Question

1. (6 points) Solve the following limit and calculate the derivatives of the funcions f(x), g(x) and h(x). 3x²+2x+3 a) lim_{x?-3} (x²+x-3) b) f(x) = x + ln(x) c) g(x) = ?x³+5x d) h(x) = (2x³+e^x)²/3x 2. (6 points) A company produces batteries for electric cars. The market research department sets the price-demand function in dollars for x items: p(x) = 5000 - 10x The financial department provides the cost function: C(x) = 150,000 + 1000x a) What is the marginal cost when the level of production is 150 units? b) What is the marginal revenue when the level of production is 150 units? c) Find the marginal profit function. d) Find the break-even points. 3. (7 points) For the funcion f(x) = -x² - 1 + ln(x²) a) Find the first derivative of the function. b) Find the critical points. c) Find the second derivative of the function. d) Find the relative maximum and minimum. e) Find the absolute maximum and minimum. f) Find the intervals of concavity. 4. (6 points) Given the price-demand equation 0.02x + p = 60 a) Find the elasticity of the demand, E(p) b) For which values of p is demand elastic? and inelastic? c) If p = $10 and the price is decreased, will revenue increase or decrease? d) If p = $40 and the price is decreased, will revenue increase or decrease?

          1. (6 points) Solve the following limit and calculate the derivatives of the funcions f(x), g(x) and h(x).
3x²+2x+3
a) lim_{x?-3} (x²+x-3)
b) f(x) = x + ln(x)
c) g(x) = ?x³+5x
d) h(x) = (2x³+e^x)²/3x
2. (6 points) A company produces batteries for electric cars. The market research department sets the price-demand function in dollars for x items: p(x) = 5000 - 10x
The financial department provides the cost function: C(x) = 150,000 + 1000x
a) What is the marginal cost when the level of production is 150 units?
b) What is the marginal revenue when the level of production is 150 units?
c) Find the marginal profit function.
d) Find the break-even points.
3. (7 points) For the funcion f(x) = -x² - 1 + ln(x²)
a) Find the first derivative of the function.
b) Find the critical points.
c) Find the second derivative of the function.
d) Find the relative maximum and minimum.
e) Find the absolute maximum and minimum.
f) Find the intervals of concavity.
4. (6 points) Given the price-demand equation 0.02x + p = 60
a) Find the elasticity of the demand, E(p)
b) For which values of p is demand elastic? and inelastic?
c) If p = $10 and the price is decreased, will revenue increase or decrease?
d) If p = $40 and the price is decreased, will revenue increase or decrease?

1. (6 points) Solve the following limit and calculate the derivatives of the funcions f(x), g(x) and h(x).
3x²+2x+3
a) limx?-3 (x²+x-3)
b) f(x) = x + ln(x)
c) g(x) = ?x³+5x
d) h(x) = (2x³+e^x)²/3x
2. (6 points) A company produces batteries for electric cars. The market research department sets the price-demand function in dollars for x items: p(x) = 5000 - 10x
The financial department provides the cost function: C(x) = 150,000 + 1000x
a) What is the marginal cost when the level of production is 150 units?
b) What is the marginal revenue when the level of production is 150 units?
c) Find the marginal profit function.
d) Find the break-even points.
3. (7 points) For the funcion f(x) = -x² - 1 + ln(x²)
a) Find the first derivative of the function.
b) Find the critical points.
c) Find the second derivative of the function.
d) Find the relative maximum and minimum.
e) Find the absolute maximum and minimum.
f) Find the intervals of concavity.
4. (6 points) Given the price-demand equation 0.02x + p = 60
a) Find the elasticity of the demand, E(p)
b) For which values of p is demand elastic? and inelastic?
c) If p = 10 and the price is decreased, will revenue increase or decrease?
d) If p =40 and the price is decreased, will revenue increase or decrease?

Added by Rafael S.

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