Show that `f(x)={{:((cosax-cosbx)/(x^(2))," if " xne0),((1)/(2)(b^(2)-a^(2))," if "x=0):}"is continuous at 0"`

Show that f(x)={{:((cos ax-cosbx)/(x^(2)),if x ne 0),(1/2 (b^(2)-a^(2)),if x =0):} where a and b are real constants is continuous at x = 0.

Is f defined by f(x)={{:((sin2x)/(x),"if "xne0),(1,"if "x=0):}" continuous"0 ?

Show that Lt_(xto0)(cosax-cosbx)/x^(2)=(b^(2)-a^(2))/2

Show that Lt_(xto0)(1-cosax)/(xsin2x)=a^(2)/4

Show that the function f given by f(x)= {{:(x^3+3," if "x ne 0),(1," if "x=0):} is not continuous at x=0.

Evaluate {:("Lt"),(xrarr0):}(cosax-cosbx)/(x^(2))

Is f defined by f(x) = {((sin 2x)/x, if x != 0),(1, if x = 0):} continuous at 0?

f(x) = {{:(4-3x " if " x le 0),(2a + x " if " x ge 0):} is continuous at x = 0 then a =

f(x) = {{:((36^(x) - 9^(x) - 4^(x) + 1)/(2sin^(2) ((x)/(4)) )" if " x ne 0),(k " if " x = 0):} is continuous at x = 0 then k =