1. Using differentials, find the approximate value of each of the following up to 3 places of decimal. (i) 25.3 (ii) 49.5 (iii) 0.6 (iv) 1 (0.009)3 (v) 1 (0.999)10 (vi) 1 (15)4 (vii) 1 (26)3 (viii) 1 (255)4 (ix) 1 (82) 4 (x) 1 (401)2 (xi) 1 (0.0037) 2 (xii) 1 (26.57)3 (xiii) 1 (81.5)4 (xiv) 3 (3.968) 2 (xv) 1 (32.15)5 2. Find the approximate value of f (2.01), where f (x) = 4x2 + 5x + 2. 3. Find the approximate value of f (5.001), where f (x) = x3 7x2 + 15. 4. Find the approximate change in the volume V of a cube of side x metres caused by increasing the side by 1%. 5. Find the approximate change in the surface area of a cube of side x metres caused by decreasing the side by 1%. 6. If the radius of a sphere is measured as 7 m with an error of 0.02 m, then find the approximate error in cal
Question 1:Using differentials, find the approximate value of each of the following up to 3 places of decimal. (i) 25.3 (ii) 49.5 (iii) 0.6 (iv) 1 (0.009)3 (v) 1 (0.999)10 (vi) 1 (15)4 (vii) 1 (26)3 (viii) 1 (255)4 (ix) 1 (82) 4 (x) 1 (401)2 (xi) 1 (0.0037) 2 (xii) 1 (26.57)3 (xiii) 1 (81.5)4 (xiv) 3 (3.968) 2 (xv) 1 (32.15)5
Question 2:Find the approximate value of f (2.01), where f (x) = 4x2 + 5x + 2.
Question 3:Find the approximate value of f (5.001), where f (x) = x3 – 7x2 + 15.
Question 4:Find the approximate change in the volume V of a cube of side x metres caused by increasing the side by 1%.
Question 5:Find the approximate change in the surface area of a cube of side x metres caused by decreasing the side by 1%.
Question 6:If the radius of a sphere is measured as 7 m with an error of 0.02 m, then find the approximate error in calculating its volume.
Question 7:If the radius of a sphere is measured as 9 m with an error of 0.03 m, then find the approximate error in calculating its surface area.
Question 8:If f(x) = 3x2 + 15x + 5, then the approximate value of f (3.02) is (A) 47.66 (B) 57.66 (C) 67.66 (D) 77.66
Question 9:The approximate change in the volume of a cube of side x metres caused by increasing the side by 3% is (A) 0.06 x3 m3 (B) 0.6 x3 m3 (C) 0.09 x3 m3 (D) 0.9 x3 m3
