Chapter 2 Homework

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Question

Chapter 2 Homework

1. True of False

The domain of the function

f (x) = \frac{x - 3}{2 x^{2} - x - 3}

(- \infty, - 1) \cup (\frac{3}{2}, \infty)

2. Let

f (x) = 3 x^{2} + 5 x - 2

Find

f (a + h) - f (a)

6 x h + 3 h^{2} + 5 h

6 a h + 3 h^{2} + 10 a + 5 h - 4

3 h^{2} + 5 h

d. None of the above

3. The membership of the newly opened Venus Health Club is approximated by the function

N (x) = 200 {(4 + x)}^{\frac{1}{2}}

$N (x) = 200 {(4 + x)}^{\frac{1}{2}}$

N (x) = 200 {(4 + x)}^{\frac{1}{2}}

where

1 \leq x \leq 24

$1 \leq x \leq 24$

1 \leq x \leq 24

where N(x) denotes the number of members x months after the club’s grand opening.

Find N(0)

4. Given the demand equation 3x + p – 40 = 0 and the supply equation 2x – p + 10 = 0,

where p is the unit price in dollars and x represents the quantity in units of thousands,

determine the equilibrium quantity and the equilibrium price.

5. Find the limit if it exists

$l i m_{x \to 0} + \frac{x - 1}{x (x - 1)}$

6. Find the limit if it exists

$l i m_{x \to 1} - \frac{\sqrt{x} - 1}{x - 1}$

7. Find the limit if it exists

$l i m_{x \to \infty} \frac{3 x^{2} + 2 x + 4}{2 x^{2} - 3 x + 1}$

8. Find the limit if it exists

$l i m_{x \to - \infty} \frac{x^{2}}{x + 1}$

9. Sketch the graph of the function

$f (x) = \{\begin{cases} \frac{1}{{(x + 1)}^{2}} x \neq = - 1 \\ 2 x = - 1 \end{cases}$

evaluate

(A)

l i m_{x \to - 1} + f (x)

(B)

l i m_{x \to - 1} - f (x)

(C)

l i m_{z \to - 1} f (x)

10. Let

y = x^{2} + 2

$y = x^{2} + 2$

y = x^{2} + 2

a. Find the average rate of change pf y with respect to x over the intervals

[ 1, 2 ], [ 1, 1.5 ], [ 1, 1.1 ]

b. Find the instantaneous rate of change of y and x = 1.

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This question is taken from Math 238 – Calculus for Business and Social Sciences » Spring 2022 » Homeworks

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