SECTION A

answer EVERY question

Question 1 (10 marks)

“Differentiate the following, simplifying the answer where appropriate:

`y = 4𝑥7 + 3𝑥2 - 2𝑥0.5 – 27`

(2 marks)

y = (3𝑥2 + 7)(𝑥3 – 4𝑥)

(2 marks)

y = (5𝑥4 + 2)6

(2 marks)

y = (x^2+1)/(2x^3-3x^4 )

(4 marks)”

Question 2 (8 marks)

“Find the stationary points of the following functions and determine whether each is a local maximum, a local minimum or a point of inflection:

`y = 𝑥3 + 1.5𝑥2 - 18𝑥 + 7`

(4 marks)

y = 1/3 x^3 – 𝑥2 + 𝑥 + 4

(4 marks)”

Question 3 (5 marks)

“For each of the following, find the partial derivatives ∂z/∂x and ∂z/∂y :

`z = 4𝑥3 + 3y4 – 17`

(2 marks)

z = 𝑥2y3 – 𝑥7y + 𝑥y5

(3 marks)”

Question 4 (5 marks)

“Find the following indefinite integrals:

`∫(3𝑥2 – 𝑥 -2) d𝑥`

(2 marks)

∫(2𝑥 + 3)(𝑥2 + 3𝑥)4 d𝑥

(3 marks)”

Question 5 (3 marks)

“Evaluate the following definite integral:”

`∫_2^6▒〖(x^3 〗 + 2𝑥 – 7) d𝑥 `

SECTION B

ANSWER EVERY QUESTION

Question 6 (15 marks)

“Consider the Total Cost (TC) function

TC 2.2q3 16q2 48q 150

Where q is the level of output.

Show that the Average Cost is at it’s minimum when q = 5.

(4 marks)

Find the output at which marginal cost is at its minimum.

(4 marks)

Show that MC = AC when AC is at its minimum.

(2 marks)

Sketch the graphs of the MC and AC functions, on the same axes.

(5 marks)”

Question 7 (8 marks)

“Given the demand function q = – 3p2 + 2p + 1965

Find the arc elasticity of demand when p increases

from 10 to 11

from 24 to 25.

(4 marks)

Find the point elasticity

when p = 10

when p = 24

(4 marks)”

Question 8 (8 marks)

“Find the stationary point of the following function, and determine whether it is a maximum, minimum, or saddle point:”

`z = 5𝑥2 + 2y2 + 4𝑥y - 2𝑥 + 10y + 1000`

Question 9 (15 marks)

“A firm’s production function is Q = K^□(1/3) L^(2/3)

Where Q is the output of a good resulting from inputs of capital (K) and labour (L).

Find the marginal products of capital and labour. Show that they can be written as:

MPK = Q/3K MPL = 2Q/3L

(4 marks)”

“Are the marginal products of capital and labour always positive? Sketch their graphs.

(3 marks)”

“Find the equations of the isoquants for

10 units of output

15 units of output.

In each case, express the isoquant both as an implicit function and also with K as an explicit function of L.

(3 marks)”

“By implicit differentiation, find the slope of any isoquant and show that this slope is given by the ratio of the marginal products of capital and labour. Is the slope always negative?

(5 marks)”

Question 10 (13 marks)

“Ben’s utility function is given by:

` U = X3Y2`

where X and Y are the weekly consumption levels of goods X and Y.”

The market price of good X is £2 and of good Y is £1.

“If Ben’s weekly budget is £100, use the Lagrange multiplier method to find the quantities of goods X and Y that Ben should buy each week in order to maximise his utility.”

(9 marks)

`“Suppose that the price of good X rises to £3. Find the new utility-maximising quantities. Comment on how the rise in price of good X effects the demand for good Y.”`

(4 marks)

Question 11 (10 marks)

“Given the inverse demand function:

p 9 q 0.1q2

`Find the consumers' surplus when quantity purchased is q 5.`

(6 marks)

How does consumers’ surplus change if q increases to q 5.5?

(4 marks)”

Sample Solution

symbols are paying an immeasurable service of presenting and apprehending the culture and the world. Theoretical background clearly immerge the interdisciplinary doctrine with vast range of topics to make consciousness on the academics and public on this purpose. One of the most prominent theories, Mick’s schema theory has fused semiotics and showed the viewer’s its capacity of specialization of the social structure, processing and involving attitudes, memory and cognition as well as written and spoken text. Goal, knowledge and text schemata are the three popular genres of schema theory of Mick proposed into marketing communication research. The goal and knowledge schemata are important factors and probably make the relations with both marketers and consumers. According to Mick, the text schemata mainly involves in the linguistic massages in marketing communication. This schema theory has the ability to enrich the marketing communication study. Some scholars like Sherry highlighted that the advertising is a cultural document, a way of presenting and apprehending the world. Each and every advertisement is included in cultural shadow and let the readers to negotiate and share the cultural subject matter. Symbols are artistic and man-made. These symbols constructed the world and made the network of social relations in much the same way as religion, science and arts. Science and arts construct the scientific and aesthetic world. Symbolic action and symbolic interaction gratify in the social stream to construct the shadows of the distinctive behaviours of human. The symbolic and iconic conversation and conventions in the advertisements moves its audience via ritualized enactments by the properties of experiences the cultural esteems . This repetitive ritual will help to maintain the culture by reducing the variance in the cultural behaviour and probably help to lead the cultural perceptions to become natural perceptions. Advertisements construct the definitive reality in the viewpoint. This>

GET ANSWER