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Question
If `(x) = 3x^2 + 15x + 5`, then the approximate value of `f(3.02)` is
Options
47.66
57.66
67.66
77.66
MCQ
Solution
77.66
Explanation:
`x + Δx` = 3.02, where `x` = 3, `Δx` = 0.02
`Δf(x) = f(x + Δx) - f(x)`
= `f(x) + f^'(x) phi Δ x` ......(1)
Now, `f(x) = 3x^2 + 15x + 5`
`f(3)` = 3.32 + 15.3 + 5 = 27 + 45 + 5 = 77
`f^'(x) = 6x + 15`
`f^'(x) = 6 xx 3 + 15` = 18 + 15 = 33
Putting there values in (1)
∴ `f(3.02) = 87 + 33 xx 0.02` = 77 + 0.66 = 77.66
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