सिद्ध कीजिए :
इस असमानता को सिद्ध करने के लिए, हम टेलर श्रेणी विस्तार और कैल्कुलस के कुछ सिद्धांतों का उपयोग करेंगे। ### असमानता: \[ e^{-x} < 1 - x + \frac{x^2}{2!}, \quad x > 0 \] #### 1. टेलर श्रेणी विस्तार: \( e^{-x} \) का मैक्लॉरिन श्रेणी ___ ________ ______ ____ _____.
_________ ____ _____ _________ _________ ___ _____ _________ ________ __________ _________.
_________ ____ _________ ____ ________.
___ ____ __________ ________ ______ ________ ________ _________.
________ _____ __________ _____ _____ ______ __________ __________ ____ __________ _________.
______ _____ _____ __________ _____ ______.
_____ _____ _________ __________ _______ ___ _________ _________ ______.
__________ ______ _________ ____ ________ ____ ________.
________ _________ ________ ____ _________ __________ _______ _____.
______ _________ _____ _______ ______.
______ ________ ____ ____ _________ ___.
______ ________ __________ _______ ___ _____ ________ _____ _______.
_______ _______ ___ ________ ____ ____ ____ ________ _________ __________ __________.
________ _______ ______ ____ __________ _______ ______ ___ _______ ___ _______ _____.
__________ _______ _______ ______ __________ _______ __________ ___.
__________ ___ ________ ______ ____ ____ ______ _____ ___ ___ _______.
________ ____ _________ _____ ___ ______ _______ ____ ______.
_____ ________ _______ ______ ________.
_______ _______ ___ ____ ____ ___ _______ ______ ______ ____ ___.
_______ _______ _____ _____ _______ __________ ________ _______ _________ ________ ________ ________.
___ ____ __________ ______ _____ ____ _________ _____ _____.
__________ ______.
Get Full Answer on WhatsApp
Show that [a,∞)is closed set.
b) Write the following statement, and its negation, using logical quantifiers. Also interpret its negation in words.
∃ x∈R such that x-1/3 > 0.
Give one example each for the following. Justify your choice of examples.
i) A sequence which is divergent.
ii) A set which is neither open nor closed.
iii) A compact set.
iv) A set which has no limit point
Show that the sequence {fn}of functions, where
is uniformly convergent in ,0[ k],where k > .0 Show further that } { n f is not uniformly convergent in ,0[ ∞[.
एक उचित प्रति-उदाहरण देते हुए निम्नलिखित कथन को असिद्ध कीजिए :
सिद्ध कीजिए कि फलनों का अनुक्रम {fn} जहाँ
दिखाइए कि समुच्चय :
विवृत नहीं है।
Find the supremum and infimum of the set: