Let A(x) = tan x i + ln x j + k. Then dA/dx =
The domain of the vector function r(t) = t³i + 1/(t − 1)j + ln(t − 2)k, t ∈ ℝ, is:
Is the vector function F(t) = cos t i + sin 2t k continuous at t = π?
The domain of the vector function B(t) = (1/t)i + (t² − 4)j + ln(t)k is:
A vector function F(t) is continuous at t = t₀ if
The velocity of a particle whose motion is given by r(t) = (t/2π)i + 3 cos t j at time t = π/2 is:
For what values of t is the vector function F(t) = sin t i + 3 cos t j + tan t k continuous?
The magnitude of the velocity of a particle at t = π, whose motion is given by r(t) = 4 cos t i + 4 sin t j + (3t²/2π)k, is:
The value(s) of t at which g(t) = −(1/2)i + |t|j + t³k is differentiable:
The rule d/dt {aA + bB} = a(dA/dt) + b(dB/dt) is called:
For what value(s) of t is the vector function F(t) = 1/(t − 2) i + sin t j continuous?
Find a′(t) if a(t) = √t i + 4j + 5/t² k.
If f(t) = t²i − e²ᵗj, then f′(t) =
The magnitude of the acceleration of a particle at t = π/2, whose motion is given by r(t) = 4 cos(t)i + 4 sin(t)j + (3t²/2π)k, is:
The function A = x + sin(x − y²) is called:
If u(t) = t²i − e²ᵗj is a vector function and h(t) = t² + 2t − 2 is a scalar function, then lim(t→0) [h(t)u(t)] =
In a vector function, the domain is:
If A(t) = (t² − 1)i + (1 − 2t)j + 5k, then A(0) =
Let a = 2i + 3j + 5k. Then da/dt =
What are the two numbers whose sum is 20 and whose product is maximum?
