9. 3x2 Let g(x) = -2x2 r<0 (b) Prove that q is not differentiable at 0.

Q: 1- f(x,y) = In(x² + y?) at (1,1)

A: As per our guidelines we are supposed to answer only one question. Kindly repost others question as…

Q: 4. Find the linear approximation to f(x) = cos(x) near a =- [Where L(x) = f(a) + f'(a)(x – a) ]

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Q: Supose z is implicitly dofimed by the equation qy+ 3x + XyZ + 32=9 in an onvanment of the point…

A:

Q: Suppose F(r, y) is a C' function such that F(0, 0) = 0. What conditions on F will guarantee that the…

A: Let us consider, F^(x,y)=F(F(x,y),y)  On applying the implicit function theorem , can get a solution…

Q: 4. Find f'(x), if f(x) = (2x – 8x²)-²(3x + 1). 5. If y is a twice differentiable function and x cos…

A: Differential equation. Solving only first ques as per bartleby guidelines.

Q: 2. Let f(x, y) = In(x² + y²). Show that fre + fyy = 0. %3D

A:

Q: 3 36 Consider a fumetion f whose first and second derivatives are f'(x) and f"(r) = 5/2 (1r² + 1)"/2…

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Q: 1. If f(x, y)=3x' cos y– y sin x– 2.x In y- yln x-4x²y, find ôf ôf d²ƒ _ô²ƒ

A: According to question given thatf(x,y)=3x3 cosy-y2 sinx-2x ln(y)-y ln(x)-4x2y

Q: Use the Mean Value Theorem to show that f(r) = 2x sinh(r – 1) +2" – r has a critical number between…

A:

Q: 7. Find the linear approximation near (2, 0) of f(x, y) = 3x e¯3ªy.

A: To find the linear approximation for the given function.

Q: 4/(A)Find the derivative of f(x, y) = xe + cosxy at the point (2,0) in the direction. дz əz (B)If Z…

A:

Q: 2. Find the interval [a, b] for which the value of the integral (2 + x − x²) dx is a maximum.

A: ∫ab(2 + x -x2 )dx here for get maximum value we have to differentiate the function  so here first…

Q: - Find the Linearization of f (x) = sinx at a 5. Provide your answer as L(x) =? %3D %3D

A:

Q: 8. What is the relationship between a and b so that F(x, y) = (ary, 3ax + bry) is source free?

A: That's easy. Have a great day!!!

Q: 2. For what value of k will x – iky F(x, y) = (x+ y)² + be analytic?

A: Given function is fx,y=x+y2+x-ikyx+iy If it is analytic then it satisfy C-R equation ux=vyuy=-vx

Q: 7. Evaluate the improper integral. -kx e (k: constant)

A: Please refer to the image below.

Q: -2? + 15z - 27 f(z) = 3z2 + 7z + 6 C, I= 3 What value of C would make f(x) continuous at z = 3?

A:

Q: 4. Suppose that F(t) is a differentiable function of one variable. Define the function z(x, y) = e'F…

A: z(x,y) ey F (exy )diff wrt xdzdx = ey F' ex/ye.1/yzx = ey.ex/yyF' (ex/y)and diff wrt ydzdy= ey…

Q: 12. Show that F(x) = sinx – x cos x+2 is an antiderivative of f(x) = x sinx.

A: Given, F(x)=sinx-xcosx+2 To show that the above function is an antiderivative of f(x)=xsins.

Q: What is most nearly the magnitude of the maximum error in the linear interpolation of the polynomial…

A: Given function is yx=cosx

Q: From the differential equati on by eliminating the arbitrary function ffrom xyz = f (x?+y'+z°).

A:

Q: Find the local linear approximation of f(x)= at 2+ x xo = 2, where Ax = x – 2. NOTE: Enter the exact…

A: while finding out the local linear approximation of any function f(x), what we do is to determine…

Q: Consider the For at function y= In(x+1) . what valves" of x is y undefined ?

A: The given function is y=ln (x+1) We know that, for the function ln x, x&gt;0

Q: Find the linear approximation of f(x) = (5 + x)n at x = 0. Use the approximation to estimate the…

A: fx=5+xn at x=0. Differentiating with respect to x, we get f'x=n5+xn-1 Now, f0=5+0n=5n &amp;…

Q: Use the Mean Value Theorem to show that f(r) = 2x sinh(x – 1) + 2" – x %3D has a critical number…

A: Given: We can see that the function is continuous in [0, 1] and differentiable in (0, 1). So, the…

Q: (9) Evaluate the indefinite integral f X+2 dx x² + 4x 2

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Q: Find the linear approximation of f(x) = In x at x = 1 and use it to estimate In(1.19). L(x) =…

A: Here f(x)=lnx at x=1We have to find the linear approximation of f(x) andAlso find the value…

Q: 3.Find the linear approximation to f(x) = cos x at x, = ÷ and use the linear approximation to…

A: We will use formula for linear approximation.

Q: if x 0 f' _(0) f',(0) Is f differentiable at 0? Yes No

A: To find f is differentiable at 0 or not

Q: 2. Use the linear approximation of f(x) = x² ln(x + 1) to estimate (1.01)² ln(2.01).

A: We need to estimate value.

Q: 25. The function g(x) = [", |u| du is not differentiable at x = 0.

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Q: -2 In(x) Consider the function f(x, y) 3y

A:

Q: 14. Give the linear near-minimax approximation for f (x) = sin a on [–1, 1].

A: To determine linear near-minimax approximation for fx=sinx on -1,1 Let the approximation be px=a+bx…

Q: Given the function y"=-6X(x²-ax+4) (x+a)³ (x -1)³ 3. with (X+2)(x-) - analysiS Enclude all maximums…

A: given that y=-x3x+2x-2find the maxima and minima for the given function

Q: 3. Determine if (х — 1)2, if x 1 is differentiable at x = 1.

A: Given  hx=x-12if x≤1x-1if x&gt;1

Q: 4x 28. If R = and errors in x, y, z be 0-001. Show that the maximum relative error at x = y = z = 1…

A:

Q: 1. Use local linear approximation to estimate In (0.99). 2. Find the absolute extremum values of…

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Q: Show that the linearization of f(x) = (1 + x)k at x = 0 is L(x) = 1+ kx.

A: We need a linear approximation formula for f(x).

Q: 3. Suppose that z = f(x, y) is a differentiable function with respect to variables !! x and y and is…

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Q: 2 f(x, y) = x² + 3xy

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Q: if z=0 ne function f(z)= )² if z+0 is differentiable at z= 0 LL

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Q: Integrate from f(x) = x4 from 0 to 1 by (Trapezoidal Rule) with h = 1, h = 0.5, h = 0.25 and…

A: Here, f(x)=x⁴ So, I=  Integrate from f(x) = x⁴ from 0 to 1. Now we can solve by Trapezoidal rule,…

Q: 1. Show that the function x2 – y2 2xy f(x,y) ={ x2 + y? if (x,y) # 0 if (x, y) = 0 is continuous at…

A: If for every ε&gt;0, there exists a δ&gt;0, such that if |x-a|&lt;δ, |y-a|&lt;δ, then the function…

Q: Find the local linear approximation L (x)of the function f (x) = lnx at x = 1 %3D

A: LINEAR APPROXIMATION

Q: 4. Suppose that y = y(x) is a differentiable function which is defined near x = 2, satisfies y(2) =…

A: Given x2+3xy2+y3=9y2=-1

Q: if f(x)=integral t^3+5t^2+6, from 0 to x. what is f''(x)=?

A:

Q: 39. Use Leibniz's Rule to find the value of x that maximizes the value of the integral px+3 1(5 – t)…

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Q: 3. Express the general solution in terms of Bessel functions: z²y" + 4ry' + (x² + 2)y = 0

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 5. What is the most general antiderivative of the function S(2) = z - 2, in other words, what is -…

A: