z = f(x, y) = +x*e +In[(2x + y)*I 2xy Determine the total differential (dg), and total derivative with respect to x g = f(x,y, z) = In(xyz) + e3x + ezy + e 6. where x = z/3 and y = 5

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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6 only. 

1.
Find the linear approximation of F(N) = AK“N®, about N = 1
2. The cost of producing q units of good is C(q) = 0.1q? + 3q + 100 pesos. The firm can sell q units when the price is p(q) =
25 – 0.05q pesos per unit. (Hint: Marginal Cost is C'(q))
Determine the marginal cost, marginal revenue and marginal profit. (Hint: p(q) is not the revenue function).
What is the approximate change in cost and revenue when the quantity increases from 20 to 25?
a.
b.
The cost of producing q units of a good is C(q) = 50q + 500, and the firm sells q units at p(q) = 500 – 2q.
Determine the approximate change in profit when quantity sold changes from 115 to 120. How different is the actual
change and the approximate change from each other?
3.
4. Consider a three-sector economy, Y = C +1+G, where both consumption and investment are a function of income.
Consumption is defined as C = a+ bY and I = e + dY
Determine the equilibrium level of income.
What is the government multiplier? (Hint: getting the derivative of the equilibrium income wrt G)
Given that 56% of income is use on consumption, and 12% of income is used on investment. Determine the value
for the multiplier effect.
If government spending increases by 168, determine the change in equilibrium income.
а.
b.
C..
d.
* Determine the total differential of z,
5.
x - y
z = f(x, y) =:
+x*e + In[(2x + y)²]
2xy
• Determine the total differential (dg), and total derivative with respect to x
g = f(x, y, z) = In(xyz) + e3* + ezy +e*
6.
where x = z/3 and y = 5
Find the total differential and total derivative. For the total derivative it is with respect m (or dg/dm)
a. g = f(x, y) = 2y3 – xy + 2x2 ,y = 3m x = 6m + 3
7.
b. g = f(t, v) = tv, t Inm v = m
Transcribed Image Text:1. Find the linear approximation of F(N) = AK“N®, about N = 1 2. The cost of producing q units of good is C(q) = 0.1q? + 3q + 100 pesos. The firm can sell q units when the price is p(q) = 25 – 0.05q pesos per unit. (Hint: Marginal Cost is C'(q)) Determine the marginal cost, marginal revenue and marginal profit. (Hint: p(q) is not the revenue function). What is the approximate change in cost and revenue when the quantity increases from 20 to 25? a. b. The cost of producing q units of a good is C(q) = 50q + 500, and the firm sells q units at p(q) = 500 – 2q. Determine the approximate change in profit when quantity sold changes from 115 to 120. How different is the actual change and the approximate change from each other? 3. 4. Consider a three-sector economy, Y = C +1+G, where both consumption and investment are a function of income. Consumption is defined as C = a+ bY and I = e + dY Determine the equilibrium level of income. What is the government multiplier? (Hint: getting the derivative of the equilibrium income wrt G) Given that 56% of income is use on consumption, and 12% of income is used on investment. Determine the value for the multiplier effect. If government spending increases by 168, determine the change in equilibrium income. а. b. C.. d. * Determine the total differential of z, 5. x - y z = f(x, y) =: +x*e + In[(2x + y)²] 2xy • Determine the total differential (dg), and total derivative with respect to x g = f(x, y, z) = In(xyz) + e3* + ezy +e* 6. where x = z/3 and y = 5 Find the total differential and total derivative. For the total derivative it is with respect m (or dg/dm) a. g = f(x, y) = 2y3 – xy + 2x2 ,y = 3m x = 6m + 3 7. b. g = f(t, v) = tv, t Inm v = m
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