The edge of a cube was found to be 15 cm with a possible error in measurement of 0.2 cm. Use differentials to estimate the maximum possible error, relative error, and percentage error in computing the volume of the cube and the surface area of the cube. (a) the volume of the cube maximum possible error (in cm3) cm3 relative error (rounded to four decimal places) percentage error (rounded to two decimal places) % (b) the surface area of the cube maximum possible error (in cm2) cm2 relative error (rounded to four decimal places) percentage error (rounded to two decimal places) %

Step-by-step explanation:

Given

-- edge length

-- possible error

Solving (a): Errors in volume

The volume of a cube is:

Differentiate

Make dV the subject

Rewrite as:

Substitute values for x and

Hence:

The relative error is then calculated as:

The percentage error is:

Solving (a): Errors in Surface Area

The volume of a cube is:

Differentiate

Make dA the subject

Rewrite as:

Substitute values for x and

Hence:

The relative error is then calculated as:

The percentage error is:

the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

the root or roots of a polynomial are the values of the variable that makes the polynomial equal to 0. we can find the roots of a polynomial making the expression equal to 0 and then, isolating the variable (it it has just one variable).

for example, given the following polynomial:

the root or zero of the polynomial, can be found by making the expression equal to 0, and then, isolating the variable, so, finding the root we have:

therefore, we have that the root of the polynomial is equal to 2.

we must remember that the number of roots that a polynomial can have, will depend on the degree of the polynomial, a first degree polynomial have will have one single root, a second degree polynomial (quadratic expression) may have two roots and so.

hence the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

have a nice day!