Chapter 13, Problem 1RE

(a)

To determine

To calculate: Value of the function $f\left(x,y\right)=3x^{2}y$ at point $\left(1,3\right)$.

Answer to Problem 1RE

Solution: 9.

Explanation of Solution

Given:

$\left(1,3\right)$ and function $f\left(x,y\right)=3x^{2}y$.

Calculation:

$f\left(1,3\right)=3\cdot 1^2\cdot 3=9$

Hence, $f\left(1,3\right)=9$.

(b)

To determine

To calculate: Value of the function $f\left(x,y\right)=3x^{2}y$ at point $\left(-1,1\right)$.

Answer to Problem 1RE

Solution: 3.

Explanation of Solution

Given:

Point $\left(-1,1\right)$ and function $f\left(x,y\right)=3x^{2}y$.

Calculation:

$f\left(-1,1\right)=3\cdot {\left(-1\right)}^2\cdot 1=3$

Hence, $f\left(-1,1\right)=3$.

(c)

To determine

To calculate: Value of the function $f\left(x,y\right)=3x^{2}y$ at point $\left(-4,0\right)$.

Answer to Problem 1RE

Solution: 0.

Explanation of Solution

Given:

Point $\left(-4,0\right)$ and function $f\left(x,y\right)=3x^{2}y$.

Calculation:

$f\left(-4,0\right)=3\cdot {\left(-4\right)}^2\cdot 0=0$

Hence, $f\left(-4,0\right)=0$.

(d)

To determine

To calculate: Value of the function $f\left(x,y\right)=3x^{2}y$ at point $\left(x,2\right)$.

Answer to Problem 1RE

Solution: $\underset{\_}{6x^2}$.

Explanation of Solution

Given:

Point $\left(x,2\right)$ and function $f\left(x,y\right)=3x^{2}y$.

Calculation:

$f\left(x,2\right)=3\cdot {\left(x\right)}^2\cdot 2=6x^2$.

Hence, $f\left(x,2\right)=6x^2$.