3

10.. FindMaclaurin series which represents cos(z) for every real number r around the point a...

Question

10.. FindMaclaurin series which represents cos(z) for every real number r around the point a

10.. Find Maclaurin series which represents cos(z) for every real number r around the point a



Answers

Find the Maclaurin series for the functions.
$e^{-x}$

For my glory In Siri's of function. Accent sounds neato acts. So first Mike Lawrence, Siri's of peaches acts is one plus x US X squared over two factory Oh, us X cube over three. Factory in class that at all. Which is he going to Psalm and from serial infinity acts to part in over in fact, a riddle. Here we assume zero factory Oh, it's you go to one, then MacLaurin series of the function acts topsy to axe is he can chew Axe harms some from zero. Yeah, I'm not. He acts to end over and factory Oh, which is equal to some from zero to infinity access to have a plus one over and fact are bill.

Okay, So find the McLaurin. Siris was a function F X is equal e to the negative X. Remember that, um, MacLaurin series is a dictator. Taylor Siri's generated by F at well X is equal to zero. Um, so by the definition of MacLaurin series, right, this holds we have some where k goes from zero to infinity of well, they kick the so that this f k means the case derivative of f um evaluated at zero k factorial times. Extricate. That's equal to well F zero plus f prime of zero times X plus F double prime of zero over two factorial times X squared, right plus ball, Doctor, about that going right plus the insta repetitive of f um evaluated at zero over in factorial times x to the n So suppose that every backs equal to, well, e to the X So, um, find next expansion. That's first calculate f of zero f prime of zero and f double crime 00 we defined in derivatives. So after backs is equal to eat too. Negative acts Well, then F prime first derivative of, uh of prov X. That's just equal to negative e to the negative. X right. Little train rolled up. Right? Either the flap is will be the Black Times, the river off the plot. So we have later eat Need Rex and then the second derivative here, um, half double crime. Oh, backs is equal. Chew. Um well, that's just going to be to the negative x. Okay, So after my prime of X is equal back to eat, too. Negative acts, Okay? And then when we can generalize here and say that the insta repetitive So the and distributive off half of acts is equal to, well, just negative one to the end. Times e to the negative, x right. So basically right, depending on if it's an outer. Even wrote of that, we're gonna have where the derivative is gonna be itself. Eat native X, um, any even growed up or allow derivative. It's gonna gonna have a native in front when I have negative e to the negative x. Okay. Um so? Well, once we have these derivatives, we couldn't find the value of the derivatives. So we get were given that well, what is f of zero? So give the effects is e to the negative X and then evaluate at zero. So say f of zero. That's just equal to, um, eat zero, which is one Okay. And then we'll have prime of zero. Okay, that's gonna be right. Each of the zeros one President Lincoln signed on front. So f prime of zero is gonna be use. He could be co two negative one. Okay, um and, well, if we did the double, it's the second derivative of after every double prime of zero. Well, that's gonna be again. You're back to the original function. So you're back to a one again. Right? So we're alternating here. Were either equal to one or negative one. We can generalize and say that the instrument tive the distributive of F A max is well equal to just negative one to the end. Right? So depending on if you're taken out or even derivative, you're either gonna be equal toe one or native one. Okay. Um, so therefore, the Siri's is as follows. We have, um, f zero plus f prime of zero plus f double crime of 0/2 factorial times X squared. Plus Keeps going, right. Plus the ends derivative of F um, evaluated at zero over in factorial times X to the end. So the McLaurin, Siri's expansion of e to the negative X is given as one minus X plus X squared over to factorial minus X cubed over three factorial plus X to the fourth over. Four factorial minus. Right. And we keep going that that that that, um well, they were, plus a negative one to the end. Right. The conservative. I'm over hoops native, one to the end, over and factorial times X to the end. So do we have, um Oh, our Lord in series for me to negative effects. All right, take care.


Similar Solved Questions

4 answers
Problem 2 A2kg particle has the xY coordinates ( 1.2 m, 0 5 m) ad a 3kg particke has _ Xy coordinale of (0.6 -0.75 m) : Both lie on : honzontal plane Atwhat (a) x and (b) coordinates must You place 4k9 particle such that the center ol Mass of (he three-particle System has the coardinates (-0 5m, 0 7m)?
Problem 2 A2kg particle has the xY coordinates ( 1.2 m, 0 5 m) ad a 3kg particke has _ Xy coordinale of (0.6 -0.75 m) : Both lie on : honzontal plane Atwhat (a) x and (b) coordinates must You place 4k9 particle such that the center ol Mass of (he three-particle System has the coardinates (-0 5m, 0 7...
5 answers
I An3*809 # 1 V tt Vcra and fulls ADAMvuIuI 3 Soefore ohe rope Dearurot nxlon 2a8 shack 'Slcucc qullcn Is(nc (OpC juudItu sxuuju buuds @ 7hi H p
I An3*809 # 1 V tt Vcra and fulls ADAMvuIuI 3 Soefore ohe rope Dearurot nxlon 2a8 shack ' Slcucc qullcn Is(nc (OpC juudItu sxuuju buuds @ 7hi H p...
5 answers
(5 pts) Complete the following ratios by scaling Up or down as necessary:10 185036So 100is what percent?10
(5 pts) Complete the following ratios by scaling Up or down as necessary: 10 18 50 36 So 100 is what percent? 10...
5 answers
5.4 Classify each carbon atom as primary; secondary; and tertiary in the following molecules
5.4 Classify each carbon atom as primary; secondary; and tertiary in the following molecules...
5 answers
Find the orthogonal trajectory of the familythrough the point (0,0).c) e d) e + e" None
Find the orthogonal trajectory of the family through the point (0,0). c) e d) e + e" None...
5 answers
The equation 2Ag2O(s) 4Ag(s) Oz(g) is a(n)24reaction_combinationb. single replacement decomposition uousnquuo?C",two of these8
The equation 2Ag2O(s) 4Ag(s) Oz(g) is a(n) 24 reaction_ combination b. single replacement decomposition uousnquuo? C", two of these 8...
1 answers
Find the extremal curve of the functional $J[y]=\int_{1}^{e}\left(x y^{\prime 2}+y y^{\prime}\right) \mathrm{d} x$, the boundary conditions are $y(1)=0, y(e)=1$.
Find the extremal curve of the functional $J[y]=\int_{1}^{e}\left(x y^{\prime 2}+y y^{\prime}\right) \mathrm{d} x$, the boundary conditions are $y(1)=0, y(e)=1$....
5 answers
Suppose that the operator << is to be overloaded for a user-defined classmystery. Why must << be overloaded as a friend function?
Suppose that the operator << is to be overloaded for a user-defined class mystery. Why must << be overloaded as a friend function?...
5 answers
Lommnor Rarea WAc KaneMS GS %a ;Zoom QutSuentSAVE
Lommnor Rarea WAc Kane MS GS %a ; Zoom Qut Suent SAVE...
5 answers
Give a possible formula for the function>#f(0) =Edlt
Give a possible formula for the function > # f(0) = Edlt...
4 answers
986,four high school students built an electric car that could reach a speed of 106.0 km/h: The mass of the car was just 60.0 kg. Imagine two of these cars used in stunt show: One car travels east with a speed of 106.0 kmlh, and the other car travels west with speed of 75.0 km/h: If cach car $ driver has mass of 50.0 kg, how much kinetic energy is dissi pated in the perfectly inelastic head-on collision?
986,four high school students built an electric car that could reach a speed of 106.0 km/h: The mass of the car was just 60.0 kg. Imagine two of these cars used in stunt show: One car travels east with a speed of 106.0 kmlh, and the other car travels west with speed of 75.0 km/h: If cach car $ drive...
5 answers
Match each function with its graph shown below.a. $f(x)=x^{2}$b. $f(x)=2^{x}$c. $f(x)=2$d. $f(x)=2 x$(GRAPH CANT COPY)
Match each function with its graph shown below. a. $f(x)=x^{2}$ b. $f(x)=2^{x}$ c. $f(x)=2$ d. $f(x)=2 x$ (GRAPH CANT COPY)...
1 answers
Find an equation for the hyperbola that satisfies the given conditions. Foci: $( \pm 6,0),$ vertices: $( \pm 2,0)$
Find an equation for the hyperbola that satisfies the given conditions. Foci: $( \pm 6,0),$ vertices: $( \pm 2,0)$...
5 answers
Use truth-table to prove whether each set of propositional formsare truth functionally equivalent1.“p v ~q” and “~(~p & q)2.“p ⊃ q” and “p ⊃ (p ⊃ q)”3.“p & (q ⊃r) and p ⊃ (q & r)”4.“~(~p v ~q)” and “~~p & q”5.“~p ⊃q” and “~q ⊃ p”
Use truth-table to prove whether each set of propositional forms are truth functionally equivalent 1.“p v ~q” and “~(~p & q) 2.“p ⊃ q” and “p ⊃ (p ⊃ q)” 3.“p & (q ⊃r) and p ⊃ (q & r)” 4.“~(~p v ~q)â€...
4 answers
Exercise 4. Show that the heat kernel:#(r,+) exp Vzknt Vzkat is a solution to the Heat Eqquation.
Exercise 4. Show that the heat kernel: #(r,+) exp Vzknt Vzkat is a solution to the Heat Eqquation....
5 answers
Athin, spherical, conducting shell of radius R is mounted on an isolating support and charged to a potential of -279 V.An electron is then fired directly toward the center of the shell; from point = at distance from the center of the shell (r > > R). What initial speed Vo is needed for the electron to just reach the shell before reversing direction?NumberUnits
Athin, spherical, conducting shell of radius R is mounted on an isolating support and charged to a potential of -279 V.An electron is then fired directly toward the center of the shell; from point = at distance from the center of the shell (r > > R). What initial speed Vo is needed for the ele...

-- 0.021574--