Cálculo diferencial

What is the limit of f(x) as x approaches infinity for 81X?

The function approaches a constant value.

What is the limit of f(x) as x approaches 2 for x²-x-2?

The limit evaluates to 4.

How does the utility function U = 10.000(1-e-0.001x) - x behave as x increases?

Utility increases but at a decreasing rate.

What does the derivative du/dx represent in the context of utility?

It indicates the rate of change of utility with respect to advertising spend.

What is the marginal cost when q = 100 for c = 0.03q + 1.2?

It reflects the cost of producing one additional unit.

How do you find the equation of the tangent line to y = 3x² + 3x - 4 at P(-1, -4)?

Use the derivative to find the slope at that point.

What is the limit of f(x) as x approaches 3 for x³?

The limit equals 27.

What is the limit of f(x) as x approaches 1 for x²?

The limit equals 1.

How do you calculate the tangent line to y = 4x² + 5x + 6 at x = 1?

Evaluate the derivative at x = 1 for the slope.

What is the average rate of income change when price increases from $4 to $6.25?

It measures the sensitivity of sales to price changes.

What does P(t) = 10.000 + 1.000 - 1201² represent in population growth?

It models population size over time.

What is the growth increment between years 3 and 5 for the population model?

It quantifies the change in population size over that period.