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##### Exercise 29: (Sandwich theorem) Let A â‚¬ R and c â‚¬ R be an accumulation point of A. Let f,g,h :A- R be functions such that for all â‚¬ 6A f(r) < g(z) < h(z) ShowIf lim__c f(z) and lim,-+c g(z) exist then lintz- = f(z) linr-+e ! 9(T). b) If lim,-re f(z) = lim_- +c' h(z) = L then linz-+c' g(z)

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##### Assume member i$ selected at random from the population member selected at random is from the shaded represenled by the graph Find the probability that the area of the graph Assume the variable is normally distributedS4T Critcal | Reading Scores200 < x < 375ScateTha probablay that he member selecled at random is from the shaded area of the graph Is (Round to four decimal places as needed )

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Conslder the wire; whchyIn 4 regon 0f Unitorm magnetic treld &f magnitude 0-5.7T, carrius J current ol |=164 35 shoin in tte fzure beinw If d-s1an 3-23m makingannnxlc Wazudcrrer detcimn te net force cUng on 1he wlte_ Expre , Jaaar ans NeT In Unit s, Df M ueng one deur}l FJcee Touin Aoon...

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##### Consider the functionf(t,y)16 (22 + yP)2 Find the do main and the range of f (â‚¬,y). Hence, sketch the domain of f (â‚¬.y).Marks)b) Given w 3r + y? + 28 where â‚¬ = ers? y = ln (+f) and z rst?. dw Find ds Marks)The relationship between E, n, L and g is given by g = Find 46L)? the maximum percentage error in g due to errors of 1% in n and 0.5% in both E and Lmarks)Verify that (0,0) is & critical point for f (â‚¬,y) = kx2 + y? _ A1y. then determine the values of k when (0,0) issaddle point ,

Consider the function f(t,y) 16 (22 + yP)2 Find the do main and the range of f (â‚¬,y). Hence, sketch the domain of f (â‚¬.y). Marks) b) Given w 3r + y? + 28 where â‚¬ = ers? y = ln (+f) and z rst?. dw Find ds Marks) The relationship between E, n, L and g is given by g = Find 46L)? the m...