The function f x defined by fx -sin 2 axx 2- x - 01-x -0 is continuous at x -0- The values of a is-areA- NB- 1C- -1D- 2

The given function f(x) will be continuous at x = 0, iff limx→0 nbsp;fx=f0⇒limx→0 nbsp;sin2 nbsp;axx2=1⇒limax→0 nbsp;a2sin nbsp;axax2=1⇒a2×1=1⇒a=±1So, ...

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Standard XII

Mathematics

Continuity in an Interval

The function ...

Question

The function f(x) defined by $f (x) = (\begin{matrix} \frac{{sin}^{2} ax}{x^{2}}, x \neq 0 1, x = 0 \end{matrix}$ is continuous at x = 0. The value(s) of a is/are

0.0

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-1

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Solution

The correct options are
B 1
C -1
The given function f(x) will be continuous at x = 0, iff
$lim x \to 0 f (x) = f (0) \Rightarrow lim x \to 0 \frac{{sin}^{2} ax}{x^{2}} = 1 \Rightarrow lim ax \to 0 a^{2} {(\frac{sin ax}{ax})}^{2} = 1 \Rightarrow a^{2} \times 1 = 1 \Rightarrow a = \pm 1$ So, a = 1 or -1

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The function f(x) defined by f(x)=(sin2 axx2, x≠01 , x=0 is continuous at x = 0. The value(s) of a is/are

The correct options are B 1 C -1The given function f(x) will be continuous at x = 0, iff limx→0 f(x)=f(0)⇒limx→0 sin2 axx2=1⇒limax→0 a2(sin axax)2=1⇒a2×1=1⇒a=±1So, a = 1 or -1

The function f(x) defined by $f (x) = (\begin{matrix} \frac{{sin}^{2} ax}{x^{2}}, x \neq 0 1, x = 0 \end{matrix}$ is continuous at x = 0. The value(s) of a is/are