Find the divergence and curl of the vector F=(3x²y² +2z)i + (3x² + y +yz )j - (3x²z² +2yx + xyz)k

Divergence:

div(F) = ∂(3x²y² + 2z)/∂x + ∂(3x² + y + yz)/∂y - ∂(3x²z² + 2yx + xyz)/∂z

div(F) = 6xy² + 1 + z - 6x²z - xy

Curl:

curl(F) = [∂(3x² + y + yz)/∂z + ∂(3x²z² + 2yx + xyz)/∂y] i

… … … … … - [∂(3x²y² + 2z)/∂z + ∂(3x²z² + 2yx + xyz)/∂x] j

… … … … … + [∂(3x²y² + 2z)/∂y - ∂(3x² + y + yz)/∂x] k

curl(F) = (-xz - 2x - y) i + (6xz² + yz + 2y + 2) j + (6x - 6x²y) k

explanation:

infrared radiation has wavelength in the range between 700 nm and 1 mm. lets' convert these values into scientific notation, keeping in mind that:

let's start from the lower value, we have:

(we moved the dot two places to the left, so we increased the exponent by 2 units, from -9 to -7)

the higher value is:

so, the range of wavelength of infrared radiation is:

answer: 3.26019516

step-by-step explanation: