ECON 4410/6410 Fall 2022 Assignment #1

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ECON 4410/6410

Fall 2022

Assignment #1

1. Evaluate the following limits:

(a) limx二0  .

(b) limx二o  . Does the function converge? If so, what is the horizontal asymptote?

(c) limx二o  . Does the function converge? If so, what is the horizontal asymptote?

2. Evaluate the following derivatives:         (a)   , where f (x) = 5x2 + x3 − 7x4 . (b)   , where f (x) = xln(x).

(c)   , where f (x, y) = (5x − y)α .

(d)   , where f (x, y) = x3y2 .

(e)   , where f (x, y) = x3y2 .

3.  Suppose a is a function of b. Implicitly differentiate the following to derive  :

(a)  (b − a)2  = a + b − 1.

(b) a3 + b3  = 4.

4.  M.A . students only. Let f be a continuously differentiable function of x. Show that if f is homogeneous of degree k, its derivatives must be homogeneous of degree k − 1.