prove that f(x) is a continuous funcation where ` f(x) {{:( (x^(4)-16)/(x-2)",", if , xne 2),( 32 ",", if , x =2):}`

Prove that f(x)= 2x-|x| is a continuous function at x= 0.

If f(x) is continuous at x=2 , where f(x)={:{((x^(2)-(a+2)x+a)/(x-2)", for " x!=2),(2", for " x=2):} , then a=

If f(x) is continuous at x=2 , where f(x)=(x-1)^((1)/(2-x)) , for x!=2 , then f(2)=

What is the value of k for which the following fucntion f(x) is continuous for all x? f(x)={{:((x^(2)-3x+2)/((x-1)^(2))","," for "xne1),(k","," for " x=1):}

Examine the continuity of the function : f(x)={{:((|x-4|)/((x-4))", if "xne4),(0" , if "x=4):} at x = 4.

Discuss the continuity of the function : f(x)={{:((|x-2|)/(x-2)", "xne2),(1" ,"x=2):} at x = 2

Prove that f(x)={(x^(2))/(a)-a,a is continuous at x=a

Prove that the function f(x)=2x-5 is continuous at x=-2

If f(x) is continuous at x=16 , where f(x)={:{((x^(8)-(256)^(4))/(x^(4)-(16)^(4))", for" x!=16),(k ", for" x=16) :} , then k=