MSc Economics Preparatory Module

1. Which relationships are always true for any function and a point ? (Multiple choice)

2. How do the Jacobian and Hessian concepts relate to each other with respect to a twice differentiable function ? (Single choice)

3. Consider . The second order partial derivative maps onto:

4. Consider a function and suppose that is differentiable. Then, its derivative is:

5. Consider . Compute the Taylor error for the first order approximation around at . To be able to enter a natural number into the solution field, perform the following operations in the given order to your result: 1. Add , 2. Multiply with 8. (Do not use spaces, letters, etc. Hint: the correct number to enter is an element of .)

6. How do integration and differentiation relate to each other?

7. Consider a function and suppose that is differentiable. Then, its partial derivative with respect to the first dimension evaluated at is:

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