A function y(t) satisfies th

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

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Q: (1) Let g(x) :| f(t) dt. What is g'(x)? a

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

A: To find the derivative

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: | f(t) dt = x*e* e + a

A: This question is based on integration.

Q: Find the minimum and maximum of A over a particular interval [0,6]. A(x) = f(t) dt

A: The solution is given below in the next step: I

Q: Dicuss the contiunity of the function f (x,y) = ln  (x+y-1)

A: We know: 1) Polynomials are continuous everywhere. That is, at every point in real number 2) Sum of…

Q: Find the linearization of f(x) = 9 – dt at x = 1. 2+t

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Q: Find the linearization L(x)of the function at a .

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

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Q: d Use the chain rule to calculate f(x), if f(x) dx, dt. -x12 f(x) =

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Q: 4) Determine the function F(x)=[ƒ(1)dt, where ƒ(x)=sgn(x-x²) for xe[-1,2]. -1

A: f(x) is discontinuous but F(x) is continuous

Q: Find the linearization L(x) of the function at a. f(x) = Vx, a = 25 L(x) =

A: The solution of the problem is given in the next step.

Q: Find the linear approximation L (x) to ƒ (x) = xcosx at a = T.

A: Given that, f(x) = x cosx and we have to find linear approximation L(x) at a = π

Q: 1losamlov ç5x3-1 Differentiate the function g(x) = [°*¯'sin t dt. -3

A: We have to differentiate the given function.

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

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

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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: x and y are functions of a third variable t. If √√x + √= 5 and dt = 2, find when = dt 1

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Q: Find the linearization L(x)of the function at a .

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

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Q: Let f(x)= I Determine f'(x). sin² (³+1) dt, x= [1,1].

A: Given: f(x)=∫-xx2sin2(t3+1)dt

Q: If f(x) t° dt then f'(x) = %3D

A: Given:-f(x)=∫-2x2t3dtUsing fundamental theorem of…

Q: Find the linearization f(x) = √x, L(x) = L(x) of the function at a. a=4

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Q: 4. F(x) = (1- t) dt %3D 4

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Q: Find the linearization L(x) of f(x) at x=a. f(x)=x/2x+9 a=0

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

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Q: III. Let g be defined by the equation g(x) = dt t²-1 Show that g'(x) = secx.

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

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Q: Show  that the function Z =1/2(eysinx - e-ySin(x) satisfies the La Place’s equation  =0

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Q: 2. Find and classify all the extrema of the function f (x, y) = 4xye e-(x²+y²)/4

A: The given function is:  f(x,y) = 4xy e-(x^2 +y^2)/4

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

A: To find the linearization of the following function

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

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

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: A) Find the linearization of the function at the given point. f (x, y) = 1+ y ln (6 – xy), at (5, 1)…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Find the linearization L(x) of the function at a. f(x) = Va, a = -8 L(x) =

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

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Q: Find the differential dy of each function: a) f(x) = 2x^1/3 - 3x^1/2 b) f(x) = ( x^2 +1) / (x+1)

A: we will find the derivative of given function using basic differentiation rules.

Q: x2 ) Find f(1) if / f(t) dt = x° – x* + 2x² – 2 , x>1.

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Q: Find the linearization L(x) of the function at a. f(x)= sin(x), a= π\4

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Q: Find the linearization L(x) of the function at a. п f(x) = sin(x), a = 6 L(x) =

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Q: FInd the linearization of the function given below at the specified point. f(x) = 5 In(x) at a = 1…

A: f(x)=5ln(x)  at x=1

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

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Q: Find the linearization of f (x) = xe¯* at a = 0. (Hint: Remember thne product rule.)

A: Given : fx = xe-x2

Q: (b). Examine the behavior of e*+iy as x → -.

A: Euler's formula states that for any real number x  Any complex number z = x + iy,  can be written…

Q: 13. Prove that the function 2x 1 dt t F(x) is a constant on the interval (0, ∞ )

A: The student has specifically asked for the solution to Question-13. Hence, that question is solved…