Find the linearization L(x) of the function f(x)=x to the 4th power +2x to the 2nd power +1 at x=2. Answer: L(x)=

Q: find a linearization at a suitably chosen integernear a at which the given function and its…

A: Given that the function is  f(x)= e-x, a= -0.1 To determine the linearization for the function.  The…

Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: Given: fx=2x−1x2+3x2+1, and gx=x2+872−3x25 To check whether: f'x=4x2x2−1+2xx2+3−2xx2+12x2−1x2+3x2+1,…

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

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Q: Find a solution of by fixed point method for f(x)=x^3+x-1=0 ?

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Q: Find a point c satisfying the MVT for the given function and interval. 2 y = x3 [0,8]

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Q: Determine the equation of the quartic function with the following characteristics x-intercepts at x…

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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 the function at a . f(x) = x 4 + 3 x2    , a = -1

A: We know that ,The linearization of the function at v=ais given by fa+f'ax-a

Q: Find the linearization of y = at x = 16.

A:

Q: At which iteration shows that the root of a nonlinear equation is Xr = 1.2017 when a = 2 and b = -1…

A: f(x) = 3x^3-5.12x^2+3.4x-1.9 we have a=2, b=-1 then f(a)f(b)<0 so we have root between -1 and 2

Q: For the function f(x) = -2x + 3x2 + 12x 1. Find all the critical points of the function f(x). 2.…

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Q: 2. Identify the iterative function f(x) = x3 – 9x2 – 6 if initial approximation x, = 2.25

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

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Q: Find the critical point for the function f(x)=-x² +3x+1

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Q: Is ƒ(x, y) = x2 - xy + y2 - 3 more sensitive to changes in x or to changes in y when it is near the…

A: Partial derivative of f w.r.t a variable is the indicator of the sensitivity of f towards that…

Q: Find the linearisation of f(x) = 4√x at a = 16. Use this to estimate 4√ 15

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Q: 5 - x f(x) = x² – 6x + 30

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Q: Use variation of parameters to find a particular solution of the ODE y" – y = 2e".

A: Given differential equation is  y''-y=2ex we have to find  the particular solution of this…

Q: Find the linear approximation of the function at the given point. ffx y)=-9x2-6y2+ 6 at (6,-10)…

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Q: Find the Quadratic approximation of the function at the given value f(x) = 1n(x + 1)     near a = 0

A: Given  The function is f(x) = ln(x + 1)     near a = 0 .   Formula for Quadratic approximation :-…

Q: Find the linearization L(x)  of the function f(x)=x^3/4  at x=16

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Q: Show that the function f(x) = e^-x^2/2 has a relative maximum at x = 0.

A: Given function is: fx=e-x22 Differentiating f(x) with respect to x we get, f'x=e-x22×-2x2f'x=-xe-x22…

Q: 1 Find the linearization of the function f(x) = 5x+4 atz-1.

A: The given function fx=15x+4 at x=-1

Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: for f'(x) see 2nd and 3rd step. for g'(x) see 4th and 5th step.

Q: Find the orthogonal trajectories of x² + y² – 2cy = 0

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Q: Find the critical numbers of the function.…

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Q: -2 Write the equation for the linear approximation of g(x) = In(vr² +5) based at x =-2. Justify your…

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Q: 8. If f(x) = 4 sin x + 6 and g(x) = 3x + 5, what is the maximum value of f(g(x))?

A: Solution is given below

Q: . (a) Find the critical numbers of . f (x) = x 4 (x -1 )3(b) What does the Second Derivative Test…

A: (a) We say that x=c is a critical point of the function fx if fc exists and if either of the…

Q: 11. If f(r) = rª and g(r) = r³, then f' (x) = 4x³ and gʻ(x) = 3x². The Chain Rule multiplies…

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Q: Find the linearization of the function at x = 1.* f (x) 2x - 3x + 7 %3D

A: From the given problem:   fx=2x3-3x+7 ; x=1   As we know that the expression for linear…

Q: find a linearization at a suitably chosen integernear a at which the given function and its…

A: The nearest integer to a=-0.9 is -1 because at this point, we can easily find the function's value…

Q: Find the Linearization L(x) of y= (3+ x)-1/2 at a = 1. L(x) =

A: To find the Linearization.

Q: find a linearization at a suitably chosen integer near a at which the given function and its…

A: (1)Given:

Q: Find the linearization of y=2^x at a=0

A: use derivative to find the Linearization of y

Q: Find the linearization of ƒ(x) = √1 + x at x = 0

A: Consider the following function: fx=1+x Differentiate fx with respect to x: ddxfx=ddx1+xf'x=121+x

Q: Let f(x) = 18xe - 1s. (a) f'(x) (b) Solve f'(x) = 0 to determine the critical values of f.

A: Recall: (uv)'=u'v+v'u

Q: Find the linearization of the function at x = 1. * f (x) = 2x³ - 3x + 7 O y = 6 + 1(x - 3) O y = 6 +…

A: Given, fx=2x3-3x+7

Q: Find the linearization of the function f(x) = 1/(9x+8) at x = -1.

A: Topic : function

Q: The function f(x)=2x^3−42x^2+270x+8has derivative f′(x)=6x^2-84x+270. f(x) has one local minimum…

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Q: Use the linear approximation (1 + x)k = 1 + kx to find anapproximation for the function ƒ(x) for…

A: It is known by linear approximation that 1+xk=1+kx for the values of x near 0. The given function is…

Q: 8. (a) For f(x) = Vx, give the linearization at a = 25. (b) Use your answer from part a to approxi-…

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Q: Use the gradient descent method in the equation f=2(x_1)^2 + (x_2)^2 with the starting point (1,2)…

A: Given : equation                fx1, x2=2x12+x22 with starting point 1, 2 Use gradient descent in…

Q: What is f (2) if the linearization of f (x) at a = 2 is L(x) = 2x + 4?

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Q: Find the linearization L(x) of y=e10xln(x) at a=1

A: y=e10xln(x)  The linearization L(x) of a function f(x) at x = a is, Now  Now differentiating given…

Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: Using the product rule of natural logarithm, it can be written that ln(ab)=ln(a)+ln(b) . Using the…

Q: If f(x)=x* and g(x)= x³, then f'(x) = 4x³ and g'(x) = 3x². The Chain Rule multiplies derivatives to…

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Q: Find the linearization of the function at the given point f(x,y)=-10x+8y-9 at (-7,4). A.…

A: I have appended the formula used in the solution part

Q: Given the function y = 8e-²x² + 7 sec² 5x – 4 ln x³, find y'. Solution: y' = 4(3)x² x³3 +8(−4x)e-²x²…

A: We will find the y' of the given function in the following step.