+ x (2 + x)} – 8 15. lim 16. lim x2/3 18. lim 1-64 Vx 1 16 17. lim I-l Vx - 1 8 tan (2x) 19. lim 1-0 tan (Tx) 20. lim cscx 21. lim sin (+ sin x 22. lim cos? (r –- tan x) cos 2r – 1 sin x &r 23. lim X-0 3 sin x - x 24. lim 25. lim In (t – 3) 26. lim 12 In (2 – Vi) 1-3+ 27. lim Võecos (m/) 8-0 2ez 28. lim 0* el/z + 1

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Q: Q4. Central limit theorem (Theory) State and prove the central limit theorem.

A: Proof:-

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.