Question

सिद्ध कीजिए कि फलन f(x) = 5x – 3, x = 0, x = – 3 तथा x = 5 पर संतत है।

Answer 1

Answer:

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Answer 2

फलन f(x) = 5x – 3, x = 0, x = – 3 तथा x = 5 पर संतत है

Step-by-step explanation:

फलन f(x) = 5x – 3, x = 0, x = – 3 तथा x = 5 पर संतत है

f(x) = 5x – 3

f(x)  x =  a पर  संतत है  यदि

$\lim_{x \to a} f(x) = f(a)$

Lim (x → a)  f(x)  = f(a)

Lim (x→ 0)  f(5x - 3) =  5*0 – 3 = - 3

f(0) = 5(0) – 3 = -3

LHS = RHS

Lim (x→ -3)  f(5x - 3) =  5*(-3) – 3 = - 18

f(-3) = 5(-3) – 3 = -18

LHS = RHS

Lim (x→ 5)  f(5x - 3) =  5*(5) – 3 = 22

f(5) = 5(5) – 3 = 22

LHS = RHS

इस प्रकार  फलन at =, at =− & at = पर संतत है

f(x) = 5x – 3, x = 0, x = – 3 तथा x = 5 पर संतत है।

और  जानें:

x = 3 पर फलन f(x) = 2x^{2} – 1 के सातत्य की जाँच कीजिए।

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