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Question
If 'f' is continuous at x = 0, then find f(0).
`f(x)=(15^x-3^x-5^x+1)/(xtanx) , x!=0`
Solution
`f(x)=(15^x-3^x-5^x+1)/(xtanx) , x!=0`
`lim_(x->0)f(x)=lim_(x->0)(15^x-3^x-5^x+1)/(xtanx) `
`=lim_(x->0)(3^x(5^x-1)-(5^x-1))/(xtanx) `
`=lim_(x->0)((3^x-1)(5^x-1))/(xtanx)`
`=lim_(x->0)([(5^x-1)/x][(3^x-1)/x])/ ((xtanx/x^2)) `
`=(log5.log3)/1 `
`=log5.log3`
As function is continuous at x=0
`f(0)=lim_(x->0)f(x)`
f(0)=log5.log3
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