Only 3 Question 2For each of the following assertions, first state whether it is true or false. Then, provide fullsupport for your statement by using theorems, definitions and/or examples where applicable.No marks will be awarded for unsupported statements.1. The function f(x, y, z) =l+3z + x² is a linear function.2. If lim xn = 1 and lim yn = 0, then it is possible to formally prove that lim(xn – Yn) = 1.3. The Cobb-Douglas production function F(x)0.2ln(x1) + 0.8ln(x2) is subject to dimin-%3Dishing marginal productivity for input r2 around the point (1, 1).4. Given that the function g(u, v) is an onto function, if f(g(u, v)) = h(u, v), then it logicallyfollows that h(u, v) is always onto.5. f(x) = x* is a one-to-one function on the subset of its domain where (-5

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Answered: 3. The Cobb-Douglas production function…

3. The Cobb-Douglas production function F(x) = 0.2ln(x1) + 0.8ln(x2) is subject to dimin- ishing marginal productivity for input r2 around the point (1, 1).

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Chapter1: Making Economics Decisions

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Question

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Question 2
For each of the following assertions, first state whether it is true or false. Then, provide full
support for your statement by using theorems, definitions and/or examples where applicable.
No marks will be awarded for unsupported statements.
1. The function f(x, y, z) =l+3z + x² is a linear function.
2. If lim xn = 1 and lim yn = 0, then it is possible to formally prove that lim(xn – Yn) = 1.
3. The Cobb-Douglas production function F(x)
0.2ln(x1) + 0.8ln(x2) is subject to dimin-
%3D
ishing marginal productivity for input r2 around the point (1, 1).
4. Given that the function g(u, v) is an onto function, if f(g(u, v)) = h(u, v), then it logically
follows that h(u, v) is always onto.
5. f(x) = x* is a one-to-one function on the subset of its domain where (-5 <x < -1).

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