Multiple Choice QuestionsIf f (x) = 3x2 + 15x + 5, then find the approximate value of f (3.02) is
47.66
57.66
67.66
67.66
D.
67.66
f (x) = 3 x2 + 15 x + 5
Let x = 3 and ∆x = 0.02
∆y = f (x + ∆x) – f (x)
∴ f (x + ∆x) = f (x) + ∆y = f (x) + f ' (x) ∆x [∵ dx = ∆x]
⇒ f (x + ∆x) = f (x) + (6 x + 15) ∆x
∴ f (3.02) = f (3)+ {6 (3) + 15} (0.02)
= [3 (3)2 + 15 (3) + 5]+ (18 + 15) (0.02)1111
= (27+ 45 + 5) + 33 (0.02)
= 77 + 0.66 = 77.66
∴ approximate value of f (3.02) is 77.66.
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Find the approximate change in the volume V of a cube of side x metres caused by increasing the side by 1%.
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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.
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.
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