Determine if f' is continuous at 0 for x^3sin(1/x)
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Things to know !!
1) sin x and cos x are continuous and differentiable bounded functions on x belongs to R .
2) f(x) is continuous at a point when Left hand limit = Right hand limit = value of function at that point.
Here,
f'(0) = 0 since sin 1/x and cos 1/x are always bounded .
Final Result f'(x) is continuous at x = 0.
For calulation Process see pic .
Hope, you understand my answer!
1) sin x and cos x are continuous and differentiable bounded functions on x belongs to R .
2) f(x) is continuous at a point when Left hand limit = Right hand limit = value of function at that point.
Here,
f'(0) = 0 since sin 1/x and cos 1/x are always bounded .
Final Result f'(x) is continuous at x = 0.
For calulation Process see pic .
Hope, you understand my answer!
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