Find the value of k for which function f(x)={(Sinx-cosx)/4x-x,x?pi/4. X, x=pi/4} where x is continuous at pi/4

Given that f(x)={(Sinx-cosx)/4x-x,x≠pi/4. X, x=pi/4} where x is continuous at pi/4

f(x) = { sinx – cosx}4x-x

{x }

x not equal to π4

x is equal to π4

lim(f(x)) = π4

Substituting π4 in the given polynomial equation

{(Sinπ4-cosπ4)/4(π4)-π4}

lim(√2sin(x-π4))

On applying the given limit x is continuous at pi/4 in the above equation we get,

k = √2/4

Leave a Comment

Your email address will not be published. Required fields are marked *

BOOK

Free Class