Maths Book back answers and solution for Exercise questions - Mathematics : Differentials and Partial Derivatives: Linear Approximation, Errors: Absolute Error, Relative Error, and Percentage Error - Exercise Problem Questions with Answer, Solution

**EXERCISE 8.1**

**1. Let f (x) = 3âˆšx. Find the linear approximation at x = 27 . Use the linear approximation to approximate 3âˆš27.2 .**

**2. Use the linear approximation to find approximate values of**

**(i) (123)2/3**

**(ii) 4 âˆš15**

**(iii) 3 âˆš26**

**3. Find a linear approximation for the following functions at the indicated points.**

**(i) f (x) = x3 âˆ’ 5x + 12, x0 = 2**

**(ii) g ( x) = âˆš[x2 + 9], x0 = âˆ’4**

**(iii) h(x) = x / x+1 , x0 = 1**

**4. The radius of a circular plate is measured as 12.65 cm instead of the actual length 12.5 cm. find the following in calculating the area of the circular plate:**

**(i) Absolute error (ii) Relative error (iii) Percentage error**

**5. A sphere is made of ice having radius 10 cm. Its radius decreases from 10 cm to 9.8 cm. Find approximations for the following:**

**(i) change in the volume (ii) change in the surface area**

**6. The time T , taken for a complete oscillation of a single pendulum with length l , is given by the equation T = 2Ï€âˆš(l/g) , where g is a constant. Find the approximate percentage error in the calculated value of T corresponding to an error of 2 percent in the value of l .**

**7. Show that the percentage error in the nth root of a number is approximately 1/n times the percentage error in the number**

**1. (i) 3.0074**

**2. (i) 24.73â€ƒ (ii) 1.9688â€ƒ (iii) 2.963**

**3. (i) 7 x âˆ’ 4 (ii) 9âˆ’4x / 4 (iii) x+1 /4**

**4. (i) 0.0225Ï€ cm2, (ii) 0.006â€‰cm2 (iii) 0.6%**

**5. (i) Volume decreases by 80Ï€ cm3 â€ƒ (ii) Surface area decreases by 16Ï€ cm2**

**6.â€‚ 1%**

Tags : Problem Questions with Answer, Solution , 12th Maths : UNIT 8 : Differentials and Partial Derivatives

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12th Maths : UNIT 8 : Differentials and Partial Derivatives : Exercise 8.1: Linear Approximation | Problem Questions with Answer, Solution

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