Define g : R → R byg(x) =(x2 cos(1/x) if x̸ = 0,0 if x = 0.Show that g is differentiable at x for every x ∈ R
Question
Solution 1
To show that the function g is differentiable at x for every x ∈ R, we need to show that the derivative of g exists at every point in R.
The function g is defined as g(x) = x²cos(1/x) for x ≠ 0 and g(x) = 0 for x = 0.
- For x ≠ 0, the function g is a product of two functions: h(x) = x² and f(x) Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.
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Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.
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