Mathematics, 25.06.2021 19:50 reterrickeyfox205

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Answer from: caggh345

See explanation.

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to Right

Algebra I

FunctionsFunction Notation

Calculus

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:

Step 1: Define

Identify

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

Step 2: Find Right Limit

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

∴ the right-side limit equals 2.

Step 3: Find Left Limit

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

∴ the left-side limit equals 2.

Step 4: Find Limit

The right and left-side limits are equal.

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

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

Unit: Limits

Book: College Calculus 10e

Answer from: Quest

1.3

step-by-step explanation:

3x2=6 9x+6

bring down the 6 on both sides

6+6=12

12= 9x

divide by 9

12/9 =

1.3 =x

Answer from: Quest

50-60=10

step-by-step explanation:

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