The f(x) 6x2 -5x-4 2x2 +x is discontinuous %3D at x = -1/2. By redefine = w , then f will be continuous at x = -1/2. Where w = 11 2 11 11 2 11 3 11

Q: Find the value of c that satisfies the MVT of f(x) = 1+x + x2 on (0,2).

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

A: Given function is

Q: Find the linearization L(x) at x= a. f(x) = - 2x +3x+ 1 a = -3 L(x) =]

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Q: Calculate the linearization L of f(x) : 5e* at x = 1. x2 Express your answer in terms of e and x.

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Q: Let f(x, y) = - 4xy² – 2x² + 8y². Find and classify the critical points of f.

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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: Define h(2) in a way that extends h(t) = (t2 + 3t - 10)/(t - 2) to be continuous at t = 2.

A: Consider the given the function,

Q: Consider the function f(x, y) = 2x4 +y² – x² – 2y. The critical points of f -

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Q: on f(x, y) = 3x + 9y subject to th %3D

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Q: sinkx) x 0

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Q: Suppose that a continuous function g satisfies: g(x)dx = 42 and g(2x)dx = 3. %3D 2 Find æg(3x²)dx.

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

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Q: Consider the function f(x) = 648x¬² + x³. Taking the initial point as x = 6 and increment value as…

A: Here, fx=648x2+x3 Take x0=6 and △=1 Iteration 1) k=0 of xk Now, xk+1=xk+2k△ Here, x0=6…

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: If L(x)=mx+b is the linearization of f(x) 2x-x +3 at x-1, then m3 Using L to approximate 2(1.01)…

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Q: dy + ydx %3D 3x²y?dx,

A: Given differential equation is bernaulli's differential equation.,  and we can solve it by reducing…

Q: Find a cubic function f(x) = ax3 + bx2 + cx + d that has a local maximum value of 2 at x = −2 and a…

A: f(x) = ax3 + bx2 + cx + d f(x) = 3ax2 + 2bx + c Now, f(x) = 0  at x = -2, 1 Hence , roots of above…

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

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Q: Find the lineari zation L (x) of the fuction at a. f) = x'+2x

A: In the given question we have to find linearization of function.

Q: -Q3/As the function f(x,y) = at (-1,2) xy 1 + x² + y² is Continuous

A: Here we have to check the continuity of the function at the given point.

Q: Show that f(x) = 2a + 3b is continuous, where a and b are constants

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Q: Find the linear approximation to f(x) = at a = 4.

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Q: d) The function +(xy)-r*r2y) exp G 18xy is homogencous in of degree X and

A: The given function is: f(x,y)=(x2+2y)e2xy+8xy...(1) The function f(x,y) is said to be homogeneous…

Q: Find the best quadratic approximation to f on the interval [ 0, 1].                     f(x) = x3

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Q: attached

A: Linearization of f(x) at x=a is given by

Q: Determine whether the function 2х + 1 f(x) %3D 2r2 2x2 – x – 1 is continuous: a. at 2; b. at 1.

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Q: Let f(x) = 6x²(x – 1) + 10. %3D Find the critical points c that correspond to local minima.

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Q: Prove that f(x) = other than the graphing method. x² – 1 is continuous at c = 0 by any method |

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Q: For what value of x does the funciton g(x)= (1/3)x^3-2x^2 strictly convex?

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Q: ) For what value of a is fx² -1 x<3 S(x)= { |2ax x23 Continuous at every x?

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Q: what is the antiderivative F(x) of f(X) = 3x1/2-x-1 that satisfies the condition  F(4)= 0? A,…

A: The given function is fx=3x12-x-1 that satisfies the condition F4=0. Find the antiderivative of Fx.

Q: Find the local linear approximation L (x) of the function f(x) = 5 – x² at =2.

A: To find the linear approximation of given function.

Q: Find the linearization of the function f (x) = x° at z = 1.

A: Given, f(x)=x6

Q: Suppose that ƒ(x) = x2 and g(x) = | x | . Then thecompositions( ƒ ∘ g)(x) = | x | 2 = x2 and (g ∘…

A: Given: The composite of the two functions are given as,

Q: Find the linearization L(x) at x = a. f(x) = - 4x3 - 3x+1 a = - 3 L(x) =

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Q: Find a point c satisfying the conclusion of the MVT for the function y(x) = 16/x on the interval [0,…

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Q: Use the comparison theorem with f(x) = = 1 √x r∞ 1 •√₂ √I-1 to show that is divergent.

A: Solution is given below:

Q: Find the values of k in f(x)=x^2-kx such that the line y=5x-4 is tangent to the function.

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Q: Showthat fo= x| is Continuous evalyuhore- 1x1+1

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Q: Use the linearization of f(x) 1 at x = 4 to approximate f(4.3) . - f(x) =

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Q: Find the linear approximation L(x)of f(x)=x^4 at the point a = −5 L(x)=

A: Given that f(x) = x4 We have to find the linear approximation L(x) of f(x)=x4 at the point a= -5.

Q: Where does the function f(x,y)=3 − 10x + 12y − 5x2 − 6y2 have a critical point?

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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 the linearisation l(x) of f(x) = √1+x3 at x=2 and use this to estimate f(2.05)

A: Given function is: fx=1+x3 At x0=2 So the linear approximation is: Lx≈fx0+f'x0x-x0…

Q: Solve the following optimization problem by using Lagrange method: Maximize f(x,x;)=2x, + x, – 3x²…

A: Lagrange Multiplier Method:- This method is used to optimize a function on a region that contained…

Q: Find the linearization L(x) of f(x) at x = a. f(x) = a = 0 4x +3

A: topic - linearization of a function

Q: If the function f (x) = } 6x – 4, x5 is continuous at x =5, then the value of k is %3D %3D O a. 10 O…

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Q: Q3: Find fxx of the function f (x, y, z) = -In/1-x2 - y2 – z2 %3D

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Q: Find ý of the function x2 - e2x+3y - In(xy) = 0. %3D

A: Consider x2-e2x+3y-ln(xy3)=0We differentiate it implicity, we…