Let h(x)=f(x)/g(x). If f(x)=−cos(x) and g(x)=4x2+2x−3, what is h′(x)?

Q: - (4y" + fy) = -A with y(-1) = -2, y(-1) = 1, y"(-1) = 0 Use x1 = y, x2 = y', and x3 = y". x + with…

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Q: Minimize f(x) = x² + 54 ; using Interval halving method for 2 ≤ x ≤ 6. E= 10-³

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Q: For f(x) = e+cos(x), calculate f (0) by using the chain rule!

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Q: Find the general antiderivative of f(x) = + C - 5x¹ x² +6√x

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Q: 1.If f(x,y) cos(4x-2y)+ln(y² -2x) find £xy fx fxy,

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Q: Find the length of the curve e^x / 2 + e^-x /2 between x=0 and x=1

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Q: dz b- Solve by chain rule to determine dx z = x²y* -2y , y = sin(x²)

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Q: Find all antiderivatives of function:  f (x) = e3x

A: Given- fx=e3x To Find- The antiderivative of the above expression.

Q: If U and V are positive constants, find all critical points of F(t) = Ue' + Vet.

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Q: 1. Find the critical points of the function 2 f(x, y) = x² + 4xy.

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Given f(X)=−xe^x whats the root of the linearization of f(x) at a = 4.3?

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Q: Let f(x) 18xe 18 %3D (a) f'(x) : (b) Solve f'(x) 0 to determine the critical values of f.

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Q: D. Fina the total differential of the function xye¬(x²+y*),

A: Given: f(x,y)=xye-x2+y2

Q: 3. Find the linearization L(x) of the function at a. F(x) = Vx, a = 4

A: Use the formula for the linearization of a function about any point.

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

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Q: Find all antiderivatives of function:  f (x) = e-3x

A: Consider the given function. fx=e-3x We have to find  I=∫e-3x dx   Substitute -3x=u -3dx=dudx=-du3

Q: et f(x) = x3- 3x2-1,  x ≥ 2. Find the value of df-1/dx at the point x = -1.

A: Let f(x) = x3- 3x2-1,  x ≥ 2. Find the value of df-1/dx at the point x = -1.

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 most general antiderivative of the functions: 1)f(X)= 2secxtanx-3sinx 2)f(X)=…

A: (1) Given, f(x) = 2secxtanx-3sinx  ∫f(x)dx = ∫(2secxtanx-3sinx )dx               = ∫(2secxtanx)dx -…

Q: Where a is a constant, then a is equal to:

A: Since, the joint probability distribution function is given .. Here, wa want to the value of 'a'

Q: find the antiderivative of the function t(x)=5/x^2

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Q: Suppose we have a function z = a > 0. f(x, y) = -x² – y² + a(x +y) where a is exogenous and a.…

A: The given equation is z=fx,y=−x2−y2+ax+y Where a is exogenous and a > 0.

Q: In Exercises, find the first and second derivatives.5. y = 4x3/ 3 - x + 2ex        6. y = x3/3 +…

A: To find the first and second derivative: y=43x3-x+2ex Solution: Here, y=43x3-x+2ex Differentiating…

Q: Find the antiderivative of f(x). f(x) = 3e6x+ sec2(x) +x3

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Q: Find the general solution for y' = x – 4xy using an integrating factor.

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Q: Let y = 4x“. Find the change in y, Ay when x = 3 and Ax Find the differential dy when x = 3 and dæ =…

A: Given that: y=4x2, x=3 and ∆x=0.4

Q: Eliminate the arbitrary constants y Iny = C,e "+ C, X-

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Q: Find all stationary (critical) points of the function g(x, y) = x³ + y³ + 3x² + 3y + 3x + 3xy +1.

A: First calculate the partial derivatives, gx, gy  for g(x,y) . Solve the equations, gx=0 , gy=0…

Q: What is local linear approximation for f(x)= e*" -6* near x = 0? Note: Must show answer is equal to…

A: Hey, since there are multiple subpart posted, we will answer the first question. If you want any…

Q: Find the antiderivative of f(x)=e^(-1/x)/x^2

A: The answer of the above question is given below.

Q: - The antiderivative of f (x) =; whose graph passes through the point (C 3+5sinx+. +3cosx 1(. 5 1(.…

A: Introduction :

Q: Find the most general antiderivative of f(x) 2x-1+x.

A: Given,            f(x) = 2x2 - 1 + x-2

Q: a.) If     f(x) dx   = 4x9 − 8x6 + C, find f(x). f(x) =

A: Given: ∫fxdx=4x9-8x6+c                                          ..1 for finding fx, we differentiate…

Q: Let y = 3x² + 8x + 3. Find the differential dy when x = Find the differential dy when x = 2 and da 2…

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Q: 4 + 9x is x2 The antiderivative of the function f(x) %3D

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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 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: Let y = 3x². Find the change in y, Ay Ay when x when x = = 5 and Ax = 0.3 Find the differential dy…

A: Given f(x)= 3x2

Q: Find the particular antiderivative of the function f(x) = e"(2" – 1) whose graph passes through the…

A: Integration

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 absolute maximum and minimum values of f(x) = e * – 3x on [0,5].

A: f(x)=ex-3x Take derivative wrt to x f'(x)= ex-3

Q: 1. Determine the nature of the stable points of the function f (x, y) = x²y – x² – 3xy + 3x + 2y –…

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Q: 16. If x x y and y x z, then how is x proportionally related to z?

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Q: Find an antiderivative of the function f(x)=e2x.

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Q: Let y = 3x² + 8x + 3. Find the differential dy when x = 1 and dx = 0.2 Find the differential dy when…

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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: Find L(x) (Linearization function), given f(x) = ev2x at the value a = 2.

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Q: Find f(3,4) for f (x, y) = ln(x + Vx² + y²).

A: We have to find out the derivative

Q: Find the linearization L(x) of the function at a. f(x) = e5x, a = 0 %3D L(x) 1 + 5x

A: f(x)=e5x point a=0