Find the linearizationsof the following functions at x = 0. ex

Q: Obtain the derivative of any of the following functions: A) f(x) = 3cotg²3x B) f(x) = 6cos7(3x2 - 1)

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Calculate the derivative of the following functions

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Q: Find the derivative of the function. f(u) = 8.u10 +14. 4" – 24. n u -9. uT – 4 eT + u2

A: Note the formula of derivative d/du (constant) = 0 d/du (u^n) = n.u^(n-1) d/du (a^u) = a^u . ln(a).…

Q: find all possible functions with the givenderivative. y' = √θ

A: We first separate the variables

Q: Find linearization of the function f(x) = Vx + 3 at a = 1 and use it to approximate V3.98

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Q: use the chain rule to find the derivative of the following function: f(x)=10cos^3(4x)

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Q: Find the derivative of the function. g(u) =√u+1(1 − 5u2)7

A: Write g(u) using exponent

Q: y=t In(\F)

A: We need to evaluate the derivative of the following function  y = t lnt

Q: Find the derivative of the following function F(x)=(from x^3 to x^4)∫(2t−1)^3dt

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Q: Consider the function f(x)= sqrt(x). Approximate sqrt(25.2) using the linearization of f(x) at a=25.

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Q: Find the linearization L(x) to the function f(x)= Vx+4 at x =4, then use the linearization to…

A: linearlization of f(x) at x=a is  L(x) = f(a) + (x-a)f'a)

Q: Find the derivative of the following functions. F(x) = √²** 1. √/20162). 2. G(x) = 3. H(x) = L √t³ +…

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Q: Find the derivative of the function. f(e) = (3t + 18)2/3 2 f (e) = 3/3t + 18

A: Topic:- derivatives

Q: Find the derivative of the following function F(æ) = [ (2t – 1)³ dt - 23 using the Fundamental…

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

A: Consider the given information. fx=x3,a=-8 The linearization of the function is defined as,…

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

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Q: Find the linearization of the function F(X) =sqrt (x+3) at a= 1 and use it to approximate the…

A: Therefore linearization at a = 1 is,

Q: Find the derivative of function defined as follows. p(z) = z(6z + 1)4/3

A: Given function is pz=z6z+143. To find the derivative of the function. Solution: Power rule of…

Q: Find the linearization of the function given below at the specified point. f(x) 4 In(x) at a = 1…

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Q: 1. Find the derivative of the following function. 4. f(w) = 3D 6w* +3w +2w f'(w) = %3D

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

Q: Let L(x) be the linearization of the cube root function at x=8. When using L(x) to approximate the…

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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 linearization L(x) of f(x) = cot(x) at x = π/4.

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Q: 17 3. f(a) = 2a3 11a %3D 8a2

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Q: a) Calculate the derivative of f Cx) by first expanding and Simplifyıng the function fCx)=(2-3x) 2

A: Given,           fx=2-3x2

Q: Find the linearization L(x) of the function f(x)=x^3/4 at x=1

A: Given, f(x)= x³/4 x=1 Therefore, f(x=1)=1³/4 f(x=1)=1/4

Q: Find the linearization of the function given below at the specified point. f(x) 2 In(x) at a = 1…

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Q: Find the linearization of the function given below at the specified p f(x) = 4 In(x) at a = 1 L(x) =…

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Q: Q1. Integrate the following functions with respect to x: y = 3x2 (1+x³)*

A: Explanation of the answer is as follows

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

A: Given,

Q: Compute the derivative of the following function. f(x) = 3x e 3x f'(x) = O

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Q: (a) Find the linearization of the function f(x) =x+ at x= a=1

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

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Q: Find the first and second order derivatives of the following function: In(Tx) q(x) = + (Tx +…

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Q: Ax) = Vã Vx = /x хх e

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Q: Find the linearization L(æ) of the function at a. f(z) = V7, a = -8 L(x)

A: We can find the linearization as below.

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: Find the linearization L(X) of the function at a. f(x) = Vx, a = 16 L(x) =

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Q: Find the derivative of the given function.   f(z)=−1/z^4.1

A: Recall the rule for differentiating powers when the exponent is a positive integer

Q: Find the linearization of the function at a. 1. f(x) = x^4 + 3x^2, a = -1 2. f(x) = sin x, a =…

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Q: Find the derivative of the function. h(t) = (t + 5)2/3(2t² – 1)3 2( 22 – 1)2[202² + 90t – 1] h'(t) =…

A: In your solution please replace x to t

Q: (b) If g(x) = [,! 1 dt, find g'(x) 4+t2

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Q: Use this definition to compute the derivative of the function at the given value. h(x) = 5x² + 1 X =…

A: We have to find derivative

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: 4. Find the linearization L of the function f(x)=Vx+3 at a = 1 and use it to approximate f(x) =…

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Q: Compute the derivative of the following function. f(x) = 2 e 2x f'(x) =L %3D

A: To find the derivative

Q: f (x) = Vx³ – 3x7 + 2

A: We can find the derivative as below

Q: asin (bvx3 f(x) = c2x + In(kx) if a = 11.23, b= 3, c = 2, and k = 5 at x=1 using CDA with Ax =0.06.

A: We have to evaluate the second derivative of  fx=asinbx3c2x+lnkx at x=1 using central difference…

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

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Q: Find the linearization L(x) of the function at a. f(x) = Vx, a = 16

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.