Limits and Continuity

The $\displaystyle \lim_{x \to 2} \frac{x^2-4x+4}{x-2} =$

Find the value of $\displaystyle \lim_{x \to 4} \frac{x^2 - 2x - 8}{x - 4}$

Evaluate: $\displaystyle \int_2^4 (3x - 2)^2 dx$

Determine $\displaystyle f(x)$, given that $\displaystyle f'(x) = 12x^2 - 4x$ and $\displaystyle f(-3) = 17$

Find $\displaystyle \frac{dy}{dx}$ where $\displaystyle x = \frac{e^t + e^{-t}}{2}$ and $\displaystyle y = \frac{e^t - e^{-t}}{2}$

What is the differential function of $\displaystyle \sqrt{x^2 + 2}$ ?

Find $\displaystyle \frac{dy}{dx}$ for $\displaystyle x^2y^2+y = 0$.

The cost function of an organisation as $\displaystyle C(x) = 500-5x^2+\frac{x^3}{3}$, where $\displaystyle x$ denotes the output. Find the level of output at which marginal cost is the minimum.

The value of $\displaystyle \int_{0}^{4} \frac{x+3}{x+2} dx$ is

The value of $\displaystyle \int_{3}^{4} \frac{2x}{1+x^2} dx$ is

If $\displaystyle f(x) = 3e^{2x}$, then $\displaystyle f'(x) - 2xf(x) + \frac{1}{6}f(0) - f'(0)$ is equal to

The cost of production of an item is given as $\displaystyle C=50x - 5x^2 + \frac{x^3}{6}$ where 'x' is number of items to be produced. If the average cost and marginal cost are equal then, what quantity of items should be produced?

The cost function of a company is given by $\displaystyle C(x) = 600x - 10x^2 + \frac{x^3}{2}$ where x denotes the output. Find the level of output (in nearest integer) at which average cost is minimum.

Evaluate the integral $\displaystyle \int_0^1(2x^2-x^3)dx$

Find the value of $\displaystyle \lim_{x \to 4} \frac{x^2 - 2x - 8}{x - 4}$

Evaluate: $\displaystyle \int_2^4 (3x - 2)^2 dx$

Determine $\displaystyle f(x)$, given that $\displaystyle f'(x) = 12x^2 - 4x$ and $\displaystyle f(-3) = 17$

Find $\displaystyle \frac{dy}{dx}$ where $\displaystyle x = \frac{e^t + e^{-t}}{2}$ and $\displaystyle y = \frac{e^t - e^{-t}}{2}$

What is the differential function of $\displaystyle \sqrt{x^2 + 2}$ ?

Find $\displaystyle \frac{dy}{dx}$ for $\displaystyle x^2y^2+y = 0$.

The cost function of an organisation as $\displaystyle C(x) = 500-5x^2+\frac{x^3}{3}$, where $\displaystyle x$ denotes the output. Find the level of output at which marginal cost is the minimum.

The value of $\displaystyle \int_{0}^{4} \frac{x+3}{x+2} dx$ is

The value of $\displaystyle \int_{3}^{4} \frac{2x}{1+x^2} dx$ is

If $\displaystyle f(x) = 3e^{2x}$, then $\displaystyle f'(x) - 2xf(x) + \frac{1}{6}f(0) - f'(0)$ is equal to

The cost of production of an item is given as $\displaystyle C=50x - 5x^2 + \frac{x^3}{6}$ where 'x' is number of items to be produced. If the average cost and marginal cost are equal then, what quantity of items should be produced?

The cost function of a company is given by $\displaystyle C(x) = 600x - 10x^2 + \frac{x^3}{2}$ where x denotes the output. Find the level of output (in nearest integer) at which average cost is minimum.

Evaluate the integral $\displaystyle \int_0^1(2x^2-x^3)dx$

Question 5 (a) SemiCon Pvt. Ltd. (SPL) is engaged in manufacturing of semiconductors from 2024. It wants to build best quality semiconductor and display design with innovative ecosystem to enable India's emergence as a global hub for electronics manufacturing. Placing core values as priority, it wants to articulate its aspirations to stakeholders with a guiding beacon to keep inspiring its workforce. Identify and explain one component of strategic intent indicating above intentions. Why is such component important? State its essentials. (1+1+1+2 = 5 Marks) (b) 'Twaran', a small and mid-sized business, wants to use latest digital technologies for improved procedures and products. Primary aim: competitive edge by digital transformation. It wants to deal with regular changes firmly and transform its management techniques. Identify the strategy required for digital transformation. State the most preferred practices. (1+4 = 5 Marks) (c) MaAi group acquired a business dealing in product 'Nota' in 2020. It was not contributing as expected. In 2023, emphasis was placed on change in management and improvement in internal efficiency. In 2024, positive outcome was still absent, and the company decided to get rid of the business. Identify retrenchment strategies in (i) 2023 and (ii) 2024. State reasons for adopting the 2024 strategy. (1+1+3 = 5 Marks)

Question 6 (a) Explain the importance of values, as one of the components of strategic intent for a company. What are common examples of values? How are values different from intent? (3+1+1 = 5 Marks) (b) In order to get better performance and sustainable competitive advantages, a company has to focus on the characteristics of its resources and capabilities. Explain the major characteristics of resources and capabilities. (5 Marks)

Question 7 (a) What do you mean by value chain analysis? Delineate the support activities in value chain analysis, as stated by Michael Porter. (1+4 = 5 Marks) (b) Explain differentiation strategy as one of the generic strategies by Michael Porter. What are the major bases of differentiation? Also outline the strategies which can help achieve the differentiation strategy. (1+2+2 = 5 Marks)

Question 8 (a) What do you mean by Key Success Factors (KSF)? Structure the questions to which can help identify KSFs of a company. Also state how the understanding can help ascertain sustainable competitive advantages. (1+2+2 = 5 Marks) (b) Explain in brief the expansion strategy as one of the corporate strategy. Also state the characteristics of expansion strategy. (1+4 = 5 Marks) OR "A manager as a strategic leader has to play many leadership roles", while explaining the statement in brief, delineate the leadership roles which a manager has to play in pushing for a good strategy execution. (1+4 = 5 Marks)

What is the value of $\displaystyle \lim_{y \to 2} \frac{y^2-4}{y-2}$