Sketch the domain of the f(x, y) = ln((x² + x² – 4)(16 – x² – y²)) |

Q: is The antiderivative of the function f(x) =. 2x а. 2 In x + c b. 1

A: Givenf(x)=12xAntiderivative of f(x)=?Antiderivative is nothing but integral.

Q: Consider the function f(x) = 2x10 + 7x° – 6x² – 9. Enter the antiderivative of f(x) -

A: To find The anti derivative of f(x).

Q: Q2 (A) At what points f(x, y, z) in which the function f(x, y, z) = -√x²+y² is Z- continuous?

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Q: Find the value of c that satisfies the MVT of f(x) = 1+x + x2 on (0,2).

A:

Q: Differentiate fx) with respect to g(x) of yx= xsiny

A: To find the derivative

Q: Find f, fy. f- f(x.y.z) = 3x - 4y 2. 2 +z?

A:

Q: Find and classify the critical points of f(x, y) = 6xy – 4x³ – 3y?

A: According to our guidelines, we can answer only one question or three subparts of a question. other…

Q: Find the linear approximation of f(x) = e(a) at a = 1.

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Q: dy Prove that dx of x2 +2x is f'(x)=2x + 2

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Q: Find the linearization L(x) of f (x) = tan x at a =

A:

Q: Find the linearization of the function f (x) = x' at x = 1. a ab Va |a| sin (a) 7 х-6 L (x) Using…

A: Given a function,

Q: dy + ydx %3D 3x²y?dx,

A: Given differential equation is bernaulli's differential equation.,  and we can solve it by reducing…

Q: Let f(x,y)=3x2-2xy+y2-8y  Find the absolute extrema over [0,1]x[0,2]

A: Consider the given function fx,y=3x2-2xy+y2-8y First, find the partial derivatives of the function…

Q: 2. Find frxz for f(x, y,z)= z² e³xy

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Q: find ∇f at the given point. ƒ(x, y, z) = (x2 + y2 + z2)^(-1/2) + ln (xyz), (-1, 2, -2)

A: Given function is  Firstly, we find all first order partial derivatives of f

Q: Find the linearization L(x) of f(x) at x = a. f(x) = Vx +15, a =7 %3D L(x) =

A: Givne that fx=x2+15, a=7To find L(x)

Q: Find the linearization L(x) of f(x) = cot(x) at x = π/4.

A:

Q: B1. Verify fy = fx for the function f(x,y) = ln(2x- 3y). %3D xy

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Q: Let f(x,y)=3x2-2xy+y2-8y  Find the absolute extrema over [0,1]x[0,2].

A: We have f(x, y)=3x2-2xy+y2-8y find critical points ∂f∂x=6x-2y=0 ... (1)∂f∂y=-2x+2y-8=0  ...(2)solve…

Q: For the function f(x, y) = (cos x)ey +v 1 + x + y. %3D Show the process of using the linearization…

A:

Q: Consider the function f(x) = 2x³ + 71° – 8z2 – 8. Enter the antiderivative of f(x) + C

A: To find the antiderivative means integration of the given function

Q: of For the function f(x.y) = In (x + 6y), find- of and dy

A: It is partial derivative so when we differentiate with respect to one variable consider other…

Q: d) The function +(xy)-r*r2y) exp G 18xy is homogencous in of degree X and

A: The given function is: f(x,y)=(x2+2y)e2xy+8xy...(1) The function f(x,y) is said to be homogeneous…

Q: Differentiate the function. y=In(x²+e' y=In(x²+ean x)

A:

Q: Let f(x, y) = ln (3x + y2). Show that fxy = fyx

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Q: Find the linearization L(x)of f(x)at x = a where f(x) = Vx² + 9 at a = –4

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Q: Find the linearization L(x) of f(x) = cot x at x = 4

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Q: Let f(x)=6x2+1f(x)=6x2+1.Enter an antiderivative of f(x) . . .

A: The given function is,

Q: Find the linearization L(x) of f(x) = cot x at x = 4 %3D -

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Q: Find the orthogonal trajectories of the family of x² – y? = cx = CX -

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Q: Find the linearization of the function f (x) = x6 at x = 1. L (x) = Using this linearlization, f…

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Q: lim, f(x)= 0, then | f(x)dx diverges

A: Statement:  limx→∞ f(x)≠0,  then ∫1∞ f(x) dx   diverges.

Q: Supposed that z is defined implicitly as a function of x and y by the equation x2 + y2 +z2 = 4. Find…

A: The given data is: x2+y2+z2=4 To find the value of dzdx

Q: Q, Frd the donain of H fallowing function: fa) = 5x -3x-4

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Q: Let f(x,y)=x°-4y where 0<x <1 and 0sysl. Find the minimam of value of f(x,y).

A: Answer

Q: Verify Young's Theorem f(x,y) = e(2x+y) In(xy)

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Q: Let f (x) = 2x* – 3x3 + 5x + 1. Find the value of at x = 1. %3D df-1 - dx

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Q: Consider the function f(x) = 6x' + 8x5 – 10x³ – 6. %3D - Enter the general antiderivative of f(x)

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Q: Find the linear approximation of f(x) = Vx +I at a = 1.

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Q: Find the linear approximation of f(x) = Vx at xo = 27.

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Q: Find the most general antiderivative of f(x) = -10x – (1 – x²)-1/2, where -1< x < 1.

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Q: Find the linearization L(x) of the function at a. f(x) = sin(x), a = %3D L(x) = %3D

A:

Q: Find and sketch the domain of the function. f(x, y, z) = ln(64 − 4x2 − 16y2 − z2)

A: Given function is      f(x,y,z) = ln(64-4x2-16y2-z2) We have to find the domain of this function.

Q: Find ý of the function x2 - e2x+3y - In(xy) = 0. %3D

A: Consider x2-e2x+3y-ln(xy3)=0We differentiate it implicity, we…

Q: Find the linear approximation of f(x)=(1+x)3 at x=0. Using this approximation to estimate (1.01)3…

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Q: Consider the function f(x) = 4x° + 7x® – 9z³ – 10. %3D Enter the general antiderivative of f(æ)

A:

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.