DefineG(x) =Z x20g(t)dt, x ∈ [0, 1].Prove that G is differentiable on [0, 1]. Compute G′(0) and G′(1)
Question
Solution 1
To prove that G is differentiable on [0, 1], we need to show that the derivative of G exists for all x in [0, 1].
The derivative of G at a point x in [0, 1] is given by the limit as h approaches 0 of [G(x+h) - G(x)]/h.
G(x) is defined as the integral from 0 to x of 20g(t)dt. So, G(x+h) is the in Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
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