The interval over which the function f(x) = becomes continuous is %3D x+8 (-3, 0) (-3, 3) (-00, -2)U(-2, ∞) [-2, 0)

Q: Suppose that g is a continuous function. Find the general solution of y" – y = g(t).

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Q: Find the Partial Derivatives of the functions with respect to each variable X+y 6) f(x,y) = -у' -1…

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Q: If f(x, y) = y° cos(x) – x³ In(y), find the second partial derivative ду дх .A ² f ду дх 3x2 -2y…

A: Calculate partial derivatives

Q: Find all first partial derivatives. f(x, y) = 9x° + 4y – 5 9x3 + 4y – 5 f,(x, y) f,(x, v) =

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Q: Find all the second order partial derivatives of g(x,y) = x°y + 5 sin (y) + 4y cos (x). 20x°y - 4y…

A: Given query is to find indicated partial derivative.

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

A: The given function is

Q: Find the linearization of f(x) = (1+ x)20 at x = 0. Use it to approximate (1.001)20.

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Q: Find the Partial Derivatives of the functions with respect to each variable 3) f(xу) - (ху-1);* Ans.…

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Q: Find the value of ∂z/∂x at the point (1, 1, 1) if the equation xy + z3x - 2yz = 0 defines z as a…

A: Given, the equation xy + z3x – 2yz = 0, defines z as a function of two independent variables x and y…

Q: Find all the first and second order partial derivatives of f(x, y) = - Vã+ In y. x3

A: While finding the partial derivative of a multivariable function, if we have to find the partial…

Q: A:- Find the orthogonal trajectories for functions In -1) = - COS X +a y

A: The given family of curves is: lny-1y=-cos x+a ,            where a is an arbitrary constant.

Q: (b) Find the first order partial af and ду af Əx ay for the derivative f(x y) = 2x² sin(x+ )…

A: To find the df/dx of partial first order differential we differentiate function with respect to x…

Q: Determine two functions, defined on the interval  ( − ∞ , ∞ ) , whose Wronskian is given by  W ( f 1…

A: To determine two functions having the prescribed Wronskian and decide on their linear independence

Q: Find the first partial derivatives of at the point (x, y) (1,2). x + y f(x, y) af -(1,2) = 2/3 af…

A: Explanation of the solution is given below...

Q: If f(x,y) = 8-2x3-6xy-3y2, locate the critical points of f and use 2nd derivatives test to find the…

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Q: The partial derivative fx(-1,0) of ƒ(x, y) = xe³ + x² + 1 is equal to −1. Select one: True False

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Q: Find the local linearization of f(x)=x^(2) at 2

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Q: Find the first partial derivatives of 3x - y f(x, y) = 3x + Y at the point (x, y) = (4, 4). af (4,…

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Q: Compute the partial derivative fxxyz for f(x, y, z) = cos(cos(x3 + z2 )) + x2 ln(y2 + z2 ).

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Q: Find the partial derivative fx for the function f(x,y)=√16x+y³ |f₂(x, y) = O f.(x,y)= f₂(x, y) = 1…

A: We have to find derivative

Q: Find the linearization of f(x) = 3+ S" sec(t - 1)dt at .2 END x = -1

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: 6) If y=x² +1+ f dt , prove that y"= 2 - x2

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Q: Find linearizing ( L(x) ) f(x) at x=a . where f(x) = tanx and a = π a) π b)  x - π c) π - x d)…

A: SOLUTION-

Q: Find the first partial derivatives of f(x, y) - 4 - (x - 4)?- (y + 3)? by holding first y, then x,…

A: Partial differentiation of function f(x,y) means differentiating with respect to one variable…

Q: What is the mixed, second order partial derivative of this function. f (x, y) = / 2x² + y²

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Q: How many second partial derivatives does f(a,b,c, d) have?

A: Let p=fa,b,c,d. Note that, for a function of two variables p=fa,b there are four second partial…

Q: If f is a function of x and y such that fxy and fyx are continuous, what is the relationship between…

A: Function: fx and fy are continuous function. Let us choose f(x,y)=x3y3+πxy Here fx=3x2y3+πy…

Q: Find all the second partial derivatives forf (x, y) = x³y5 + 2x*y.

A: All the solutions are given below.

Q: Find all first partial derivatives, and evaluate each at the given point. f(x,y,z) = xycosxz ,…

A: Here given as fx,y,z=xycos xz

Q: Find all critical points of f and use the second partial derivative test to determine if there exist…

A: find critical points by putting fx and fy = 0

Q: x-1, -1 sx< 0 0<x <1 x = 1 1<x< 2 2 <x<3 2r, f(x) = 1, -2r + 4, 0, Is f(x) is continuous at x = 1…

A: Given: f(x)=x2−1,−1≤x&lt;02x,0&lt;x&lt;11,x=1−2x+4,1&lt;x&lt;20,2&lt;x&lt;3 A function f(x) is…

Q: 1. Integrate the function f(x, y) = x – y over the triangle T with vertices (0,0), (1,0), and (1,2).

A: Given triangular region is bound by the vertices 0,0, 1,0 and 1,2. The sides of the given triangular…

Q: Find all second order partial derivatives of f(x, y) = 6x²e3y

A: Consider the function fx,y=6x2e3y

Q: Find the second-order partial derivative fxx ( x , y ) of the function f ( x , y ) = x 4 y 4 - sqrt…

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Q: Find the first partial derivatives of the funct f(x, y) = x8 + 7xy5 fx(x, y) =

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Q: Find all the first and second order partial derivatives of f(x, y) = -4 sin(2x + y) + 1 cos(x – y).

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Q: Use the Chain Rule to calculate the partial derivative. Express the answer in terms of the…

A: Given

Q: What can you conclude about a real function f(x,y) that has continuous partial derivatives at a…

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Q: Find the partial derivative fx for the function f(x,y)=√16x+y³ f(x,y)= fx(x,y)= Of(x,y)= f₂(x, y) =…

A: We need to find partial derivative.

Q: Both first partial derivatives of the function f(x,y) are zero at the given points. Use the…

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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: Compute f -f(g(x)), where f(x) = x° and g(x) = 8x – 1. dx -f(g(x)) =| dx

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Q: find a point c satisfying the conclusion of the MVT for the given function and interval y = x−1, [2,…

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Q: )The value of partial derivative f-(1,-1,2) of the function f(x, y, 2) - x - Vy2 + z? is: %3D

A: Given function f(x,y,z)=x-y2+z2

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 partial derivative of fy for the function * 3 f (x, y) = (3x² + y²) ³ 3x² (3x² + y²)²…

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Q: Find the linearization of ƒ(x) = 2x at x = 0. Then round its coefficients to two decimal places.

A: Given function is,

Q: Find the first partial derivatives of 3x – 2y f(x, y) = at the point (x, y) = (1,4). 3x + 2y af…

A: I am going to solve the given problem by using some simple calculus to get the required result of…