₁) = sin (8t₁)i + sin (9t₁)j + tik and r₂(12) = ti + 7t₂j + tk at the point of intersection (0, 0, 0). (Give your answer as an exact number. Use symbolic notation and fractions where needed.) 0 =