5

QUESTION $ fx) 4x + Thissame question nunooiced(7'(x)go an additiomal step _ ard find dernative .(lY(x)1'r()V 'J(x)J5points...

Question

QUESTION $ fx) 4x + Thissame question nunooiced(7'(x)go an additiomal step _ ard find dernative .(lY(x)1'r()V 'J(x)J5points

QUESTION $ fx) 4x + This same question nunoo iced (7'(x) go an additiomal step _ ard find dernative . (lY(x) 1'r() V 'J(x) J5points



Answers

Set $f(x)=\ln (1+x) .$ Using a graphing utility or a CAS, draw a figure that gives the graph of $f$ and the graphs of the Taylor polynomials $P_{2}, P_{3}, P_{4}, P_{5}$.

This question we are required to find the antidote, debatable. It fixed is equal to x square minus four x plus seven. Let us start with the simplification. Anti derivative of fx is represented as integral of F x. Dx. This will be equal to the integral off X squared minus 48 plus seven D. X. Now this integral can be broken into three parts has integral of X square D. X minus four times integral of X. Dx plus seven times in the drill off the X. The first integer becomes excess Cube divided by three -4 x square divided by two plus seven X plus a constant of integration, say capital D. We can simplify this form further as XQ divided by three minus two X square plus seven X plus D. This will become the final answer.

Question is given if FX equals two X. Is good plus four X plus seven. So we have to find the value of by using four step formula 50 shades F dishman F. two and f. 1st 3. So now firstly come to stir when in this japanese we have to find the value of F explicit. So in place of X we will substitute explicit. So it can be a dentist explicit. H fully spin plus ford into X plus H plus seven. So opening the bracket by using the identity A plus B. Holy spirit. So access will plus to wear checks Plus actress. Well now it is four X plus forage plus seven. No tell me similar. So this is the value of this happened now come to that step to in a step to we have to find the value of F. X plus edge and minus efforts. Fx. Is the value from the caution and F. X plus H will be put it from step one so X square plus two H. X plus inches square plus four H. X. Plus four. H plus seven and minus X squared plus four X plus seven. As we know when we opened the bracket access where we'll weekends along plus four X minus four X plus seven minus. And it means remaining terms are two H. X. Plus at your square plus food. Edge. Now come to chapter three In the step three. Evil right? F explicit minus fx upon edge. It means if we take Common edge as from the numerator it can be written as two X. Yes. Edge plus four divided by H. H. And H. Well weekends and now so we can't the value two X plus H. Plus for now in step food So it is step four. We will take limit extends to zero so limit H tends to zero. It means we have to put the value of edge zero. So limit extends to zero. F explicit minus effects upon edge. It can be a dentist applying the limit so two X plus zero plus at it means we get two x. This is four to express forwardly. No we can see the value of F dash access the works plus food. Now value of F-1 will be putting the value of excess well Plus four at me it will be six. The value of F. Test two will be value of access to hear two multiplied by two plus four. This is eight. And lastly F-3 will be two multiplied by three plus 46 This poll he close to 10 so we can say our answer. Mm dash access to express food. F-1 will be six. Only F. This too will be eight and F dash David. We then these are final answers.

For this problem. You want to find the 4th Taylor polynomial for the function Ln of co sign of X. Now we recall that the and stellar polynomial of a function is given by. So the first thing we have to do is to find the derivatives of the function Until the 4th order. So we have for the first one F prime of X. This is equal to one over cosine X times the derivative of Goldstein X. Which is negative Synnex. That will be negative tangent X. And we have F double prime of X. This is equal to negative seeking squared of X. And then we have F triple prime of X. This is gonna be negative two time seek end of X time seek index tangent X. Which is the same as -2. She can square decks times tangent X. And then lastly the fourth derivative of the function that's equal to my product rule negative two time seeking square decks times seeking square decks plus we have tangent of X times -4 2nd. Time. 2nd x Tangent X. So when S0 we have for the first one, F of zero. This is l. N Times go sign of zero. That's Ln of one which is equal to zero. And then we have F prime of zero. That's equal to negative tangent of zero, which is also zero. And then you have F double prime of zero. That's equal to negative 2nd squared of zero or -1. And then we have F triple prime of zero. This is equal to zero since we have tangent there, Which makes it zero. And then lastly the fourth derivative, this is going to be Equal to -2. and so the 4th Taylor polynomial is just F of zero, which is zero plus F prime of zero, which is also zero plus F double prime, which is negative 1/2 factorial times X squared, And then f dribble from zero and then F forced derivative. That will be negative two over four factorial Times x rays to the 4th power. This gives us negative X squared over two minus X rays to the fourth power over 12. So this is our forrest taylor polynomial.

For this problem, we want to find the 4th Taylor polynomial for the function F. Of X, which is equal to seek an X. Now we recall that the and taylor polynomial is given by the formula. And with this formula, the first thing I have to do is to find the Derivatives of the function to the 4th degree. So 1st 1 to Find F. Prime of X. And this is equal to seek in tax times tangent tax. And then we want to find F double prime of X. This will be my product rule that's seeking X times Seacon square ducks lost tangent X times 2nd X. Tangent X. So we have second cube X plus we have second X times tangent squared decks. That will be she can't Squared X -1. So we have 2 2nd Cube X minus. He can tex. So the third derivative will be two Times three times he can square decks times seek index, tangent X minus, seeking to extend index, which is the same as second X tangent X times six. Seeking square decks And then -1. So that the fourth derivative will be my product ruled that second X times tangent X times 12. 2nd X times seek and exchange index. Plus we have six seconds squared x minus one times we have product will again seek and X times Seacon square decks plus we have tangent X times second X times tangent X. So at Texaco zero We have for the first one, F prime of zero. That's equal to zero Since standard of 0, 0. And then for the F double prime of zero, we have here Equal to 2 -1, that's one. And then the third derivative at zero will be zero. Given that we have here the Tangent X. That makes it zero. So this is equal to zero. And then the 4th derivative, we have 4th derivative evaluated at zero. That's equal to zero for the first term because of this tangent x. And then we add six minus one times one plus zero. So this gives us a value equal to five. Not also that f of zero Which is sick and of zero is equal to one. So our 4th Taylor polynomial is just We have FF0 which is equal to one plus we have F prime of 0-0 plus F double parameters one divided by two factorial times X squared Plus f triple premature zero plus The 4th derivative at zero, which is equal to five. That's divided by four factorial times X. Rays to the 4th power, simplifying this, we have one plus X squared over two Plus five times x rays to the 4th power over 24


Similar Solved Questions

5 answers
Suggest a chemical teSt that would allow YOu t0 distinguish between tert-butyl alcohol and1-butanol, both of which give positive ceric nitrate teSL
Suggest a chemical teSt that would allow YOu t0 distinguish between tert-butyl alcohol and 1-butanol, both of which give positive ceric nitrate teSL...
5 answers
Problem 23.5640f 4ConstantsPart AHor far apant are an object and Imaje fonmed Dy 85-€- ~focal-lenglh converging lens and $ tear? the image @ 2.20 X larger than Ihe object Express Youransurtr using two signilicant figures_ValueUnitsSubmitMIueELAnecerRetum to Assignment"Provije Feedback
Problem 23.56 40f 4 Constants Part A Hor far apant are an object and Imaje fonmed Dy 85-€- ~focal-lenglh converging lens and $ tear? the image @ 2.20 X larger than Ihe object Express Youransurtr using two signilicant figures_ Value Units Submit MIueELAnecer Retum to Assignment" Provije F...
5 answers
Ax ft)e ke End PDF 0) PCxz2)
Ax ft)e ke End PDF 0) PCxz2)...
5 answers
XZ 3=Y 4x +2XC2o <443-14
XZ 3=Y 4x +2XC2o <443-14...
5 answers
For a closed rectangular box, with a square base % by x cm and a height h cm; find the dimensions giving the minimum surface area, given that the volume is 13 cm3 NOTE: Enter the exact answers, or round to three decimal places.1cmhcm
For a closed rectangular box, with a square base % by x cm and a height h cm; find the dimensions giving the minimum surface area, given that the volume is 13 cm3 NOTE: Enter the exact answers, or round to three decimal places. 1 cm h cm...
4 answers
Point) Let B be the basis of R? consisting of the vectors {L:] [&]}and Iet C be the basis consisting of{[:] [2J}Find matrix P such that JJc = PlzJB for all z in R?.
point) Let B be the basis of R? consisting of the vectors {L:] [&]} and Iet C be the basis consisting of {[:] [2J} Find matrix P such that JJc = PlzJB for all z in R?....
5 answers
Show that if Y~Gamma(@, 8) , then X 1/Y~InvGamma(a, 8).
Show that if Y~Gamma(@, 8) , then X 1/Y~InvGamma(a, 8)....
5 answers
To calculate the maxlmum sustainable yield (MSY) for population that is belng harvested, managers must have accurate estimates of and [mux for the population in question_A fishery manager sets catch Iimit based on a Inaccurate estimate of fmyx: the true value of this parameter is higher= than one used In calculating the limit (Le. Tmu has been underestimated): What will be the consequences of this error for the fishary? Explain vour reasoning:
To calculate the maxlmum sustainable yield (MSY) for population that is belng harvested, managers must have accurate estimates of and [mux for the population in question_ A fishery manager sets catch Iimit based on a Inaccurate estimate of fmyx: the true value of this parameter is higher= than one u...
5 answers
If y= S+f(-3x), then y = OA -3f '(~3x) B.f '(-3x) C. S+f'(-3x) On.5 -3f '(~3x) f'(-3x) OE -3
If y= S+f(-3x), then y = OA -3f '(~3x) B.f '(-3x) C. S+f'(-3x) On.5 -3f '(~3x) f'(-3x) OE -3...
5 answers
In an observational study in Atlanta, 43% of men were observed not washing hands after going to the bathroom Let p be the proportion ofmen washing hands after going to the bathroom in a random sample of size 81.A. If all possible sample of size 81 is obtained, what percentage of p will be within 2.0 standard deviations of the population proportion?
In an observational study in Atlanta, 43% of men were observed not washing hands after going to the bathroom Let p be the proportion ofmen washing hands after going to the bathroom in a random sample of size 81. A. If all possible sample of size 81 is obtained, what percentage of p will be within 2....
1 answers
Use deductive reasoning to tell whether reach statement is true or false. If it is false, give a counterexample. If true, use properties of real numbers to show the expressions are equivalent. For all real numbers $a$ and $b,-a \cdot b=a \cdot(-b)$
Use deductive reasoning to tell whether reach statement is true or false. If it is false, give a counterexample. If true, use properties of real numbers to show the expressions are equivalent. For all real numbers $a$ and $b,-a \cdot b=a \cdot(-b)$...
5 answers
Part AIf the electron follows a circular path with a radius of 25 cm what is the magnitude of the magnetic field? Express your answer using two significant figures_Azd
Part A If the electron follows a circular path with a radius of 25 cm what is the magnitude of the magnetic field? Express your answer using two significant figures_ Azd...
5 answers
0 wordsQuestion .An clectron in a hydrogen atom the state (3, +1/21 Whlch = these numbers most Important tor dctcrmining the orbital" s cncrey? Wht thte angle betwcen and thc z-axls? How ould tne cnciey ol tna otbital be changed I there wvere mugnctk field In the positive z-direction? Would it Eo dowm?FormarTable4120tPwrarraph20 pts
0 words Question . An clectron in a hydrogen atom the state (3, +1/21 Whlch = these numbers most Important tor dctcrmining the orbital" s cncrey? Wht thte angle betwcen and thc z-axls? How ould tne cnciey ol tna otbital be changed I there wvere mugnctk field In the positive z-direction? Would ...
5 answers
If f(c) = 524 6e? find:f' () f'(4):f" '() f''(4)
If f(c) = 524 6e? find: f' () f'(4): f" '() f''(4)...
5 answers
One question of interest is whether_Qnot thc survey results match the parameters of the US population, which are given below: Smile 5090Eyes 30%0Smell [090Clothes 590Hair 590
One question of interest is whether_Qnot thc survey results match the parameters of the US population, which are given below: Smile 5090 Eyes 30%0 Smell [090 Clothes 590 Hair 590...

-- 0.019417--