Quiz 1: Multivariable Function

Which one of these -- is an example of multivariable function?

• velocity which depends on displacement and time

• weight which depends on mass and gravitational force

• y = 3x³ + 2

Choose the false statement from the following below:

• In f(x,y) : x and y are dependent variables

• From a graph, we can determine the domain as in x - axis

• The domain is the set of values for which a function is define

The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain. True or false?

• True

• False

What is the function that represent in the graph above?

• exponential function

• squareroot function

• logarithmic function

What is the domain for cos x?

• x = { x : -2π ≤ x ≤ 2π, x ∊ ℝ }

• y = { y : -1 ≤ y ≤ 1, y ∊ ℝ }

• x = { x : x ∊ ℝ }

What is the range for the graph y above?

• x = { x : x ≠ 0 , x ∊ ℝ }

• y = { y : y ≠ 0, y ∊ ℝ }

• y = { y : y ∊ ℝ }

Differentiate y = π³

• y' = 3π²

• y' = π⁴/4

• y' = 0

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Find zₓ if given z = x³ + y³ - 2x²y ?

• 3y² - 4xy

• 3x² - 2x²

• 3x² - 4xy

Find fᵥ if given f (u,v) = uv sin (3u + 4v)?

• 4u cos (3u + 4v)

• u sin (3u + 4v) + 4uv cos (3u + 4v)

• 3v cos (3u + 4v) + u sin (3u + 4v)