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Find the value of a such that the functi...

Find the value of a such that the function f defined by
`f(x)={((sinax)/(sinx) if xne0),(1/a if x=0):}`
is continuous at x=0.

Text Solution

Verified by Experts

f(0)=1/a
`if f(x) is continuous at x=0
then `lim_(xto0)f(x)=f(0)`
`implieslim_(xto0)(sinax)/(sinx)=1/a`
`a=1/a[becauselim_(thetato0)(sintheta)/(theta)=1`
a^2=1impliesa=+-1`
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