Find the value of `a + b` if `f(x) = {((a e^(1//|x+2|) - 1)/(2-e^(1//|x+2|)),; -3 lt x lt -2), (b,; x = -2), (sin((x^4-16)/(x^5+32)),; -2 lt x lt 0):}` is continuous at `x = -2.`

Show that f(x) = {:{(5x-4, when, 0 lt x le 1), (4x^(2) - 3x, when, 1 lt x lt 2):} is continuous at x = 1 .

f(x)= {((1)/(2)-x ",",0 le x lt (1)/(2)),(1",",x= (1)/(2)),((3)/(2)-x",",(1)/(2) lt x le 1):} Discuss the continuity of f(x)

continuous at x = 0 Let f(x) = {{:((1 + |sin x| )^((a)/(|sin x|)), - (pi)/(6) lt x lt 0 ),(b , x = 0 ),(e^(tan 2x //tan 3x), 0 lt x lt (pi)/(6)):} Determine a and b such that f(x) continuous at x = 0 .

Let f(x) = {((1+|sin|)^(a/(|sin x|)),",",-(pi)/6 lt x lt 0),(b, ",",x = 0),(e^((tan 2x)/(tan3x)),",",0 lt x lt pi/6):} Then the value of a and b if f is continuous at x = 0, are respectively

Let a , b in R,(a in 0) . If the funtion f defined as f(x)={{:(,(2x^(2))/(a),0 le x lt 1),(,a,1 le x lt sqrt2),(,(2b^(2)-4b)/(x^(3)),sqrt2lt x lt oo):} is a continous in [0,oo) . Then, (a,b)=

Function f(x)={{:(2x-1", if "x le 1 ),(x^(2)", if "1 lt x ),(3x - 4 " , if " 2 lt x lt 4 ):} is continuous on

Let f(x) = {{:({1 + |sin x|}^(a//|sin x|)",",-pi//6 lt x lt 0),(b",",x = 0),(e^(tan 2x//tan 3x)",",0 lt x lt pi//6):} Determine a and b such that f(x) is continuous at x = 0