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प्रश्न
If f and g are continuous functions with f(3) = 5 and `lim_(x -> 3) [2f(x) - g(x)]` = 4, find g(3)
उत्तर
Given f and g are continuous functions.
∴ `lim_(x -> 3) f(x) = f(3)` ........(1)
`lim_(x -> 3) g(x) = g(3)` ........(2)
Given `f(3)` = 5 and
`lim_(x -> 3) [2f(x) - g(x)]` = 4
`lim_(x -> 3) 2f(x) - lim_(x -> 3) g(x)` = 4
`2 lim_(x -> 3) f(x) - lim_(x -> 3) g(x)` = 4
2f(3) – g(3) = 4
2 × 5 – g(3) = 4
10 – 4 = g(3)
g(3) = 6
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