AC 2311 - Calculus I uiz # 11 Name: 1. Find a point on the curve y = x2 that is closest to the point (18,0). AY y = x (х, у) (18, 0) 2. Find the coordinates of the point on the line 2x + y = 3 closest to the p (-2, 2). 3. Let f(r) = x. (i) Find the domain of the function f. (ii) Find the critical point(s) of the function f.

Q: (a) Find a function f(x, y) with gradient F, where F = (y cos(xy), x cos(xy) + y² + 2y) (b) Use your…

A: Solution of given question is followed by:

Q: 6. Find the absolute maximum and minimum of the function f (x, y, 2) = x + 2y on the intersection…

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Q: The function f(x, y, z) = x² – y² = z² increases in the direction at the point (1, 1, 1).

A: We need to find if the statement is true or false.

Q: Q3/ Find the directional derivative of the function f(x,y,z)=xy+yz+zx at the point Po(1,-1,2) in the…

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Q: The function f(x, y, z) = x² − y² − z ² increases in the direction 〈六〉 (1, 1, 1). at the point

A: Please check step 2 for solution.

Q: 4.97 The function z(x, y) at the point (0, 0) lo has a gradient 4î + 6j. .oor a bvsH (a) What is the…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 1. find the derivative of the function f(x, y, z)= xy+ yz + zx ,at the point P,(1.–1,2) in the…

A: 1. *The function f(x,y,z) is f(x,y,z)=xy+yz+zx *The point of the function is Po=(1,-1,2) *The vector…

Q: a) Find the directional derivative of the function f(x, y, z)= x² y2 (2z+1)2 at the point P:(1, - 1,…

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Q: re GIPTA of following is the the function P12,212) =D 31 -6f+22 Whic value of dicectional derivative…

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Q: ye-(²²+y²+z²). Find all points (x, y, z) such that Vf(x, Y, z) = Question 2. Consider the function…

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Q: 1. Let f(x, y) = xcos(2x + y). a) Find the value of the directional derivative of f(x, y) at |in the…

A: Solve the following

Q: II. Let f(x,y) = (x³ – y², x² y). Obtain a linear approximation of f(x, y) at the point(-1,1) and…

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Q: 8 Find the linearization L(x, y) of the function at the given point f(x, y)=1+xIn(xy-5), (2,3)

A: Given: f(x,y)=1+xln(xy−5)(2,3)L(x,y)=?

Q: 2B. Find the analytic function f(z) = u+iv for which v= e(xcos y+ ysin y)

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Q: Find the linearization L(x,y) of the function f(x,y) = 8x – 7y + 8 at the points (0,0) and (1,1).…

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Q: 4. a) Find an approximation for f (x, y) = at the point (1.97,1.02). V10-r-5y b) Check Euler's…

A: (a) Approximate f(x,y)=410-x2-5y2 at the point (1.97,1.02) (b) Check Euler Theorem for…

Q: Find y" in Exercises 71-78. 71. y - (1 + 2) 72. y - (1 - vī) 73. y - cot (3x – 1) 74. y - 9 tan 75.…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 44. The discriminant fufy – fw² is zero at the origin for each of the following functions, so the…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: 2. (a) Find the linear approximation L(x, y) near the point (1, 2) of the function f (X,Y)=(0=Y) +…

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Q: 6. (a) Let f(x, y) = x³y*. Find the directional derivative of f in the direction of T = (3, 4) at…

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Q: mence Jove Q 6. Find the orthogonal trajectories of the functiony = x + ce-, which is passing…

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Q: 13 Find the linearizatian z=L(x.y) f the function 2=f(x.y) =4x²-y²42y at the point (x.y) = (3,2).…

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Q: Check that the equation x³ + y³ + 2³ = x + y + z implicitly defines at least one differentiable…

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Q: 7. Find and classify all stationary points of the function f(r, y) = 1 +y? - 12r + 6y-3

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Q: Given f(x, y) = x³e#Y. a. Find the linearization, L(x, y), of the function at (1,0). b. Use the…

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Q: Bnak ant to basqz srll norw rigdt and 25 2. The height of a ball t seconds after is thrown upward…

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Q: Find the linearization of f(x, y) = −x² + 2y² at the point (3,-1). Use the linearization to estimate…

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Q: 14. Find the linearization, L(x,y,z) of the function f(x, y, z) = x³Vy? + z? at the pointP, (2,3,4).…

A: We have to find L(x,y,z) and by use of that we have to find the value of 1.9833.012+3.972

Q: ) Find the linearization L(x, y) of the function f(x, y) = ez+y at (0,0). Use it to estimate f(0.01,…

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Q: 7. Given (x, y)= x' + y² a) Find the derivative at P(1,1) in the direction of " = u,i +u ;j b) In…

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Q: OFind the linearization L (1, y) of the function f (z, y) = /176 – 4,' - 16y at %3D L (z, y) = Note:…

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Q: The slope of the secant line of the function y =Vx +x through the points x, = 1 and the point xz = 4…

A: y=x+x

Q: A. Find the linearization of the function f(x) at the x = 0. %3D Vx+1 dy B. Let y = u20 and u = x +…

A: Applications of the diffraction, linear approximation and slope of the tangent line , total…

Q: Consider the function f(x, y) = ln(25 – x² – y²). а. Find and sketch the domain for this function.…

A: We will find out the required solution.

Q: 2. Use suitable linearization to find the approximate value for the function at point P. f(x,y) (x-…

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Q: #2. Consider the function f (x, y,z) = xy+3xz² + 5y at the point (1,0, 2) (a) Find the direction in…

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Q: Find the linearization L(x.y) of the function f(x.y) = 2x- 7y + 3 at the points (0,0) and (1,1). The…

A: f(x,y)= 2x-7y+3 fx  = 2 fy = -7 The linearization of a function f(x,y) at (a,b) is given by L(x,y) =…

Q: 4x5-x*y2-2y5 12x5-6y5 Define the function f (x,y) = at the origin so that it becomes continuous…

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Q: Find the linearization L(x, y) of the function f(x,y)= at the point (1,2) and use it to 3xy…

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Q: Find the linearization L(x,y) of the function f(x,y) = 2x – 3y + 4 at the points (0,0) and (1,1).…

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Q: Find a linear approximation to f(x,y) at (-1, 1). [2хy] y Use your result to find an approximation…

A: Given function is fx,y=xy2xy                  (i) To find a linear approximation to the function…

Q: Riemann sits on the line normal to the curve y=x2 -3x+2 at x = 1

A: Given           y=x²-3x+2 and x=1  Slope of the curve is given by =dy/dx

Q: Maria thinks that the maximum point of y= -(z – 1)* + 1 is (0, 1), Jena disagrees. Who is CORRECT?…

A: Maria thinks that the maximum point of y=-(x-1)2+1 is (0, 1)

Q: Do the equations x2 + ys + yt? = 13 and y? + x²s + xt2 = 9 define s and t as functions of x and y…

A: We will find out the required value.

Q: 1. How do you find the linearization of f(x) at x = a? Illustrate with a concrete example

A: We have to solve

Q: Find the domain of the function f(x, y) = ln(8 – x° ? – 4y²). | - > 1} 2. {(r, v) : + 1} 4. {(x, v)…

A: We need to find the domain of the given function.

Q: Find all stationary points of the function f (x, y) = (x² + y²)² – 2(x² – y²) + 1. | Determine the…

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Q: Let f(x)=x+2 A Find the linear approximation of f at =7 In other words, find the tangent line to the…

A: This question can be solved using the concept of linear approximation of a function about a point.

Q: Let f(x, y, z) = 5x – y + z?. Find the maximum value M for the directional derivative at the point…

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.