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Each of these functions can be computed using the stack, or using algebraic entry, whichever way you prefer:

Computing
‘`sin(x) / x`’:

Using the stack: `C-x ( RET S TAB / C-x )`.

Using algebraic entry: `C-x ( ' sin($)/$ RET C-x )`.

Computing the logarithm:

Using the stack: `C-x ( TAB B C-x )`

Using algebraic entry: `C-x ( ' log($,$$) RET C-x )`.

Computing the vector of integers:

Using the stack: `C-x ( 1 RET 1 C-u v x C-x )`. (Recall that
`C-u v x` takes the vector size, starting value, and increment
from the stack.)

Alternatively: `C-x ( ~ v x C-x )`. (The `~` key pops a
number from the stack and uses it as the prefix argument for the
next command.)

Using algebraic entry: `C-x ( ' index($) RET C-x )`.