Word Count : 503

---

Let's go through each statement one by one. ### (i) \(\lim_{x \to 0} \frac{x^2 \sin\left(\frac{1}{x}\right)}{\sin x} = 1\) False. To evaluate this limit, we first note that: - \(\sin\left(\frac{1}{x}\right)\) oscillates between -1 and 1 as \(x \to 0\). - Thus, \(x^2 \sin\left(\frac{1}{x}\right)\) is bounded between \(-x^2\) and \(x^2\), which goes to 0 as \(x \to 0\). - \(\sin x \approx x\) for small \(x\), so \(\frac{x^2 \sin\left(\frac{1}{x}\right)}{\sin x} \approx \frac{x^2}{x} = x \to 0\). Therefore, the limit does not equal 1; it approaches 0. ### (ii) A real-valued function of three variables which is continuous everywhere is differentiable. False. Continuity _________ ___ _________ ____ _______ ________ _______ _______ __________ ____ _____.
_____ ___ _________ _______ ______ _____ _____ ___ ________ _________.
___ _____ __________ ___ __________ _________ _______ _______ ____ ___ _____.
_________ ___ ______ _______ ____ ______ ___ __________ _________ ___.
______ _______ ____ _____ ______ _________ ________ _____ _______ ________ _______.
_________ ________ _______ _________ ________ __________ ___ ________ ______.
___ _______ ____ __________ ________ ___ ____ ______ _______.
___ _______ ________ ____ ____ _______ __________.
________ ________ _________ _______ ___ _____ _______ _________.
_______ ________ ___ _________ ___.
__________ __________ _______ _______ __________.
__________ _________ __________ ____ ____ ________ ___ _______ ___ _______.
__________ ______ ________ ___ _________ _________ _____ __________.
_____ ____ ____ ___ ___ _______ __________ _____ _________ _____ ___ _____.
___ _____ _______ ___ ______ ___ _____ ______ _____ _______.
__________ ________ _____ ___ ________ ________ _____.
_______ ____ ________ _________ ___ ____ __________ __________ ___.
____ _________ _________ ____ _______ ___.
________ _______ ____ ______ __________ _________.
_________ __________ ____ ___ ______.
_________ _____ __________ ___ _________ ____ _______.
_____ ___ __________ ______ _______ _________ _______ ___.
_______ ____ ____ ________ ___ _________ __________ ________ ______ _____ ________ _____.
________ __________ ____ ____ ____ ____.
__________ ________ ________ ___ ______ _______.
___ __________ _____ _______ ___ ________ ___.
___ _____ ____ _________ __________ _________ ______ _______ _______ ______ _______ ___.
_______ _____ ________ ___ _________ _____ _______ ___ ___ __________.
__________ ___ _________ ______ _____ _____ ________.
____ __________ _________ ______ _______ ______ _____ _______ _______ _____ _________ ____.
__________ __________ _________ ___ __________.
_______ ____ _____ ______ ____ _________.
_____ ________ _____ ____ ______ ______ _______ ___ ________.
_______ _________ ________ _________ _____ _____ __________ _________.
_________ _________ ________ _________ ________ _____ _________ __________ _____.
______ _________ __________ _______ ___ ___ ________.
_________ __________ _______ _____ _________ _________ ___ __________ _______ ________ ____.
________ _______ ______ ___ _____ _____ __________ ________ _____.
_____ __________ ____ ______ _____ _________ _________.
_____ ________ ________ ___ ______ _______ ______ ________ __________ ______ _________ _________.
_________ __________ __________ ________ _______.
____ ___ _______ _______ _______ __________ ____ ______ _______.
_______ ______ __________ ____ ____ ________ ____ _________ ______ ____.
_____ _________ _________ ________ ____ _________ _______ ____.
___ _________ _________ ____ __________.
_____ ___ __________ _______ ____ ____ _______.
_________ ________ ________ ______ ___ _______ ___ ______ ___ ______ ______.
_______ ________ ________ ________ ________ ____ _______ ______ ______.
Get Full Answer on WhatsApp