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1) Let f:R-->R be defined by f(x) = |x+2|. Prove or Disprove: f is differentiable at -2 f is differentiable at 1 2) Prove the product rule. Hint: Use f(x)g(x)− f(c)g(c) = f(x)g(x)−g(c))+f(x)− f(c))g(c). 3) Prove the quotient rule. Hint: You can do this directly, but it may be easier to find the derivative of 1/x and then use the chain rule and the product rule. 4) For n∈Z, prove that xn is differentiable and find the derivative, unless, of course, n...
In order to prove this proposition: (P (x)-+ Q (z)) <-(R (z) Л Q (z))you must prove which of the following propositions? Select all (if any) that apply. B) (Q (z) л P(x)) (R (z) Q (z)) F) All of the Above G) None of The Above In order to prove this proposition: (P (x)-+ Q (z))
Real analysis 10 11 12 13 please (r 2 4.1 Limit of Function 129 se f: E → R, p is a limit point of E, and limf(x)-L. Prove that lim)ILI. h If, in addition, )o for all x E E, prove that lim b. Prove that lim (f(x))"-L" for each n E N. ethe limit theorems, examples, and previous exercises to find each of the following limits. State which theo- rems, examples, or exercises are used in each case....
Question l: Consider the function f(x) = sin(parcsinx),-1 < x < 1 and p E R (a) Calculate f(0) in terms of p. Simplify your answer completely fX) sin(p arcsinx) f(o) P The function fand its derivatives satisfy the equation where f(x) denotes the rth derivative of f(x) and f (b) Show thatf0(n2p2)f(m)(o) (x) is f(x). (nt2) (nti) (I-x) (nt 2 e 0 (c) For p E R-仕1, ±3), find the MacLaurin Series for f(x), up to and including the...
Apologies for the long question! L M N O P Q R S at 10 at A1 ✓ fx Part 2 C D E F G H I J K 7 The budget director for Bird House Unlimited, Inc., has gathered the following data for use in developing the budgeted income statement for January 2020. Estimated sales for January Bird House 34,000 units $42 per unit Bird Feeder 25,000 units $70 per unit Direct materials Estimated inventories at January 1(beginning)...