How to find the limit of a complicated function using L'Hopital's rule?

[don23]

can someone help me out with a simple calc question?

we are asked to find the limit of a function as t approaches zero. the function is:

(sint/2t)i + (e^2t)j + (t^2/e^t)k

why is the answer not just j?

the answer given is 1/2i + j, but I have no idea how that first term came about.

help!

 

[shmoe]

sin(t)/(2t) as t->0 is one of those indeterminate 0/0 forms, it's not 0 as you seemed to hope. You should know the limit of sin(t)/t as t->0, it's a pretty standard one (or you can use l'hopital's rule).

 

[yourdadonapogostick]

can someone help me out with a simple calc question?

we are asked to find the limit of a function as t approaches zero. the function is:

(sint/2t)i + (e^2t)j + (t^2/e^t)k

why is the answer not just j?

the answer given is 1/2i + j, but I have no idea how that first term came about.

help!

$$\lim_{t{\to}0}\frac{\sin{t}}{t}=1$$

edit: i can't remember the diravation at the moment

 

[don23]

thank you

thank you:) it's been a while...i forgot about l'hopital's rule. thanks again