Chapter 14  Differentials, Errors and Approximations Ex 14.1

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9(ii)

Solution 9(ii)

Question 9(iii)

Solution 9(iii)

Question 9(iv)

Solution 9(iv)

Question 9(v)

Solution 9(v)

Question 9(vi)

Solution 9(vi)

Question 9(vii)

Solution 9(vii)

Question 9(viii)

Solution 9(viii)

Question 9(ix)

Solution 9(ix)

Question 9(x)

Using differentials, find the approximate values of the following:

log₁₀10.1, it being given that log₁₀e = 0.4343.Solution 9(x)

Question 9(xi)

Solution 9(xi)

Question 9(xii)

Solution 9(xii)

Question 9(xiii)

Solution 9(xiii)

Question 9(xiv)

Solution 9(xiv)

Question 9(xv)

Solution 9(xv)

Question 9(xvi)

Solution 9(xvi)

Question 9(xvii)

Solution 9(xvii)

Question 9(xviii)

Solution 9(xviii)

Question 9(xix)

Solution 9(xix)

Question 9(xx)

Solution 9(xx)

Question 9(xxi)

Solution 9(xxi)

Question 9(xxii)

Solution 9(xxii)

Question 9(xxiii)

Solution 9(xxiii)

Question 9(xxiv)

Solution 9(xxiv)

Question 9(xxv)

Solution 9(xxv)

Question 9(xxvi)

Using differentials, find the approximate values of the following:

Solution 9(xxvi)

Question 9(xxvii)

Using differentials, find the approximate values of (3.968)^3/2Solution 9(xxvii)

Question 9(xxviii)

Using differentials, find the approximate values of the following:

(1.999)⁵Solution 9(xxviii)

Question 9(xxix)

Using differentials, find the approximate values of the following:

Solution 9(xxix)

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16

Solution 16

Question 9(i)

Using differentials, find the approximate values of the following:

Solution 9(i)

Consider 

Let x = 25 and 

Also,