EXERCISE . . Find differential dy for each of the following functions : (i) y (ii) y sin( )) / (iii) y cos ( . Find df for f x ( ) = and evaluate it for (i) x = and dx = .
(ii) x = and dx = . Find D f and df for the function f for the indicated values of and compare (i) f x ; ∆ (ii) f x ; . , = − ∆ . Assuming log e = , find an approximate value of log .
and - - . The trunk of a tree has diameter cm. During the following year, the circumference grew cm. (i) Approximately, how much did the tree’s diameter grow?
(ii) What is the percentage increase in area of the tree’s cross-section? . An egg of a particular bird is very nearly spherical. If the radius to the inside of the shell is mm and radius to the outside of the shell is .
mm, find the volume of the shell approximately. . Assume that the cross section of the artery of human is circular. A drug is given to a patient to dilate his arteries.
If the radius of an artery is increased from mm to . mm, how much is cross-sectional area increased approximately? . In a newly developed city, it is estimated that the voting population (in thousands) will increase according to V t ≤≤ where t is the time in years.
Find the approximate change in voters for the time change from to year. . The relation between the number of words y a person learns in x hours is given by . What is the approximate number of words learned when x changes from (i) to .
hour? (ii) to . hour? .
A circular plate expands uniformly under the influence of heat. If it’s radius increases from . cm to . cm, then find an approximate change in the area and the approximate percentage change in the area.
. A coat of paint of thickness . cm is applied to the faces of a cube whose edge is cm. Use the differentials to find approximately how many cubic centimeters of paint is used to paint this cube.
Also calculate the exact amount of paint used to paint this cube.