Pharmacy exam 2017-11-06
Degrees: Pharmacy and Biotechnology
Date: Nov 6, 2017
Question 1
Adenoma is a benign tumor, which grows usually in spherical shape. Suppose the rate of growth of the radius of a certain adenoma is equal to half the size of the radius per second; compute the rate of growth of the volume of the tumor when the radius is 5mm.
If the measurement of the radius has a possible error of
Note: The volume of a sphere of radius
Error in the volume:
Question 2
The weight of a baby during the first few months of life grows at a rate proportional to the reciprocal of the weight. Suppose a baby’s weight was 3.3 kg at birth, and 4.3 kg a month later.
- What will be the weight of the baby one year after birth?
- When will the weight be equal to 8 kg?
- Is this model of the weight good to determine the weight of a person during his whole life?
Let
- Differential equation:
Particular solution: .
kg. - At 7 months.
- No, because the function is always increasing.
Question 3
The function
- Compute the maximum value of
assuming that and . - What will be the variation of
at and when increases twice as much as ? - Compute the second degree Taylor polynomial of
at the point .
has a local maximum at and the maximum value is .- Directional derivative of
at along the direction of : . .
Question 4
Given
- Tangent line:
. - Normal plane:
.