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If the function f(x) = (( 3x + 4 tan x)...

If the function ` f(x) = (( 3x + 4 tan x))/x ` continuous at x=0? If not, hwo may the funcation be defined to make it continuous at this point ?

A

`f(x)={((3x+4tanx)/(x)",",x ne 0),(7",",x=0):}`

B

`f(x)={((3x+4tanx)/(x)",",x ne 0),(6",",x=0):}`

C

`f(x)={((3x+4tanx)/(x)",",x = 0),(7",",x ne0):}`

D

None of the above

Text Solution

Verified by Experts

The correct Answer is:
A
`because lim_(x to 0)f(x)=lim_(x to 0)(3x+4tanx)/(x)`
`=lim_(x to0) [3 +4*(sinx)/(x)*(1)/(cosx)]`
`=lim_(x to 0) [3+4]=7`
[since, f(x) is not defined at x = 0, so it cannot be continuous at x = 0]
`therefore` Defined function should be
`f(x)={((3x+4"tan"x)/(x)",",x ne 0),(7",",x =0):}`
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