Q1: Find the extreme values of the function F(x,y)=x² +n + y² +7 n=(3y)

Q: The local linear approximation for f (x) = Vx2 + 16 near x = -3 is

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Q: 5. Find absolute maxima and minima of the function f(x, y) = x² + y² on the closed triangular plate…

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

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Q: The function f (x, y) = 3x3+y2-9x+4y is given. a) Find the critical points of function f. b)Do…

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Q: Q3/ Optimize the function Z = x + xị ? Subject to: x1 + x2 = 4 x1, x2, 20 Using Lagrange…

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Q: f(x) = x – e2x

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Q: 3x-1 Find the critical points of the function f (x) = x+6

A: Here the given Any point x is said to be a critical point of the function f(x) if f(x) is not…

Q: 3. Find the relative extrema using any method. f(x) = (3xe*)².

A: A function f(x) has relative extremum at a point x=a if f'(a)=0. We first find the derivative of f…

Q: Find the critical numbers of the function. g(y) = y2 - 2y + 8

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Q: Q2:- Find the maximum value of the function f(x,y) 49-x-y? on the line x+ 3y = 10. %3D

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Q: Find all the critical points of the function 1 3 f(x,y) = x° -6y-7x+18y-3 What are the critical…

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Q: Find the critical numbers of the function. y- 2 g(y) = %3D y2 - 2y + 4

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Q: Find the absolute maximum and minimum of f(x, y) = 3z +y within the domain z² +y? < 4.

A: Use lagrange multiplier.

Q: Find and classify the critical points of the function f (x, y) = 16x³ – 12x2 + 12xy? + 3y?

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Q: Q3/ Optimize the function Z = x + x ? Subject to: x1 + x2 4 x1, x2, 2 0 Using Lagrange multipliers.

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Q: Find the critical numbers of the function. y-4 g(v) = y2 - 2y + 8

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Q: Q.2 Discuss the function f (x, y) =x'+y'-2(x +y')+3xy for all relative maximum, minimum and saddle…

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Q: 1. Come up with the equation of any function f (x, y) satisfying fx = x + y and fy = x + 3y³

A: The objective is to find the function f(x,y) satisfying fx=x+y and fy=x+3y3 Now take, fx=x+y Now…

Q: Maximize f(x, y) = 3xy Зху subject to x + y = 1

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Q: 13 Find the critical points of the function f (z) = 26x 7 +x 7. Enter your answers in increasing…

A: Given  f(x) = 26 x(6/7) + x(13/7)  To find the critical point we differentiate and find the value of…

Q: Find the values of x, y and z that correspond to the critical point of the function: 23D f(+, у) —…

A: Given  z = f(x, y) = 2x2-6x-3y+3y2+5xy We have to find the critical point of the function.

Q: Find the maximum and minimum values of the function f(r, y) = x²y subject to 5æ² + 4y² = 60 Maximum…

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Q: Find the critical point of the function f(x, y) = – 7 2x + 5x2 - 8y – 5y? |

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Q: Q4: Find and classify all critical points for the function: z2 = (x3/3)-(y3/3)+2xy

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Q: 2. Find an equation and sketch the graph of the level curve of the function f (x, y) = 16 – x² - y2…

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Q: b. Find the orthogonal trajectories for the family of curves x² + y² =C².

A: we have to find the orthogonal trajectory of the given family of curve

Q: Given n1=10, n2=14 find F-Critical value

A: F critical value is a specific value to compare the F calculated value. if F critical value &gt; F…

Q: y = 3 – 2x + x?

A: In this question, we need to find the critical points and test for maxima/minima of y=3-2x+x2.

Q: Find the maximum and minimum values of the function f(x, y) = e²Y subject to + y° = 16

A: Given data: The expression for the first function is f(x, y)=exy. The expression for the second…

Q: Find the extreme values of the function f(x; y) = x2 + y2 + xy on the curve x2 + 2y2 = 1.

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Q: Q3. Find local maxima, local minima, and saddle point of the function f (x, y) = x² + 2xy.

A: The given function is f(x,y)=x2+2xy

Q: Q2:Find all critical points of the function f(x)=(3x)/[(x^2)+9] Final answers should be ordered…

A: To evaluate the critical point of the following function  f(x) = 3xx2+9

Q: Find the critical points of y= 2x^3 +3x^2–12x and apply the Second Derivative Test to find the…

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Q: Find the local maximum and minimum values and saddle point(s) of the function x² y² – 8x + y f(х, у)…

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Q: Q2.Find all the local maxima, local minima and saddle points of the function f(x, y) = In(x + y) +…

A: Using the rule of saddle point on f(x,y).

Q: Find the critical point of the function f(x, y) —7- 5х — бх?+ 5у — 4у? This critical point is a:…

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Q: Q.4. locate the critical points of the function f(x) = x²(x-1)³ and identify critical points which…

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Q: Find the critical numbers of the function. y - 3 y2 – y + 3 g(y) = y = 0 (smaller value) y = 3 |×…

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Q: Find the critical points of the function h(x) = 3x – 4r³ – 72a + 5 Enter your answers from smallest…

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Q: Find the critical point of the function f(x, y) = - 5 – x + 4x? + y + 3y? This critical point is a:…

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Q: Q.20 For the function f(x) = x2 ex, the maximum occurs when x is equal to

A: Introduction :

Q: (b) Find the linearization of function S(x) = Vx V220 at a=216 and use approximate number (c)Find…

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Q: B3(a): Find the critical points of the function f(x) = 6x² – 12x. %3D

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Q: Q3/ Optimize the function Z = x + xị ? Subject to: x1 + x2 = 4 11,x2, 2 0 Using Lagrange…

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Q: 5. Find the local extreme values of f(x, y) = x²y on the line a +y = 3.

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Q: 2. Integrate the function (x+2/x)ax using multiple-application trapezoidal rule with n= 3

A: Trapezoidal Rule: ∫abf(x) dx≈∆x2(f(x0)+2f(x1)+ ... +2f(xn-1)+2f(xn))where ∆x=b-an

Q: 4) Where is the function g(x) = 3x2 -x+ 5 differentiable?

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Q: At what x-value(s) on the interval [-2, 3] does the graph of f (x) = x² + 2x – 1 satisfy the M.V.T.?

A: According to mean value theorem,Let f be continuous on [a,b] anddifferentiable on (a,b). Then…

Q: Find the critical point of the function f(x, y) - 4+ 7x – 5x² + 6y + 7y?

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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.