Prove that `f(x)=5x-3` is continuous at `x=0`

Prove that the function f(x)= 5x-3 is continuous at x=0, at x= -3" and at " x=5 .

f(x)=x+|x| is continuous for

Show that the function f(x)=5x-|2x| is continuous at x = 0

Let f(x)={({1+|sinx|}^(a//|sinx|), -pi//6ltxlt0),(b, x=0),(e^(tan2x//tan3x), 0 Determine a and b such that f(x) is continuous at x=0

A function f (x) is defined as follows: {{:(5+2x,"for"-(5)/(2)lexlt0),(5-2x,"for "0lexlt(5)/(2)),(-5-2x,"for "xge(5)/(2)):} Show that f (x) is continuous at x =0 and discontinuous at x=(5)/(2) .

A function f (x) is defined as followes: f(x)={{:(xsin.(1)/(x),"when " xne0),(0,"when " x=0):} Show that f (x) is continuous at x =0 .

A function f (x) is defined as follows: f(x)={{:(x^(4)-3,"when " xle2),(x^(3)+5,"when "xgt2):} Prove that the function f (x) is continuous at x = 2 .

Let f(x+y)=f(x)+f(y) for all xa n dydot If the function f(x) is continuous at x=0, show that f(x) is continuous for all xdot

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

If f(x)={{:(x+sinx,"when "xlt0),(0,"when "xge0):} examine whether f(x) is continuous at x = 0.