Show that the Maclaurin series for sin x converges to sin x. Hint: If
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- |a) Consider the function f (x) = -х + 1, —пarrow_forwardAnswer the following points i. Find the first three nonzero terms of Maclaurin series for the functions f(x) = e* and other function f(x) = ex ii. By depending on point (i), find the series for function f(x) = Cosh(x) where ex +e-x Cosh(x): Ans./ i) ex 2 1arrow_forwardQ 4. Apply Taylor's series expansion and find first five terms of the following function f(x)=x+e* about x= 2.arrow_forwarda. Show that if two power series E-oa„x" and E-o b,x" are convergent and equal for all values of x in an open interval (-c, c), then a, = b, for every n. (Hint: Let f(x) = E0a,x" = show that a, and b, both equal f®(0)/(n!).) b. Show that if Eo a,x" = 0 for all x in an open interval (-c, c) then a,n E=ob,x". Differentiate term by term to 0 for every n.arrow_forwardhelp me with part abc pleasearrow_forward3. Use the series reine, for some 0arrow_forwardhelp me with part e and f pleasearrow_forwardV3.arrow_forwardGiven the below function and graph, determine the following. a. A Fourier series representation of the function. b. Write out the series explicitly with the first four terms after ao. 64 f(x): = x + 4, l-x + 4, 3 2 -1- -4 < x < 0 0 < x < 4arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
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