## Linearization Questions and Answers

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Given f(x) = 2x^2 + 3x + 2, look the linearization of f at a = 2. a. Compare l(x) and f(x) for x = 2.02. b. Compare y and dy when x changes from 2 to 2.01.

Find the linearization of f(x) = xe^{-x^2} at a = 0. a. L(x) = x b. L(x) = -x c. L(x) = 1 d. L(x) = 0

Calculate the value of the given function by using the indicated number of terms of the appropriate series. Round to seven decimal places. sqrt[3]{0.85} (3 terms)

Find the linearization of the function f(x) = sin(x) and use it to estimate sin(5\cdot). What is the percentage error of your approximation?

We are given that f(3) = 4, f'(3) = 8, f"(3) = 11. Use this information to approximate f(3.15). Is f increasing at x = 3? Justify your answer.

Linearise the non linear d.e : h'=(qi-b*h^{1/2})/(\pi(2*r*h-h^2) about h(0) using taylor series expansion, just first two terms of taylor series.

Use local linearization to find the estimate of f(-0.9), given f(x) = 2x^3 + 5x.

Find the linearization, L(x,y), of f(x,y) = \sqrt(7 - x^2 - 2y^2) at the point P(2,-1).

Use Linear Approximation to estimate the change \Delta f = f(a + \Delta x, b + \Delta y) - f(a,b) in f when

Use Linear Approximation to estimate the value of f(-1.1, 1.9) when f(-1, 2) = 2 and f_(x)(-1,2) = -2. f_(y)(-1, 2) = 1.

Find the linearization, L(x,y) of the function f(x,y) = tan^(-1) (x + 8y) at the point (9,-1).

a) Use a linear approximation to estimate 1/(103). b) Use the Intermediate Value Theorem (IVT) to show that sin (x) = x - 1 has a solution in the interval [0, pi].

Find the linearization L(x,y) of the function f(x,y) = sqrt(54-4x^2-1y^2) at (3,3).

Find the linearization of the function f(x,y) = \sqrt{39 - 5x^2 - 3y^2} at the point (-2,-1). Use the linear approximation to estimate the value of f(-2.1,-0.9) =

For \ a \ function \ f(x,y), \ we \ are \ given \ f(100,20)=2750, \ and \ f \ x(100,20)=4 \ and \ f \ y(100,20)=7. \ Estimate \ f(105,21)

Find the linearization of the function z=x sqrt y at the point (-3,49).

An unevenly heated metal plate has temperature T(x,y) in degrees Celsius at a point (x, y). If T(2, 1) =138, T_x(2, 1) =8 and T_y(2, 1) =-11, estimate the temperature at the point (2.05, 0.95).

Find the linear approximation of the function f(x,y) = \sqrt{14 - x^2 - 4y^2} at the point (1,1). Use this approximation to find f(0.94, 1.09)

Find the linear approximation of the function f(x,y,z) = \sqrt{x^2 + y^2 + z^2} at (2,3,6) and use it to approximate the number \sqrt{2.03^2 + 2.99^2 + 5.98^2}

Approximate the root by using a linearization centered at an appropriate nearby number. \sqrt{147}

Let f(x)=(3ln(x)+1)^(ln(x)+2sin((pi/2)x)) . (a) Find the linearization of f(x) about x = 1. (b) Use part (a) to estimate f(1.001).

Find the linearization L(x) of the function at a. f(x) = x^{\frac{2}{3}}, a = 27

Find the linearization L(x, y, z) of the function f(x, y, z) at the point P_0. f(x, y, z) = (sin(xy))/(z), P_0(pi/2, 1, 1).

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

a. Find the linear approximation for the following function at the given point f(x,y) = \sqrt {x^2 + y^2} (8,-15) b. Use part (a) to estimate the given function value f(8.04,-14.93).

Let f: (0,\infty) \to R be the function defined by f(x) = ln(x^4) + x^4 + 3cos(x-1). a) Find f'(1) b) Use your answer in a) to find the linearization L(x) of f at x = 1. Your answer must be a function of x.

Use linear approximation, i.e. the tangent line, to approximate 4.8^6 as follows: Let f(x) = x^6. The equation of the tangent line to f(x) at x = 5 can be written in the form y = mx + b where m is: and where b is: Using this, we find our approximation

Find the linearization L(x,y,z) of the function f(x,y,z)at P_0. Then find the upper bound for the magnitude of the error E in the approximation f(x,y,z) \approx L(x,y,z) over the region R. The lineari

Use linearization of the function w = \ln(x^2 - 3y) to calculate the approximate value of w(4.02,4.97).

Find the linearization L(x) of the function g(x) = xf(x^2) at x = 2 given the following info: f(2) = -1, f'(2) = 8, f(4) = 4, f'(4) = -3 .

Find the linear approximation f(x) = \sqrt {x} at x = 16. The answer should be the equation of a line in slope-intercept form y = mx + b in the variables x and y.

Find the linerization L(x) of the function f(x) = x^4 - x^2 + 3 at x = -2.

Find the Linear approximation of (16+u)^{1/4} then u is close to 0.

Estimate the square root. Round to the nearest integer. sqrt{242} .

Let f(t) be the number of US billionaires in the US in year t. a) Express the following statements in terms of f . i) In 1990 there were 17 US billionaires. ii) In 1995 there were 93 US billionair

Find the linearization of the system x' = 7x -x^2 -xy \\ y' = -5y + xy

The table of some values of f(x, y) is given below. | | y=2 | y=5 | x= 1 | 18 | 36 | x=2 | 13 | 26 Find the local linearization of f at (1, 2).

Identify the surface with the given vector equation. r(u, v) = 4 sin u l + 5 cos u j + v k, 0 \leq v \leq 2

Let f(x, y) = x^{4} y^{-3}. Estimate the change \Delta f = f(3.03, 4.9) - f(3, 5) using the equation below. \Delta f \approx f_x (a, b) \Delta x + f_y (a, b) Delta y

a) Find the linear approx for the following centered at a b) find the quadratic approx polynomial for the following centered at a c) use polynomials from parts a and b to approx the given quantity f(x

From the local linearizations of e^x and \sin x \ \text{near} \ x = 0 , write down the local linearization of the function e^x \sin x . From this result, write down the derivative of

For { g(x,y) = \sqrt{(x^2+y+14)}, \\ (a)\Delta g(3,2)=...................... } (b) Find the best linear approximation of g(x,y) for (x,y) near (3,2). Linear approximation =.................... (c)

What is the area of the line 2^x using linear approximation.

Let f(x) = (x - 1)^2, g(x) = e^{- 2x}, and h(x) = 1 + \ln(1 - 2x). a) Find the linearizations of f, g, and h at a = 0.

The linearisation of the function f at the point x = 2 is L(x) = 5x - 8. Let K be the linearisation of the function u(x) = f(x)/x at x = 2. Find K.

Consider the function f(x) = 3 + \int^{1+x^2}_2 5/2(1 + t^2) dt. (a) Find the linearization of f(x) at a = 1. (b) Use the linearization in (a) to approximate \int^{1+(1.1)^2}_2 5/2(1 + t^2)dt.

Use the linearization approximation (1+x)^k=1+kx to find an approximation for the function f(x)=(1/square root of 4+x) for values of x near zero.

A) Use the linearization of y = ln (x) near x = 1 to estimate the value of ln (1.1). Calculate the error of this approximation with the value of ln (1.1) given directly by your calculator. B) Verify t

a) Use the linearization of y= ln(x) near x = 1 to estimate the value of ln (1.1). Calculate the error of this approximation with the value of ln (1.1) given directly by your calculator. b) Verify tha

In this problem, we will use linearization to approximate the solution of e^t-1=t/ 20 +1 which occurs near t=1. (a) Without using a calculator, show that the equation e^t-1= t/20 +1 must have a solut

A right circular cone of height h and base radius r has total surface area S consisting of its base area plus its side area, leading to the formula: S= \pi r^2 + \pi r \sqrt{r^2+h^2} . Suppose you sta

Determine if the given functions are linearly dependent or independent in (0, infinity). cos (ln x), sin (ln x).

(a) Find the local linearization of f ( x ) = 1 1 + 3 x near x = 0 . (b) Using your answer to (a), what quadratic function would you expect to approximate g ( x ) = 1 1 + 3 x 2 ? (c) Using your

The wave heights h in the open sea depend on the speed v of the wind and the length of time t that the wind has been blowing at that speed. Values of the function h = f(v, t) are recorded in feet in t

Find the linearization of the function f(x, y)= (68 - 3x^2 - 4y^2)^{1/2} at the point (4, 2). Use the linear approximation to estimate the value of f(3.9, 2.1).

A function f is given by the formula f(x)= Ae^{kx} for constants A and k. We also know that f(3)= 4 and f(7)= 11. Find numerical values for the constants A and k.

Recall that the volume of a sphere of radius r is V(r) = \frac{4}{3} \pi r^3 . Find L, the linearisation of V(r) at r = 50.

Given that f(3)= 5 and f '(x)= \frac{x}{x^3 + 3}, find the linear approximation of f(x) at x= 3.

a) Approximate \sqrt {26} by using the linearization of y = r\sqrt x at the point (25,5). Show the computation that leads to your conclusion. b) Approximate \sqrt[3] {26} by using an appropriate line

Linearize the equation y= (\frac{a + \sqrt{x}}{b\sqrt{x}})^2