Question 1

v = f(x, y, z) is a real valued function of 3 variables.

Express the partial derivative of v with respect to z in standard mathematical notation.

Options :

A :

B :

C :

D :

Answer: B

Question 2

Identify the condition that fully describes the existence of independence between two events A and B.

Options :

A : P(A|B) = P(A)/P(B) and P(B|A) = P(B)/P(A)

B : P(A|B) = P(A) - P(B) and P(B|A) = P(B) - P(A)

C : P(A|B) = P(A) and P(B|A) = P(B)

D : P(A|B) = P(A) + P(B) and P(B|A) = P(B) + P(A)

Answer: C

Question 3

Determine which of the following is the Maclaurin expansion (up to the second order term) of: e2x

Options :

A :

B :

C :

D :

Answer: D

Question 4

State what the limit of a function with input variable x represents.

Options :

A : The limit represents the smallest value that the function can take over its considered range.

B : The limit represents the behaviour of a function as x approaches a certain value.

C :

The limit represents the value of x for which the function is incalculable.

D : The limit represents the value of the function when x=0.

Answer: B

Question 5

Determine the coefficient of x3 in the binomial expansion of (2 + x)5.

Options :

A : 10

B : 40

C : 64

D : 80

Answer: B

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