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List the values F(3, 5), F(3, 10), F(8, 5), F(8, 10) in the ascending order.

Question:

List the values F(3, 5), F(3, 10), F(8, 5), F(8, 10) in the ascending order.

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Answer and Explanation:

Given: {eq}F \left ( 3, 5 \right ), F \left (3, 10 \right ), F \left ( 8, 5 \right ), F \left ( 8, 10 \right ) {/eq}

observe that, the point on the surface {eq}z = F \left (x, y \right ) {/eq} which is highest above the XY plane has an x co-ordinate of 3 and y-coordinate of 5.

That is, {eq}z=F \left ( 3, 5 \right ) {/eq} is the largest value of F among the given points.

The second highest point is: x- co-ordinate of 8 and y-coordinate of 5.

So, {eq}F \left ( 8, 5 \right ) < F \left ( 3, 5 \right ) {/eq}

Similarly, the third highest point on the surface {eq}z = F \left (x, y \right ) {/eq} is: x co-ordinate of 3 and y-coordinate of 10.

So, {eq}F \left ( 3, 10 \right ) < F \left ( 8, 5 \right ) < F \left ( 3, 5 \right ) {/eq}.

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Similarly, the fourth highest point (or the lowest of the four points) is: x co-ordinate of 8 and y-coordinate of 10.

So, {eq}F \left ( 8, 10 \right ) < F \left ( 3, 10 \right ) < F \left ( 8, 5 \right ) < F \left ( 3, 5 \right ) {/eq}.

Hence, the list of value of the function F in ascending order is:

{eq}F \left ( 8, 10 \right ) < F \left ( 3, 10 \right ) < F \left ( 8, 5 \right ) < F \left ( 3, 5 \right ) {/eq}.


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