Find a potential function for f or determine that f is not conservative. (if f is not conservative, enter not conservative.) f = cos(z), 10y, - x sin(z)

For to be conservative, we need to have

Integrate the first PDE with respect to :

Differentiate with respect to :

Now differentiate with respect to :

So we have

so is indeed conservative.

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step-by-step explanation:

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b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.