Mathematics OpenStudy (anonymous):

Use linear approximation, i.e. the tangent line, to approximate 999^4 as follows: Let f(x)=x^4. The equation of the tangent line to f(x) at x=10^3 is best written in the form y=f(a)+f'(a)*(x−a) where a=10^3, f(a)=(10^3)^4, and f'(a)=4(10^3)^3. Using this, we find our approximation: 999^4 approximately equals? ______ I'm stuck at the last part and can't figure it out. Can someone walk me through it without giving me the answer? OpenStudy (mathmate):

Straight substitution of your formula gives: f(x)=x^4 f'(x)=4x^3 let a=1000, f(x)=f(a)+f'(x)(x-a) =1000^4 +4(1000^3)(999-1000) =996000000000 compare with exact value of 999^4 =996005996001 OpenStudy (anonymous):

OOOHHH!! So I plug 999^4 into x in the equation! OpenStudy (mathmate):

You probably made a miscalculation for f'(a)=4(10^3)^3 with a ^3 too many. OpenStudy (mathmate):

The only time you use 999 is (999-1000). You do not need 999 for f(a) nor f'(a), since a=1000. OpenStudy (mathmate):

Sorry, I had a typo above for the equation, but the calculation that followed is correct. should read: f(x)=f(a)+f'(a)(x-a) OpenStudy (anonymous):

Why do I use 999 instead of 999^4 at the end of the equation? OpenStudy (anonymous):

I did not, I put in 999^4 as x in 1000^4 +4(1000^3)(x-1000) and got the wrong answer. I put in 999 for x and got the right answer. OpenStudy (anonymous):

I think it's because 999 is x and f(x)=x^4, which is where the rest of my equations come from. OpenStudy (anonymous):

I put that in and the program counted it as wrong, make 999^4 just 999 and it counts it right. OpenStudy (anonymous):

Dude, I don't know, I copied and pasted the question and put in the correct symbols where they needed to be. I was surprised I made it to the end without help. If the program says 999 is x, instead of 999^4, and I get the problem right I won't argue. I'm sure it was just the wording of the problem that threw us off. OpenStudy (mathmate):

Sorry I was offline. (999-1000) represents delta-X in the differential, that's why it is not raised to the fourth power. The equation that you correctly stated was: f(x)=f(a)+f'(a)(x-a) where a=1000, (x-a) = dx, so the linear approximation becomes: f(x)=f(a)+f'(a)[delta-x] which geometrically is shown in the figure below:|dw:1326861483536:dw|

Latest Questions cuzican: Since the Constitution placed the sole power of impeachment in two political bodies, it is qualified as a political question.
4 hours ago 1 Reply 0 Medals rthrth: Your gross income is \$4,520.00/month. Your deductions are FICA (7.65%), federal tax withholding (11.
7 hours ago 1 Reply 0 Medals bonnie: Which lines in this excerpt from act V of Shakespeare's Romeo and Juliet create d
9 hours ago 1 Reply 0 Medals jeovonniwells21: Of the four sections of Justinian's Code, Institutiones was meant for:
6 hours ago 2 Replies 0 Medals emilee234: wrote somethin... lemme know what you guys think Its called Why? its not a poem or anything.
10 hours ago 12 Replies 0 Medals Sailor: Stuff i madeu2026 just gimme a second for the stuff to post in chat alright?
2 hours ago 10 Replies 4 Medals 81828: i need help Which function has an inverse that is also a function? g(x) = 2x u201
10 hours ago 1 Reply 2 Medals Olive2006: Help Please!
10 hours ago 2 Replies 0 Medals djmatthies12: Choose the correct sum of the polynomials (6x3 u2212 8x u2212 5) + (3x3 + 6x + 2)
11 hours ago 2 Replies 1 Medal djmatthies12: Zoya has to earn at least \$300 to meet her fundraising goal. She has only 100 bracelets that she plans to sell at \$5 each.
11 hours ago 1 Reply 0 Medals