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3 years ago

Determine the value of k

Mathematics

2 answers:

Pavel [41]3 years ago

6 0

Answer:

k=6

Step-by-step explanation:

For a piecewise function to be continuous, the left-side and right-side limits must be equal to each other. Therefore, the left-side limit of f(x) is 8 because the derivative of 2x^2 is 4x, and then directly substituting x=2 gives us 4(2)=8. Therefore, the right-side limit must also equal 8. Therefore, k must be 6 because 2+6=8.

KATRIN_1 [288]3 years ago

4 0

Answer:

$\displaystyle k = 6$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Algebra I

Functions
Function Notation

Algebra II

Piecewise Functions

Calculus

Limits
Continuity

Step-by-step explanation:

Step 1: Define

Identify

Continuous at x = 2

$\displaystyle f(x) = \left \{ {{2x^2 \ if \ x < 2} \atop {x + k \ if \ x \geq 2}} \right.$

Step 2: Solve for k

Definition of Continuity: $\displaystyle \lim_{x \to 2^+} 2x^2 = \lim_{x \to 2^-} x + k$
Evaluate limits: $\displaystyle 2(2)^2 = 2 + k$
Evaluate exponents: $\displaystyle 2(4) = 2 + k$
Multiply: $\displaystyle 8 = 2 + k$
[Subtraction Property of Equality] Subtract 2 on both sides: $\displaystyle 6 = k$
Rewrite: $\displaystyle k = 6$

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

Unit: Limits - Continuity

Book: College Calculus 10e

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3 years ago

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Answer:

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Step-by-step explanation:

Given

x plus y equals 81
x and y are non-negative

Find

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Solution

a. Solve x plus y equals 81 for y.

y equals 81 minus x

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3 years ago

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ivanzaharov [21]

Answer:

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Step-by-step explanation:

Given: GCF of two numbers is $170$ . neither number is divisible by the other.

To Find: smallest of these two number.

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As GCF of two numbers is $170$ , both number are divisible by $170$ .

Prime factor of $170$ $=2\times5\times17$

multiples of $170$ are $1\times2\times5\times17=170$

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Step-by-step explanation:

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