(a) Find the following: x1/3 + 9x1/5 (2х — 1)1/2 — 3 i. Lim- X-0 6x1/2 – 4x1/4 ii. Lim X-+5+ х— 5 (b) The total revenue curve of a firm is R(q) = 40q – 12q² and its %3D 1 400 average cost A(q) =9? – 12.85q + 20 +, where q is the firm's output. i. Derive an expression C(q) for the firm's total cost function. ii. Derive an expression II(q) for the firm's profit function. iii. Is the rate of change of profit increasing or decreasing when the ouput level of the firm is 10 units? iv. Determine the level of output for which the firm's profit is maximized. v. What is the firms's maximum profit?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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(a) Find the following:
x1/3 + 9x1/5
(2х — 1)1/2 — 3
i. Lim-
X-0 6x1/2 – 4x1/4
ii. Lim
X-+5+
х— 5
(b) The total revenue curve of a firm is R(q) = 40q – 12q² and its
%3D
1
400
average cost A(q) =9? – 12.85q + 20 +, where q is the firm's output.
i. Derive an expression C(q) for the firm's total cost function.
ii. Derive an expression II(q) for the firm's profit function.
iii. Is the rate of change of profit increasing or decreasing when the
ouput level of the firm is 10 units?
iv. Determine the level of output for which the firm's profit is maximized.
v. What is the firms's maximum profit?
Transcribed Image Text:(a) Find the following: x1/3 + 9x1/5 (2х — 1)1/2 — 3 i. Lim- X-0 6x1/2 – 4x1/4 ii. Lim X-+5+ х— 5 (b) The total revenue curve of a firm is R(q) = 40q – 12q² and its %3D 1 400 average cost A(q) =9? – 12.85q + 20 +, where q is the firm's output. i. Derive an expression C(q) for the firm's total cost function. ii. Derive an expression II(q) for the firm's profit function. iii. Is the rate of change of profit increasing or decreasing when the ouput level of the firm is 10 units? iv. Determine the level of output for which the firm's profit is maximized. v. What is the firms's maximum profit?
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