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(a) Find the MRS of

`x_(1)`

for

`x_(2)`

for each of the following utility functions: I.

`,U(x_(1),x_(2))=x_(1)+x_(2)`

II.

`,U(x_(1),x_(2))=x_(1)^((1)/(2))x_(2)^((1)/(2))`

III.

`,U(x_(1),x_(2))=x_(1)^(2)+x_(2)^(2)`

IV.

`,U(x_(1),x_(2))=2x_(2)+x_(1)`