verify whether the function f defined by f(x)= x sin(1/x), x≠0 , 0 if x=0 is continuous at x=0 or n

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Show that the function f defined by f(x) = xsin(1/x) and 0 when x=0 is continuous at x=0. Show that the function f defined by f(x) = xsin(1/x) and 0 when x=0 is continuous at x=0.
71. Show that the function f(x)=(x^4 sin⁡(1/x)if x≠0, 0 if x=0} is continuous on (-∞,∞). 71. Show that the function f(x)=(x^4 sin⁡(1/x)if x≠0, 0 if x=0} is continuous on (-∞,∞).
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Limit of x*sin(1/x) as x approaches 0 | Calculus 1 Exercises Limit of x*sin(1/x) as x approaches 0 | Calculus 1 Exercises
x Sin(1/x) is continuous at x=0 but not differentiable x Sin(1/x) is continuous at x=0 but not differentiable
Examples not uniformly continuous functions| f(x)=sin(1/x) is not uniformly continuous on (0 1) Examples not uniformly continuous functions| f(x)=sin(1/x) is not uniformly continuous on (0 1)
59. Determine whether f 59. Determine whether f'(0) exists. f(x)={x sin⁡(1/x) if x≠0, 0 if x=0
f(x)=sin(1/x), x not equal to 0, f(x)=1, x=0 f(x)=sin(1/x), x not equal to 0, f(x)=1, x=0