Find Limit of Vector: i+(Sin(4t))/(4t)+e^(-5t)k

[iberhammer]

Find the limit (if it exists). (If an answer does not exist, enter DNE.)
lim t → 0
e^9t i + (Sin(4t))/(4t) j + e^(-5t) k

My approach was to plug in 0 and get i+k but that didn't go through with webassign. So I tried the DNE answer because maybe since the y could be undefined, the whole thing is, but that was wrong. So lastely I punched it into my calculator, got the decimal answer and that didn't work for i + (decimal) j + k.

Does anyone know how to solve for the limit?

 

[Mark44]

The only tricky one here is the limit for the j coordinate,
$$\lim_{t \to 0} \frac{sin(4t)}{4t}$$

This is related to the following well-known limit from calculus,
$$\lim_{t \to 0} \frac{sin(t)}{t} = 1$$