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pashok25 [27]
3 years ago
5

I NEED HELP PEOPLE LAST TIME

Mathematics
1 answer:
Hoochie [10]3 years ago
3 0

29.

f(x) = -x^2-7x-6

As x \to \pm \infty, y \to - \infty.

This can be easily verified by looking at the graph (graph of a quadratic equation).

30.

The growth of a population is not linear, it's exponential.

31.

Exponential growth > polynomial, so y = 3^x.

35.

V(t) = 30\cdot (25)^{\frac{t}{20}}

The question is asking V(t) for t = 40.

V(40) = 30\cdot (25)^{\frac{40}{20}} \\~\\V(40) = 30\cdot 25^2 \\~\\V(40) = 30\cdot 625 \\~\\V(40) = 18750

36.

The point of symmetry of a quadratic equation y = ax^2+bx+c is at its vertice:

V_x = \dfrac{-b}{2a}

V_x = \dfrac{6}{2}

V_x = 3

The line is x= 3.

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Step-by-step explanation:

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3 years ago
Find the indicated limit, if it exists.
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Answer:

d) The limit does not exist

General Formulas and Concepts:

<u>Calculus</u>

Limits

  • Right-Side Limit:                                                                                             \displaystyle  \lim_{x \to c^+} f(x)
  • Left-Side Limit:                                                                                               \displaystyle  \lim_{x \to c^-} f(x)

Limit Rule [Variable Direct Substitution]:                                                             \displaystyle \lim_{x \to c} x = c

Limit Property [Addition/Subtraction]:                                                                   \displaystyle \lim_{x \to c} [f(x) \pm g(x)] =  \lim_{x \to c} f(x) \pm \lim_{x \to c} g(x)

Step-by-step explanation:

*Note:

In order for a limit to exist, the right-side and left-side limits must equal each other.

<u>Step 1: Define</u>

<em>Identify</em>

\displaystyle f(x) = \left\{\begin{array}{ccc}5 - x,\ x < 5\\8,\ x = 5\\x + 3,\ x > 5\end{array}

<u>Step 2: Find Right-Side Limit</u>

  1. Substitute in function [Limit]:                                                                         \displaystyle  \lim_{x \to 5^+} 5 - x
  2. Evaluate limit [Limit Rule - Variable Direct Substitution]:                           \displaystyle  \lim_{x \to 5^+} 5 - x = 5 - 5 = 0

<u>Step 3: Find Left-Side Limit</u>

  1. Substitute in function [Limit]:                                                                         \displaystyle  \lim_{x \to 5^-} x + 3
  2. Evaluate limit [Limit Rule - Variable Direct Substitution]:                           \displaystyle  \lim_{x \to 5^+} x + 3 = 5 + 3 = 8

∴ Since  \displaystyle \lim_{x \to 5^+} f(x) \neq \lim_{x \to 5^-} f(x)  , then  \displaystyle \lim_{x \to 5} f(x) = DNE

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit:  Limits

5 0
2 years ago
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