Show that the function: f(x)= x^2 *sin(1/x) at x!=0 f(x)= 0 at x=0 is continuous at x=0 ?#shorts

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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 (-∞,∞).
Let f(x) = { x^2 sin(1/x), x≠0 0 , x=0 ; Then at x = 0 Let f(x) = { x^2 sin(1/x), x≠0 0 , x=0 ; Then at x = 0
x Sin(1/x) is continuous at x=0 but not differentiable x Sin(1/x) is continuous at x=0 but not differentiable
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.
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
Limit x tends to zero sin(1/x)|Continuity|Differentiability at x=0|Behaviour of sin(1/x) at x=0 Limit x tends to zero sin(1/x)|Continuity|Differentiability at x=0|Behaviour of sin(1/x) at x=0
`f(x) = {{:(x^(2)sin\ `f(x) = {{:(x^(2)sin\'1/x, if x ne 0),(0, if x = 0):}` at `x = 0`.
Checking the Continuity of a Function #jeedailyconcepts #limitsandcontinuity Checking the Continuity of a Function #jeedailyconcepts #limitsandcontinuity