If f : ` R to R ` is defind by
` f(x) = {:{ ( a^(2) cos x + b^(2) sin^(2) x , xle 0) , ( e^(ax + b) , x gt 0) :}`
is a continuous fucntion , then

If f : R to R be defined f(x) = {(a^(2) cos^(2) x + b^(2) sin^(2) x " if " x le 0),(e^(ex + b) " if " x gt0):} is a continuous function show that b = 2 log | a| (a ne 0) .

If R rarr R b e defined f(x)= {{:(a^(2)cos^(2) x+b^(2) sin^(2)x,if xle0),(e^(ax+b),if xgt0):} is a continuous function show that

If f : R rarr R is defined by f(x) ={(a^(2)cos^(2)+b^(2)sin^(2)x, x le 0),(e^(ax+b), x gt0):} is continuous function, then

If f(x) = {:(a^(2)sin^(2)x+e^(2) cos^(2)x", if " x le 0 ),(=e^(ax+b)", if " x gt 0):} is continuous at x = 0 , then b = …..

If f : R to R is defined by f(x) = {:{ ((cos 3x - cos x)/(x^(2) ), " for " x ne 0), (lamda , " for " x =0):} and if f is continuous at x =0 , then lamda is equal to

If f: R to R is defined by f(x) = {:{((2 sin x - sin 2x)/( 2 x cosx) , " if x ne 0), (a, if x ne 0):} then the value of 'a' so that f is continuous at 0 is

If f:R rarr R defined by f(x)={[a^(2)cos^(2)x+x^(2)sin^(2)x,,x 0] is continuous then

If f(x) ={(a^2 cos^2 x+b^2 sin^2 x"," , x 0):} f(x) is continuous at x=0 then