5

Problem 5Let g(w) be a differentiable function which satisfiesg(x) + x sin(g(z)) = x2What is g (0)?...

Question

Problem 5Let g(w) be a differentiable function which satisfiesg(x) + x sin(g(z)) = x2What is g (0)?

Problem 5 Let g(w) be a differentiable function which satisfies g(x) + x sin(g(z)) = x2 What is g (0)?



Answers

If $ g $ is a twice differentiable function and $ f(x) = xg(x^2), $ find $ f" $ in terms of $ g, g', $ and $ g". $

Hello. And the question is given that if G is not a cause to zero is the differential function then dy dx d upon dx one up on jacks. We have to solve this where Z is not a cause to zero and it is the difference will function. Yeah. So we can write it the upon the X jfx To the power of -1 by using the power rule. If you can solve it minus one into GFX. to the power of my husband -1 into differentiation of Yes. So this will be cause to minus of your facts to the power of -2 into G D S X. So further this will be close to minus off G D S X upon GOP to the power of two. Yeah. So this is the onset, our defenses and evolves von upon gx. I hope you understood. Thank you.

He's chained real here for this because we know that she is differentiable, which is nice. So then and take the truth of the outer layer, which is the second power on the outside and followed by the threat of achieved. And the final layer is the inside there is negative X squared, right? So deriving this year got that, going to have to times G. Of negative X squared to the first power. Here's what does sleep like that. And then times that by G. Prime of negative X. Squared. And then multiply that by the dread of the inside, which is times -2 x. So this is our filter over here.

So we're trying to prove that this distributive is equal to will be out on the right side here. And so we're going to go ahead and use the chain earlier, which is basically if we have our coverage here, we're trying to derive that. Yeah, that is equal to G F prime minus F G prime on her G squared. All right, So or F in this case is one so that we have the derivative of one over G of X, and that's equal to so G fx times F prime during 210 something minus one times of G of X. All over G F X squared. So we see it at this close to zero. And so we're left with negative G fx over G of X squared. And that is what we want. And so we verified that does.

To prove this. We are going to find the limits As a church tends to zero of um If of X plus H minus F. Of X. All divided by age. Okay, so F F X plus H is equals two X plus H. That's it. Times G. X plus H. And F of X have already defined. So let's make the substitution. So then this becomes the limit At age 10- zero. Uh Okay. Of um X plus H times she of X plus age minus X. G. Of X. Okay. And then we divide this by H. So now we want to prove that this is differentiate will at zero. So we have to let X equals to zero. So we substitute X to be zero. So this will be the limit at age 10-0. Um off. So it's 0-plus eight which is going to be a church. Then we have G exit sara. So this will be a change minus zero. All divided by H. And this is equals two H times G. Of H. All right, divided by H. And we can see that these two are actually going to cancel and then we are left with so I left with the limit as H tends to zoo uh of Uh sorry I forgot the limit here. So it's the limited h tends to zero. This is equals to the limit in exchange 20 of G. F. H. So at this point now we can actually substitute um H H equals to zero. Okay, so this is going to be um G off the sarah. So we know that this exists because um G is continuous. She is continuous. It zero. So um GF zero must exist. So this is true. Um Okay, F is differentiable at zero. Yeah. So to find the derivative of if in terms of all with respect to X who are going to use the product rule, we were going to treat this as a constant first. So we're going to have X. And then we find the derivative of G. So it's going to be cheap prime uh X of X plus now we treat G of X as a constant, so the derivative of X is one. And then we're going to have um G of X unchanged. Right? So now we are looking for the derivative of if we're X s equals to zero and this is equals two. So we substitute X equals to zero. So to be zero times G prime zero plus G of zero, and this will be equal to G of zero. The exact same G that we got earlier. Yeah. Mhm.


Similar Solved Questions

5 answers
Find the average rate of change of the function over the given interval: f (c) =1" + 31, [1, 8]
Find the average rate of change of the function over the given interval: f (c) =1" + 31, [1, 8]...
2 answers
ProblcmConsider the following Ll problem314 Tf3~T} + 33 TT | 2 5 252 FT, - +314 T+T2 31 {T4 < -3 +3r =I [ree, I > 0 Ja<uFil the dual of this prollem by converting first dnal, and then sitnplifying tha (min Jeunonical form 6inding Verify that tht: dual of the cual the priml by "sing canonical form). synimetry relatiouship (skipping
Problcm Consider the following Ll problem 314 Tf3 ~T} + 33 TT | 2 5 252 FT, - +314 T+T2 31 {T4 < -3 +3r =I [ree, I > 0 Ja<u Fil the dual of this prollem by converting first dnal, and then sitnplifying tha (min Jeunonical form 6inding Verify that tht: dual of the cual the priml by "sing...
5 answers
Find the indefinite integra and check the result by differentiation (Use C for the constant of integration_ x(9x2 + 2)6 dxNeed Help?Rond [d~I9 palnta LarCalc 11 5.020. Find the indefinite integral and check the result by d fferentiation: (Use for the constant of integration: )6u8 , u7
Find the indefinite integra and check the result by differentiation (Use C for the constant of integration_ x(9x2 + 2)6 dx Need Help? Rond [d ~I9 palnta LarCalc 11 5.020. Find the indefinite integral and check the result by d fferentiation: (Use for the constant of integration: ) 6u8 , u7...
5 answers
Point) Solve the given initial value problem y 6 + e"-C 6x+2 y(0) = -2The solution in the implicit form is F(x,y) = 1, where F(x,y)
point) Solve the given initial value problem y 6 + e"-C 6x+2 y(0) = -2 The solution in the implicit form is F(x,y) = 1, where F(x,y)...
5 answers
Question #8 Find the equation of the tangent line at 0 = % for the function belowr= 2cos(20)
Question #8 Find the equation of the tangent line at 0 = % for the function below r= 2cos(20)...
5 answers
The empirical formula for the solid sodium thiosulfate pentahydrate is NazS_O3*5Hz0. Determine the molar mass for this solid, .(1 mark)6 , Gxto" b. Determine the number of oxygens that would be present In 3.381 g of the solid.marks)
The empirical formula for the solid sodium thiosulfate pentahydrate is NazS_O3*5Hz0. Determine the molar mass for this solid, . (1 mark) 6 , Gxto" b. Determine the number of oxygens that would be present In 3.381 g of the solid. marks)...
5 answers
Polassium chromate + hydrochloric_acid 5 peroXide Tadd Catalysl = 4+ Manganese 6_ Hydrogen doxide7 IronCopper_(i Sulfate (nitrate Sodlum phos_ phatc 8 Copper Magncsuum nitric_acid 1O. Copper Silver nitrate
Polassium chromate + hydrochloric_acid 5 peroXide Tadd Catalysl = 4+ Manganese 6_ Hydrogen doxide 7 Iron Copper_(i Sulfate (nitrate Sodlum phos_ phatc 8 Copper Magncsuum nitric_acid 1O. Copper Silver nitrate...
5 answers
What is vector? What is the difference between a vector object and an array object?
What is vector? What is the difference between a vector object and an array object?...
1 answers
The middle term of each trinomial has been rewritten. Now factor by grouping. $$ \begin{aligned} 3 x^{2} &-x y-14 y^{2} \\ &=3 x^{2}-7 x y+6 x y-14 y^{2} \end{aligned} $$
The middle term of each trinomial has been rewritten. Now factor by grouping. $$ \begin{aligned} 3 x^{2} &-x y-14 y^{2} \\ &=3 x^{2}-7 x y+6 x y-14 y^{2} \end{aligned} $$...
1 answers
Find the indefinite integral. $$\int \sin \theta \sin 3 \theta d \theta$$
Find the indefinite integral. $$\int \sin \theta \sin 3 \theta d \theta$$...
5 answers
0/5 POINTSPREVIOUS ANSWERSSPRECALC7 7.2.015,Use an Addition Subtraction Formula to write the expression as trigonometric function of one number: sin(1 cos(190) cos(1 sin(198)Flnd Its exact valuc_
0/5 POINTS PREVIOUS ANSWERS SPRECALC7 7.2.015, Use an Addition Subtraction Formula to write the expression as trigonometric function of one number: sin(1 cos(190) cos(1 sin(198) Flnd Its exact valuc_...
5 answers
Find the first three nonzero terms of the Maclaurin expansion of the following function: f(x)
Find the first three nonzero terms of the Maclaurin expansion of the following function: f(x)...
2 answers
Consider an 8 point DFT:Obtain DFT matrix for an 8-point DFT using paper and pencil method: Prove the efficiency of the FFT algorithm and simplification on matrix elements discussed in class to prove the efficiency of FFT algorithm: Show how symmetry helps simplifying the matrix Draw the butterfly diagram for an 8 point FFT: Show the repeating pattern 0f the coefficients on unit circle
Consider an 8 point DFT: Obtain DFT matrix for an 8-point DFT using paper and pencil method: Prove the efficiency of the FFT algorithm and simplification on matrix elements discussed in class to prove the efficiency of FFT algorithm: Show how symmetry helps simplifying the matrix Draw the butterfly ...
5 answers
If the marginal average cost of a company is MAC = 1 600x 2 , then 60 the number of units must be produced so that the average cost is minimm is
If the marginal average cost of a company is MAC = 1 600x 2 , then 60 the number of units must be produced so that the average cost is minimm is...

-- 0.019372--