Johns Hopkins University Math Methods for Economists & Indefinite Integral HW I will upload the original file below. The hand written version will be good

Johns Hopkins University Math Methods for Economists & Indefinite Integral HW I will upload the original file below.

The hand written version will be good!

1. Evaluate the following indefinite integral: � 2 6 2. Evaluate the following definite integral: � 12 5 + 8 3 − 16 + 4 6 + 4 − 4 2 + 2 − 6 10 5 3. For the following system of equations find solutions to the values of x, y, and z using the matrix inversion technique shown in this course. 1 23 2 3 2 xyz x yz xyz ++= + −= −−= 4. Find the partial derivative of the following equation with respect to x and y: = � 2 + 2 5. Without substituting u or v into Z, please find the total derivative of Z with respect to x: = ( 2 + 2) − ln � 2 2 − 6 + 3 � = = 2 − 3 6. Determine the critical points of functions for the following function: ( , ) = 4( − 2) − 2 − 3 Determine whether or not they correspond to local maxima, minima, or saddle-points. Clearly distinguish the first-order conditions and the second-order conditions. 2 7. Given the constraint, find the stationary points for the following function and evaluate the second order conditions. Use the Lagrange technique. f xy x y ( , ) ln 2ln = + Subject to 2 2 x y + = 6 Johns Hopkins University
Math Methods for Economists
Fall 2019 Final
Please show all your work. Failure to show all intermediate steps will result in
zero credit. Also, please remember to write your name on your answer sheet.
Finally, please use white unlined paper if possible and submit your file as a PDF.
1. Evaluate the following indefinite integral:
�
2
6
2. Evaluate the following definite integral:
�
10
5
12 5 + 8 3 − 16 + 4

6 + 4 − 4 2 + 2 − 6
3. For the following system of equations find solutions to the values of x, y, and z using
the matrix inversion technique shown in this course.
x+ y+z =
1
2x + 3y − z =
2
3x − y − z =
2
4. Find the partial derivative of the following equation with respect to x and y:
= � 2 + 2
5. Without substituting u or v into Z, please find the total derivative of Z with respect
to x:
= ( 2 + 2 ) − ln �
2
�
2 − 6 + 3

= 2 − 3
=
6. Determine the critical points of functions for the following function:
( , ) = 4( − 2 ) − 2 − 3
Determine whether or not they correspond to local maxima, minima, or saddle-points.
Clearly distinguish the first-order conditions and the second-order conditions.
7. Given the constraint, find the stationary points for the following function and
evaluate the second order conditions. Use the Lagrange technique.
6
f ( x,=
y ) ln x + 2 ln y Subject to x 2 + y 2 =
2

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