# Find k if the following function is continuous at the points indicated against them: f(x)=(1+kx)1x , for x ≠ 0 = e32 , for x = 0, at x = 0 - Mathematics and Statistics

Sum

Find k if the following function is continuous at the points indicated against them:

f(x) = (1 + kx)^(1/x)  , for x ≠ 0

= e^(3/2)                  ,  for x = 0, at x = 0

#### Solution

f is continuous at x = 0

∴ lim_(x→0) "f"(x) = f(0)

∴ lim_(x→0) (1 + "k"x)^(1/x) = "e"^(3/2)

∴ lim_(x→0) [(1 + "k"x)^(1/("k'"x)]]^"k" = "e"^(3/2)

∴ "e"^"k" = "e"^(3/2) ....[lim_(x→0) (1 + x)^(1/x) = "e"]

∴ k = 3/2

Concept: Examples of Continuous Functions Whereever They Are Defined
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#### APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board
Chapter 8 Continuity
Miscellaneous Exercise 8 | Q II. (3) | Page 113