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′) by choosing h(x) = g(x) and bk = βk ckπ ℓ This tells us that ckπ ℓ βk = 2 ℓ Rℓ 0 g(x)sin kπx ℓ dx So we have a solution u(x,t) = X∞ k=1 sin kπ ℓ x αk cos ckπ ℓ t) βk sin ℓ t (8) with αk = 2 ℓ Z ℓ 0 f(x)sin kπx ℓ dx βk = 2 ckπ Z ℓ 0 g(x)sin kπx ℓ dx While the sum (8) can be very complicated Example 1 Determine the linear approximation for f (x) = 3√x f ( x) = x 3 at x = 8 x = 8 Use the linear approximation to approximate the value of 3√805 805 3 and 3√25 25 3 Show Solution Since this is just the tangent line there really isn't a whole lot to finding the linear approximation f ′ ( x) = 1 3 x − 2 3 = 1 3 3 √ x 2One is to check the continuity of f (x) at x=3, and the other is to check whether f (x) is differentiable there First, check that at x=3, f (x) is continuous It's easy to see that the limit from the left and right sides are both equal to 9, and f (3) = 9 Next, consider differentiability at x=3 This means checking that the limit from the

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Lim f(x).g(x) = l.m

Lim f(x).g(x) = l.m-Benton by county tax code EH Chelan by state tax code !Graph functions using reflections about the xaxis and the yaxis Another transformation that can be applied to a function is a reflection over the x – or y axis A vertical reflection reflects a graph vertically across the x axis, while a horizontal reflection reflects a graph horizontally across the y

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Choi and Burm, 08;X G H c L c x E R R G E T L R G E E O H R c D G x c W O U B 1 x 1 1 D W B D Y E H U L G H w O O M Y w L M R B L B L N E M x s O B U w B L H D w L w O E K 1 c w M c L x L S R x z E c R E E z c D R A G R G 1 T s G C CIRCLE THESE WORDS IN THE WORD SEARCH ABOVE Beehive Pollinate Drone Queen Guard Stinger Nectar WaggleK, so f(x) = g(x)c nxn Now g(x) is a polynomial of lower degree so we can apply the induction hypothesis to it If q(x) = g(x a), q is also polynomial of the same degree as g, and we can write q(x) = P n 1 k=0 d kx k Therefore p(x) = f(x a) = g(x a) c n(x a)n = q(x) c n(x a)n = = 4 = 4

Picc Fl Cl Bsn F Hn Tpt Tbn Tba Strngs Strngs Strngs Strngs Strngs Strngs b b b a a b b b a a b a a a L L L L L L L L L L L L L L L L L L L L L L L L L L G G Z ZTwo Letters Three Letters Four LettersL x,L 2 = 0, e L y,L 2 = 0, f L z,L 2 = 0 8 In exercise 7 above you determined whether or not many of the angular momentum operators commute Now, examine the operators below along with an appropriate given function Determine if the given function is

 DMD # 8 verapamil in human, while CYP3A1/2 govern the metabolism of verapamil in rats (Tracy et al, 1999;Q 2 # p$yD9 H ) e A @ 5zGDo!Molar concentration (also called molarity, amount concentration or substance concentration) is a measure of the concentration of a chemical species, in particular of a solute in a solution, in terms of amount of substance per unit volume of solution In chemistry, the most commonly used unit for molarity is the number of moles per liter, having the unit symbol mol/L or mol⋅dm −3 in SI unit

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Lineary approximate functions at given points stepbystep \square!Math 115 / Exam 2 () page 8 6 10 points a 4 points Below is a table of values for a differentiable function g(x) Also shown are some Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers Visit Stack Exchange

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(b) Sketch the graphs of f(x) = abs(x), g(x) = f(x) 4, and h(x) = f(x) 3 in the same coordinate plane You can use a graphing utility to check your work, but you should be able to sketch these graphs without help To check your work with the Java(14) yg(x) g'(x)s O Unfortunately, there are manyexamples that defeat this trick For instance, if one takes (15) g(x)= 1exIx with gR2, then 0,s 0 is the unique solution to (14) for all x I Thedifficulty hereis that gt(x) neverhasfull rank Themethodintroducedin 5has Downloaded to~v350b11 300 wx#dcXhVckdUi^EWdc x$PKO\LMQhVQYXXaQRPKUPTkUbVYWVZYX ~w169 9 552 597 0 70 0 0 ~k4984 ?

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^is L~ ^R jH ^ H !1 25% Find all separated solutions u(x,t) = F(x)G(t) of the advection equation ut cux = 0 where c is a constant Show that the separated solutions have the same form as the general solution u(x,t) = f(x−ct) for a suitable function f Solution • Using the separated solution in the PDE, we get FG˙ cF′G = 0 Separation of variablesN x g x b L n x L an u x B π π π Compare the coefficients of the like sine terms, we see = = ∫ L n n L dx n x g x L b L an B 0 ( )sin π 2 π Therefore, = = ∫ L n n L dx n x g x an b an L B 0 ( )sin 2 π π π As we have seen, half of the particular solution is determined

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Hanada et al, 08)See the answer See the answer See the answer done loading Show transcribed image text Expert Answer Who are the experts? Fourier Series for Odd Functions For an odd function `f(t)` defined over the range `L` to `L` (ie period `= 2L`), we find that `a_n= 0` for all `n` We have `a_n=1/Lint_(L)^Lf(t)\ cos{(n pi t)/L}dt` So the zero coefficients in this case are `a_0= 0` and `a_n= 0` The coefficients `b_n` are given by `b_n=1/Lint_(L)^L\ f(t)\ sin{(n pi t)/L}dt`

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