a. Find the linear approximation for the following function at the given point. b. Use part (a) to estimate the given function value. f(x,y) = x+y; (12, - 5), estimate f(11.93,-5.04)

Q: F(X) = x,3+x,3 – 3x,x2

A: Given:- F(x) = X1 + X2  -3 X1 X2  TO FIND:- Classify all stationary points

Q: Find the abscissa of the point on the graph of y=V 2x – 1 that is parallel to the line 2x - y+1=0

A:

Q: Find an equation of the secant line containing (1, f(1)) and (2, f(2)). f(x) = x² - 2x %3D

A: Given , the function f(x) = x2 - 2x Now we find      f(1) = 12 - 2•1 = 1 - 2 = -1,…

Q: The position function of a particle is given by r(t) = ⟨-3t2, 5t, t2 - 4t⟩ At what time is the…

A: rt=-3t2, 5t, t2-4t To find the velocity, differentiate the position function with respect to t, we…

Q: If  P=27/47 +r2 , determine the value of r for which P will be a minimum. Use the second derivative…

A:

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A: topic - equation of tangent line

Q: Find y as a function of t if 3y′′+31y=0 y(0)=7, y′(0)=3

A: Find y as a function of t if 3y′′+31y=0 y(0)=7, y′(0)=3

Q: Graph the function f(t) = (/t, 2t +1) by eliminating the parameter.

A:

Q: Let  f(x)=1/2x^2-1.  Find the slope  of the secant line that contains points P=(2,f(2)) and…

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Q: Let f (x) = Vx. %3D Find the slopem and the point-slope equation of the line tangent to the graph of…

A: If a function gx represents a curve then g'a represents the slope of curve at x=a.

Q: Differentiate the function with respect to y. A Z = + Bey уб Z' + Bey = 8A 9 y 20 -

A: In this question we have to differentiate the function with respect to y.

Q: 8. Given the relation x² – xy +y³ = 7, determine the slope of the line tangent to the curve at…

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Q: w = (2x – 7)(x +5)/ Establezca dw dw dx 2.

A:

Q: Find the curve in the xy-plane that has a slope at each point given by 1 and passes through the…

A: See attached file for a step by step explanation.

Q: Find the slope of the secant line between the values x1 and x2 for each function y = f (x). f (x) =…

A:

Q: Find the coordinates of the point(s) at which the line tangent to the graph of the function f (z)…

A:

Q: Use the linear approximation to estimate the value. Compare with the value given by a calculator.…

A: Think of 4.19.9 as a value of fx,y=xy f4.1, 7.9=4.17.9 Then it makes sense to use the linear…

Q: The following linear plot is derived from a function of the form aez a and where b are constants.

A:

Q: The range of the function f(x, y) = 1 3+Vx+y is equal to:

A:

Q: Sketch the following curve y f(x, y) = x² + 1

A: Given function, fx,y=yx2+1 To sketch the curve of the function.

Q: Find y as a function of t if 5y′′+31y=0 y(0)=4,y′(0)=7y(t)=

A: The given differential equation is  5y''+31y=0   ......(1) and the initial condition is y(0)=4 and…

Q: Find the length of the part of the curve y = = between x = 1 and x = 2.

A:

Q: The level curves of the function f (x, y) = Vx² – y² – 1 are

A: We have to find the level curves .

Q: Find the linear approximation to the following function at the given point a. ƒ(x) = 9(4x + 11)2/3;…

A: To find the linear approximation of the following function at the given point a. f(x)=9(4x+11)23,a=4

Q: Use the linear approximation to estimate the value. Compare with the value given by a calculator.…

A: The given number is (2.01)3(1.02)2

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A:

Q: Find the stationary points of the function: f(x,y,z) = 2*y*z + 7*x*z - z + 5*x*y + y x = ? y = ?…

A: The solution is given below

Q: For an F-curve with df = (6, 10), find a. F0.05. b. F0.01. c. F0.025.

A: Using Excel, The vale for the F-curve with df = (6,10) is shown below

Q: The position function of a particle is given by s(t) = 3t2 – t3, t> 0.

A: We have given the position function S(t) which gives us the position of the particle at time t…

Q: Determine the point(s) at which ƒ(x) = x3 - 12x has a horizontaltangent line

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Q: Find the Maximum value of the function f(x, y) = x² – y² – 2y on the curve x? + y? = 25. %3D -

A: By langrange multiplier method n

Q: Find the slope of the curve at the indicated point. y = x2 + 3x - 5, x = 2 O m = 7 O m = 2 m = 10…

A:

Q: 8) Determine if the line given by r(t) = intersects the xz-plane. If so, determine at what point.

A: we have to find the point of intersection.

Q: Find an equation for the linear function g(z) which is perpendicular to the line 7z – 6y = 12 and…

A: Given the equation of a line 7x−6y=12

Q: Find the number  a such that the line x = a  bisects thearea under the curve  y = 1 / x 2  , 1<…

A: Our Aim is to find a number such that line x=a bisects the area under the curve y=1x2, 1≤x≤4.

Q: The area (in square units) between the curve defined by y = x³, the x-axis, and the lines x = -1 and…

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Q: 1) Establish two linear functions shown below and find X and Y coordinate of the intercept P of two…

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Q: Find f, for the function f (x, y) = yx-2z'y %3D

A: we have to partially derivative

Q: Consider the function R° → IR Draw f(x, y) = y2 + x(x - 1)2(x – 2) alignment curves. |

A: Consider the function f:ℝ3→ℝ. Draw f(x,y)=y2+x(x-1)2(x-2) alignment curves.

Q: 3 f(x) = x2, with 0 < x < 1

A:

Q: c) Find the exact lenght of the curve y = 100x – 100 between on the interval 0 < x < 11/2 Answer:

A: We can find the arc length as below.

Q: f(x) = + 2x' with 1 < x< 2

A: Given: fx=x36+12x with 1≤x≤2

Q: Find the relative maximum and minimum values. f(x.y) = e 2x2 + 9y2 +11 Select the correct choice…

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Q: Find the linear approximation to the following functions at the given point a.

A: Since, Linear Approximation is defined by the given formula:-L(t)≈g(a)+g'(a) (t-a) -(i) Where g (a)…

Q: Compute the length of the curve: f (x) = x² 2x, 0<x<2

A: Given:- f(x) =x2 -2x  To find:-  Length of curve over interval [0, 2]

Q: The wave heights h in the open sea depend on the speed v of the wind and the length of time † that…

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Q: W) = 3 = 1, x2= 3

A: Given: f(x)=43x-1; x1=1, x2=3

Q: (d) Calculate the coordinates of the stationary points of the function z(x,y) = x³ – y³ – xy + 6.

A: We have to find the stationary points i.e., the critical points of the function zx,y=x3-y3-xy+6.…

Q: Find y as a function of t if y(0) = 4, y(0) = 9. y(t) = 576y" +624y + 169y = 0,

A:

Q: Find and classify all stationary points of the function f(x, y) = 2y³ + 6yx² – 3x³ – 150y

A: