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larisa86 [58]
3 years ago
5

Giving brainliest!! *easy*

Mathematics
2 answers:
Debora [2.8K]3 years ago
8 0
60.458 cm


Reasoning it says so on the pic
olya-2409 [2.1K]3 years ago
3 0

Answer:

60.458

Step-by-step explanation:

it says the answer lol

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Answer:

See explanation.

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

<u>Algebra I</u>

  • Functions
  • Function Notation

<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

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

\displaystyle f(x) = \left \{ {{\sqrt{x + 1}, \ x < 3} \atop {5 - x, \ x \geq 3}} \right.

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

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

∴ the right-side limit equals 2.

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

  1. Substitute in variables [Left-Side Limit]:                                                       \displaystyle  \lim_{x \to 3^-} \sqrt{x + 1}
  2. Evaluate limit [Limit Rule - Variable Direct Substitution]:                           \displaystyle  \lim_{x \to 3^-} \sqrt{x + 1} = \sqrt{3 + 1}
  3. [√Radical] Add:                                                                                             \displaystyle  \lim_{x \to 3^-} \sqrt{x + 1} = \sqrt{4}
  4. [√Radical] Evaluate:                                                                                       \displaystyle  \lim_{x \to 3^-} \sqrt{x + 1} = 2

∴ the left-side limit equals 2.

<u>Step 4: Find Limit</u>

<em>The right and left-side limits are equal.</em>

∴  \displaystyle  \lim_{x \to 3} f(x) = 2

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

Unit: Limits

Book: College Calculus 10e

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rational, whole, integer, natural

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5^2 = 25

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