Question 38 that 41 references is as follows...T F 38. If f is continuous at x = a, then f is differentiable at x = a. TTTF 38. Iffis continuous at x = a, then fis differentiable at x = a.F 39. Iff is differentiable at x = a, then fis continuous at x = a.F 40. Question 38 is logically equivalent to: fis discontinuous at x = a or f is differentiable at x = a.

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Answered: T F 38. Iff is continuous at x = a,…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Which of the following is true? O If the function is continuous at x = c then you can use the tangent line approximation at x = c. O The function does not need to be differentiable at x = c to use the tangent line approximation at x = c. O The function needs to be differentiable near x = c, to use the tangent line approximation at x = c.
Can you please help me with this question?
Consider the following function. A.) Find f(2). B. Is f(x) continuous at x=2? Why?
Question 2. Our goal is to prove that f(x)= x + e* has exactly one root (i.e. f(x) = 0 for exactly one value of x)." a) First, we really need this function to be both continuous and differentiable. Explain in words how we know this is true. b) Now, let's prove that f(x) has at least one root. What theorem do we need for that? Hint: This is a review problem! We're looking all the way back at section 2.5. c) Use the theorem you stated in part a) to prove that f(x) has at least one root. d) Now that we've proven there is at least one root, we will now prove there is not at least two roots. We'll do this using contradiction. Let's (incorrectly) assume that there are in fact two different roots, and use that to blow up math. The logic here is that if we assume something, and end up breaking math using that assumption, then our assumption should be wrong and we can correctly conclude its opposite. Let's call those two roots a and b. Mean Value Theorem then states that the derivative of f(x)…
Q6.5 Please include a formal proof. Thanks!

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T F 38. Iff is continuous at x = a, then f is differentiable at x = a. T F 39. Iff is differentiable at x = a, then fis continuous at x = a. T F 40. Question 38 is logically equivalent to: fis discontinuous at x = a or fis differentiable at x = a.