Q4) Find the linearization of: f(x) = x³ + 10 when a = -3

Q: Use linearization to determine an approximation of V1002.

A:

Q: (a) Solve and plot the orthogonal trajectories of the family of lines whose point of intersection is…

A:

Q: (b) ruz – 2yuy + u = eª , for x> 0

A: 1.(b) Given partial differential equation xux-2yuy+u=ex, for x>0 This can be written as…

Q: 11. Differentiate the function (use chain rule): y = x²(x-1)³(2x-5)² ;

A:

Q: Find the linearization of-ƒ(x, y) = x2 - xy + 1- 2 y2 + 3?

A: Here we have,  f(x,y) = x2-xy+1-12y2+3 at (3,2)

Q: Use Cramer’s Rule to solve x + 6y − 4z = 10 4x − y − 3z = −8 x + y − 2z = 7

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Q: Use chain Rule to find for 2. y = . +x²+x+1 I.W | 3. y = estn 3x Н.W

A: We have to find dydx using chain rule for the given function: 2.  y=1x3+x2+x+13.  y=esin 3x We know…

Q: To the reci max z Ax1 +B x2 A=6 s.t. 2x +4x 2 12, B=1 -X1 + 2x2 S 2, X1 20, x2 Free.

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Q: (b) Using linearization, approximate f(-0.1, 1.8).

A:

Q: If f (x) = x* and g(x) = x³, then f'(x) = 4x³ and g'(x) = 3x². The Chain Rule %3| multiplies…

A: It is given fx=x4, gx=x3, f'(x)=4x3 and g'(x)=3x2.

Q: What is the counterexample of x+x>x ?

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Q: Solve 2sinx- V3 = 0 on interval [0,2 t)

A: We have to solve  2sinx - √3 = 0 on interval [0 , 2π)  Since ,  2sinx - √3 = 0  2sinx = √3

Q: find the orthogonal trajection of the family of curves x2+y2=a2

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Q: When x = 2s+7t, y=5st and z= 3.x2 – 3, in the form of s and t. express

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Q: Find fxy when f(x, y) = 8xeXy.

A: To find fxy when fx, y=8xexy.

Q: Q2. Solve the DE. y"" = x2sinx 1. by using inverse operator method. 2. by using variation of…

A: As per bartleby guidelines for more than one questions asked, only one questions is to be answered,…

Q: If x < 0 and y > 0, determine the sign of the realnumber. xy2

A: Given that, x < 0 that is x is negative. y > 0 that is y is positive.

Q: h(x) = Vx – 2 on the domain [2, 5]. -

A: The given graph is:

Q: The function y== In (3z - 2) satisfies the IVP: (3z – 2)°y" + 9 = 0, y(1) = 0, y'(1) = 8. Select one…

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Q: Differentiate the function (use chain rule): y = 2x2 /x+1

A: as per our guidelines, we are supposed to answer only the first question in the serial number.

Q: -2 Write the equation for the linear approximation of g(x) = In(vr² +5) based at x =-2. Justify your…

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Q: By using false position method find f(x) = e* - 2 u %3D

A: Attached solution :

Q: Find the quadratic fúnction y= ax²+ bx +C whose graph pabses through the given points :(1,6),…

A: Given  The quadratic function y=ax2+bx+c and its graph is passing through the points 1,6,-1.-4  and…

Q: x^2=Axy+By

A: Simple value put

Q: Find yll of x³+y²=3 by implicit ditferetlal C1o pants

A:

Q: 4. Find dyax and d2 x =V4- t , go t²-2t ye t'-2 get'.

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Q: I Sdve for dy using the four-step rule 2. y = x"- x 5X-3 ソ= 4- 3X

A: We have to solve the problem

Q: uO The correlation coefficent is found to be 0.567. We can say that the relationshp between the high…

A: The obtained correlation coefficient between high daily temperature and number of traffic accidents…

Q: Give the family of orthogonal trajectories for the equation: y2 = Cx5+5

A: To obtain the family of orthogonal trajectories for the equation: y2 = Cx5+5. Find a differential…

Q: What is the value of x in (2x - jy) + (y - jx) = 1 - j5?

A: We have to find the value of x where 2x-jy+y-jx=1-j5

Q: Find the orthogonal trajection of the family of curves x2+y2=a2

A:

Q: II. Verify that ду дх дх ду 3 2 2. f(x, у) %3Dх'у? — ху 'y² – xy ³

A: Given function: Now,

Q: What is the counterexample of x/x=1

A: Follow the steps.

Q: Find the linearization L(x) of y = (64+3x2)-1/2 at a = 0. L(x) = %3D

A: The given function is: y=f(x)=(64+3x2)-12 So, f'(x)=-1264+3x2-32(6x)        =-3x64+3x232

Q: (P-rule) 9. y=XN2X+ | %3D rewrite y

A: Given that:y=x2x+1

Q: What is the fxx, fyy, and fxy of f=(2x^4)+(y^2)-(x^2)-(2y)?

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Q: Using the principles 2y. -3y + y = 5-3" Vn20 where y=1 and y₁=1

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Q: 3)으 rcose de Jsine 1-x2 d ¿= xp 2

A: LEIBNIZ RULE

Q: Find the linearization of f(x) = V16 – x² at a = 3. %3D

A: Given: The formula used for linearization:

Q: 11. Perpendicular to 5y = 2x – 6 and passes through the point (-1, 5)

A: Given, The line is perpendicular to 5y=2x-6 and It is passing through the point (-1, 5). Concept…

Q: Calculate Vf when f 3x 2- y z' + 4x'y + 2x - 3y - 5 at the point (1, 1, 0).

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Q: Find y' for x°y* + 2x + 2y = 128 at the point (2, – 2). At (2, – 2), y' = Preview -

A: The given equation is: x3y4+2x+2y=128...(1) To find y' at the point (2,-2).

Q: (a) Solve and plot the orthogonal trajectories of the family of lines whose point of intersection is…

A: The equation for the family of straight lines y=c x By differentiating with respect of x…

Q: Use Cramer’s Rule to solve:…

A:

Q: Solve Utt - c²uxx = 0, –n 0, %3D и(х, 0) %3D f(x), и(-п,t) %3D0 %3D и(п,t), и,(-п,t) %3D 0 %3Du,…

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Q: find orthogonal trajectories of   x2+(y-c)2=c2.

A: x2+(y-c)2=c2 now differentiating both side with respect x , we get 2x+2(y-c)dydx=0 or, dydx= -x(y-c)…

Q: ,2,,2 Suppose that f(x, y) = 10x²y² + 6x? + 2y? then find the discriminant of f.

A: We have to find the discriminant from the given function

Q: 12. Differentiate the function (use chain rule): y = 2x2 Vx+1'

A: To differentiate the given function

Q: If x < 0 and y > 0, determine the sign of the realnumber. xy

A: Let x<0 and y>0