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प्रश्न
Prove that the function f(x) = 5x – 3 is continuous at x = 0, at x = –3 and at x = 5.
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उत्तर
The given function is:
f(x) = 5x – 3
f(0) = 5(0) – 3 = –3
`lim_(x → 0)` f(x) = 5(0) – 3 = –3
`lim_(x → 0)` f(x) = f(0)
Hence, the function is continuous at x = 0.
f(–3) = 5(–3) – 3
= –15 – 3
= –18
⇒ `lim_(x → -3)` f(x) = 5(–3) – 3
= –15 – 3
= –18
⇒ `lim_(x → -3)` f(x) = f(–3)
Hence, the function is continuous at x = –3.
f(5) = 5(5) – 3
= 25 – 3
= 22
⇒ `lim_(x → 5)` f(x)
= 5(5) – 3
= 25 – 3
= –22
⇒ `lim_(x -> 5)` f(x) = f(5)
Hence, the function is continuous at x = 5.
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