If fx-9- 2-x2- x - 0 is continuous at x-0- then the value of f 0 is

Given : nbsp; f(x)=9^ 2/x^2, x ≠ 0 At x=0, R.H.L.=lim_h→0f(0+h)=lim_h→09^ 2/h^2= 0 (∵ h→0, 2h^2→ ∞) Since f(x) is nbsp;continuous at x=0 ⇒ nbsp; R.H.L.=f ...

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Standard XII

Mathematics

Rationalization Method to Remove Indeterminate Form

If fx=9- 2/x2...

Question

If $f (x) = 9^{- 2 / x^{2}}, x \neq 0$ is continuous at $x = 0,$ then the value of $f (0)$ is

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Solution

The correct option is D $0$
Given : $f (x) = 9^{- 2 / x^{2}}, x \neq 0$
At $x = 0$ ,
$R . H . L . = lim h \to 0 f (0 + h) = lim h \to 0 9^{- 2 / h^{2}} = 0$
$(∵ h \to 0, \frac{- 2}{h^{2}} \to - \infty)$
Since $f (x)$ is continuous at $x = 0$
$\Rightarrow R . H . L . = f (0) = 0$
$∴ f (0) = 0$

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Rationalization Method to Remove Indeterminate Form

Standard XII Mathematics

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If f(x)=9−2/x2,x≠0 is continuous at x=0, then the value of f(0) is

The correct option is D 0Given : f(x)=9−2/x2,x≠0 At x=0, R.H.L.=limh→0f(0+h)=limh→09−2/h2=0 (∵h→0,−2h2→−∞) Since f(x) is continuous at x=0 ⇒R.H.L.=f(0)=0 ∴f(0)=0

If $f (x) = 9^{- 2 / x^{2}}, x \neq 0$ is continuous at $x = 0,$ then the value of $f (0)$ is

The correct option is D $0$
Given : $f (x) = 9^{- 2 / x^{2}}, x \neq 0$
At $x = 0$ ,
$R . H . L . = lim h \to 0 f (0 + h) = lim h \to 0 9^{- 2 / h^{2}} = 0$
$(∵ h \to 0, \frac{- 2}{h^{2}} \to - \infty)$
Since $f (x)$ is continuous at $x = 0$
$\Rightarrow R . H . L . = f (0) = 0$
$∴ f (0) = 0$