Find the limit or indicate that it does not exist.

ModifyingBelow lim With t right arrow pilimt$$left bracket left parenthesis font size decreased by $3$ Bold sin font size decreased by $3$ three fourths t right parenthesis Bold i plus left parenthesis font size decreased by $3$ Bold cos font size decreased by $3$ seven fourths t right parenthesis Bold j plus left parenthesis font size decreased by $3$ Bold tan font size decreased by $3$ two thirds t right parenthesis Bold k right bracket$$sin$34$ti$+$cos$74$tj$+$tan$23$tk

Question content area bottom

Part $1$

Select the correct choice below$$ and, if$$ necessary, fill in the answer boxes in your choice.

A$.$

ModifyingBelow lim With t right arrow pilimt$$left bracket left parenthesis font size decreased by $3$ Bold sin font size decreased by $3$ three fourths t right parenthesis Bold i plus left parenthesis font size decreased by $3$ Bold cos font size decreased by $3$ seven fourths t right parenthesis Bold j plus left parenthesis font size decreased by $3$ Bold tan font size decreased by $3$ two thirds t right parenthesis Bold k right bracket$$sin$34$ti$+$cos$74$tj$+$tan$23$tkequals$=$left parenthesis nothing right parenthesis Bold i plus left parenthesis nothing right parenthesis Bold j plus left parenthesis nothing right parenthesis Bold kenter your response herei$+$enter your response herej$+$enter your response herek

$($Type exact$$ answers.$)$

B$.$

The limit does not exist.