Let `f(x)={((log)_ecosx)/(1+x^2 4-1),x >0(e^(sin4x)-1)/((log)_e(1+tan2x),x<0` Find the value of `f(0)` which makes the function continuous at `x=0`

let f(x)=(lncosx)/{(1+x^2)^(1/4)-1} if x > 0 and f(x)=(e^(sin4x)-1)/(ln(1+tan2x)) if x < 0 Is it possible to difine f(0) to make the function continuous at x=0 . If yes what is.the value of f(0) , if not then indicate the nature of discontinuity.

let f(x)=(lncosx)/{(1+x^2)^(1/4)-1} if x > 0 and f(x)=(e^(sin4x)-1)/(ln(1+tan2x)) if x < 0 Is it possible to difine f(0) to make the function continuous at x=0 . If yes what is.the value of f(0) , if not then indicate the nature of discontinuity.

let f(x)=(lncosx)/{(1+x^2)^(1/4)-1} if x > 0 and f(x)=(e^(sin4x)-1)/(ln(1+tan2x)) if x < 0 Is it possible to difine f(0) to make the function continuous at x=0 . If yes what is.the value of f(0) , if not then indicate the nature of discontinuity.

lim_(x rarr0)(sqrt(1+sin3x)-1)/(log(1+tan2x))

let f(x)=(ln cos x)/((1+x^(2))^((1)/(4))-1) if x>0 and f(x)=(e^(sin4x)-1)/(ln(1+tan2x)) if x<0 Is it possible to difine f(0) to make the function continuous at x=0. If yes what is.the value of f(0), if not then indicate the nature of discontinuity.

Let f(x)=(lim)_(xvecoo)(tan^(-1)(tanx))/(1+((log)_e x)^n),x!=(2n+1)pi/2 then AA1 e ,f(x) is a constant function

Integration of 1/(1+((log)_e x)^2) with respect to (log)_e x is (tan^(-1)((log)_e x)/x)+C (b) tan^(-1)((log)_e x)+C (c) (tan^(-1)x)/x+C (d) none of these

e^(tan^(-1)x)log(tan x)

int((1+(log)_e x)^2)/(1+(log)_e x^(x+1)+((log)_e x^(sqrt(x)))^2)dx=

Integration of (1)/(1+((log)_(e)x)^(2)) with respect to (log)_(e)x is ((tan^(-1)((log)_(e)x))/(x)+C(b)tan^(-1)((log)_(e)x)+C(c)(tan^(-1)x)/(x)+C(d) none of these