# Find a and b if the following function is continuous at the point indicated against them. f(x)=x2+a , for x ≥ 0 = 2x2+1+b , for x < 0 and f(1) = 2 is continuous at x = 0 - Mathematics and Statistics

Sum

Find a and b if the following function is continuous at the point indicated against them.

f(x) = x^2 + a    , for x ≥ 0

= 2sqrt(x^2 + 1) + b , for x < 0 and
f(1) = 2 is continuous at x = 0

#### Solution

Since, f(x) = x2 + a,   x ≥ 0
∴ f(1) = (1)2 + a
∴ 2 = 1 + a    ...[∵ f(1) = 2]
∴ a = 1
Also f is continuous at x = 0

∴ lim_(x→0^-) "f"(x) = lim_(x→0^+) "f"(x)

∴ lim_(x→0^-) (2sqrt(x^2 + 1) + "b") = lim_(x→0^+) (x^2 + "a")

∴ 2sqrt(0^2 + 1) + "b" = 0^2 + 1

∴ 2(1) + b = 1
∴ b = –1
∴ a = 1 and b = –1

Concept: Continuity in the Domain of the Function
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#### APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board
Chapter 8 Continuity
Miscellaneous Exercise 8 | Q III. (1) | Page 113