Find the limit $\lim _ { t \rightarrow 0 } \left[ \left( t ^ { 2 } + 3 \right) \mathbf { i } + \cos 5 t \mathbf { j } - 6 \mathbf { k } \right]$
Select the correct answer.
A) $3 \mathbf { i } - 6 \mathbf { k }$
B) $4 \mathbf { i } + \mathbf { j }$
C) $\quad 3 \mathbf { i } + \mathbf { j } - 6 \mathbf { k }$
D) $4 \mathbf { i }$

Question

Quizplus · Accepted Answer

We can simply take the limit of each component separately:

$$\lim_{t \rightarrow 0} (t^2+3) = 3$$
$$\lim_{t \rightarrow 0} \cos(5t) = 1$$
$$\lim_{t \rightarrow 0} -6 = -6$$

Therefore, the limit is:

$$\lim_{t \rightarrow 0} [(t^2+3)\mathbf{i} + \cos(5t)\mathbf{j} - 6\mathbf{k}] = 3\mathbf{i} + \mathbf{j} - 6\mathbf{k}$$

So the correct choice is C.

Find the Limit lim⁡t→0[(t2+3)i+cos⁡5tj−6k]\lim _ { t \rightarrow 0 } \left[ \left( t ^ { 2 } + 3 \right) \mathbf { i } + \cos 5 t \mathbf { j } - 6 \mathbf { k } \right]limt→0​[(t2+3)i+cos5tj−6k]

Find the Limit $\lim _ { t \rightarrow 0 } \left[ \left( t ^ { 2 } + 3 \right) \mathbf { i } + \cos 5 t \mathbf { j } - 6 \mathbf { k } \right]$