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1. For each of the following statements, determine whether it is true or false and justify your answer. a. If the function f: R → R is continuous at xo, then it is differentiable at xo. b. If the function f : R → R is differentiable at xo, then it is continuous at xo. c. The function f:R → R is differentiable if the function ƒ²:R → Ris differentiable.

1. For each of the following statements, determine whether it is true or false and justify your answer. a. If the function f: R → R is continuous at xo, then it is differentiable at xo. b. If the function f : R → R is differentiable at xo, then it is continuous at xo. c. The function f:R → R is differentiable if the function ƒ²:R → Ris differentiable.

Advanced Engineering Mathematics
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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1. For each of the following statements, determine whether it is true or false and justify your answer. a. If the function \( f : \mathbb{R} \rightarrow \mathbb{R} \) is continuous at \( x_0 \), then it is differentiable at \( x_0 \). b. If the function \( f : \mathbb{R} \rightarrow \mathbb{R} \) is differentiable at \( x_0 \), then it is continuous at \( x_0 \). c. The function \( f : \mathbb{R} \rightarrow \mathbb{R} \) is differentiable if the function \( f^2 : \mathbb{R} \rightarrow \mathbb{R} \) is differentiable.
Transcribed Image Text:1. For each of the following statements, determine whether it is true or false and justify your answer. a. If the function \( f : \mathbb{R} \rightarrow \mathbb{R} \) is continuous at \( x_0 \), then it is differentiable at \( x_0 \). b. If the function \( f : \mathbb{R} \rightarrow \mathbb{R} \) is differentiable at \( x_0 \), then it is continuous at \( x_0 \). c. The function \( f : \mathbb{R} \rightarrow \mathbb{R} \) is differentiable if the function \( f^2 : \mathbb{R} \rightarrow \mathbb{R} \) is differentiable.
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