1 and g(x) 3x Let f (x) = %3D X + 3 X + 3 Find f+ g, f- g, fg, f/g and their domains. NOTE: Enter DNE in any unused blanks.

Q: 3. Determine an equation that may represented by the graph shown below. A) f(x) =-1+VT – x B) f(x)…

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Q: Find the limits in Exercises 41–54.

A: Since you have posted multiple questions, as per our policy we will answer first question. Please re…

Q: 3. Find the largest domain (in R2) for the function In(3 + y) 1- x + y f (x, y) :

A: Let's find.

Q: slane using GraphiI Hethod Max Z=3X+2k2 2X + Xe loo X+X+ 80 Onpt-

A: first we will draw the feasible region bounded by the constraints. then comparing the value of…

Q: S2x³ – 18x + 11 x² – 4x + 3 ln(x) x 21 x < 1 (you may assume g is continuous). Find all critical…

A: Given   function gx=2x3-18x+11        x&lt;1x2-4x+3lnx         x≥1

Q: 5. Using the graph of y= f(x), determine the equation for the transformed function g(x)in the form y…

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Q: Find the coefficients of a quartic function f(x) = axt + bx³ + cx² + dx + e whose graph passes…

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Q: (5) The point p = -4 is a fixed point of the function g(x) = Vx + 20. Show if it is attractive or…

A: Given that, the function is gx=x+20 and the point is p=-4. Note that, x0 is attractive if f'x0&lt;1…

Q: a) If x, y and z are independent variables and f(x,y,z)= x sin(y +3z) of then find ôz . b) Find all…

A: (a) Given- fx,y,z=xsiny+3z To find- The value of ∂f∂z.

Q: 3. The function (x, y)= 8r-/4x +3y is homogenous in x and y of degree 2х 4. The function (x,y)= (x'…

A: Here ,                We have given some of functions f(x,y) which are homogeneous in x,y so we have…

Q: If f (x) is an invertible, differentiable function with tangent line y = 4 x + 7 at the point (0, 7)…

A: we have to swap variable for finding the inverse function

Q: 1. If the graph of y = f(x) contains the point (0,2), and f(x) > 0 for all x, then f(x) = dx (a)…

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Q: x2 -9 + т, х# 3 Let f(x) = x-3 тx + 3k, x = 3 Is cont. at x = 3, find the value m&k if f(-1) = 8.…

A: Givenf(x)=x2-9x-3+m, x≠3           mx+3k ,    x=3To check f is continuous at x=3.

Q: Find local minima, local maxima, and saddle point of: f(x, y) = 4 + x³ + y3 – 3xy.

A: Given: fx,y=4+x3+y3-3xy Solution: fx=∂f∂x=3x2-3y=0  or y=x2 fy=∂f∂y=3y2-3x=0  or x=y2 Hence we get,…

Q: 4/5elue f(X)= X'-2X- 5 Using Secant methed, Cerreet apto 2decimal elases.

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Q: 1. The graph of the function g(x) consists of two straight lines and a semicircle. Use it to…

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Q: Step 3 of 5 In order to maximize V(x), we need to find the critical points of V(x). Find the…

A: To find the derivative of V(x)

Q: x2 + x-2 dx If J +B f(x) dx +D g(x) dx, then dx can be resolved into + B (x2 – 1)(2x- x2) 2 f(x) dx…

A: We have given indefinite integration with respect to x. While solving the indefinite integral, we…

Q: 3. a) Use REGRESSION to find a quartic function y = ax* + bx3 + cx² + dx + e that fits the data. b)…

A: given y=ax4+bx3+cx2+dx+eUsing the regression to find the quadratic function

Q: 1. Any function y = f(x) can be expressed as x = f(y) in standard mathematical methods for solving…

A: Given: For any function y=f(x) can be expressed as x=f(y) in standardmathematical methods for…

Q: 4. DETAILS SCALCET9M 3.10.001.MI. Find the linearization L(x) of the function at a. f(x) = x - x² +…

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Q: Find the extrema of the given function f(x, y) = 2 cos (x² - y²) subject to x² + y² = 1. (Use…

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Q: x² + 2x 15 x → -00, f(x)→ x → 0o, f (x) → _ - f(x) %3D x² + 10x + 25 horizontal asymptote (HA)…

A: Let us first find limx→∞x2+2x-15x2+10x+25. So,…

Q: A cubic polynomial function f is defined by f(x) = 4x3 + ax2 + bx + k where a, b, and k are…

A: f(x) = 4x3+ax2+bx+k local minimum at x=-1point of inflection at x=-2At point of inflection ;…

Q: -4 Find the linearization L(x) of the function at a. 3. f(x) = /x, a = 4

A: fx=x=x12 f'x=12x12-1=12x-12   At a=4,  f4=412=2 f'4=124-12=1212=14

Q: f(x) = 3 x4-4 x3 -12 x2+1, has local minimum at x = OA. OB 2- OC. OD.

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Q: Need answer for C

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Q: Along the path x = ey find lim (1,y)→(1,0) y²-6zy 3r-y-3 does not exist O 3 0 2 0 -3 O 2 0

A: Find limitx,y→1,0lim y2-6xy3x-y-3calculate limit along the curve x=eyconcept:- convert limit in one…

Q: (3–x*) ane d 2x. Calculate the Wronskian of functions

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Q: xsin 1x Vx+1 2tan-x Vx+1 2tan-1x QI) Find of y=: e2x+1

A: We will find dy/dx as following .

Q: 4. a) Solve the equation 5sin-'x- 2n = 2sin-'x-3n 6) Graph, find x where f(x) = g(x), bounded by…

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Q: DETER Derer mine the fieSt os: mine the キ)12ST oこ: derivative F6) = aresee(3x) %3D

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Q: a) Find the extreme values of f(x, y) = x' + y' - 3xy +1 by using the Second Derivatives Test. b)…

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Q: Q1: lim Q2: lim (x-1)(x-2) x+1 x-001+stnx Q3: f(x) = x²-16 đêm 5244 A) 3 (A) B) 00 (B) 00 18 (C)-8…

A: We need to find limit.

Q: 7. The function (x, y)= (2x* + y* )exp + xy' is homogenous in x and y of degree

A: .Given,f(x,y) = (2x4+y4) ey2x +x y3Put y= xSo we get,f(x,x)= (2x4+x4) ex2x +x x3 f(x,x)= (3x4) e0.5…

Q: 3. The horizontal asymptote(s) of f (x) = Vx² – 1- væ² +x.

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Q: f Goiny )= x*x f -6x+ g fundtion depending 2. on the gCxy) =y -x² 0 condition with 2

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Q: -3x2 — 16х — 16 x + (-4) f(x) = 4x2 + 23x + 28 С, X = (-4) What value of C would make f(x)…

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Q: Find the linearization of y : at x = 16. (Use symbolic notation and fractions where needed.)

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Q: [3 Marks] B1(a): Determine whether the function e12x x 0 %3D 12x 1 - [3 Marks] B1(b): Solve the…

A: Follow the steps .

Q: f(x) = x2 − 2x − 1   Give the vertex, axis of symmetry, and intercepts. (If an answer does not…

A: By the definition of vertex,  axis of symmetry and intercepts,  we solve this in next step.

Q: (a) Give the linearization L(x) of f(x) at x = 2. (b) Use your answer from Part (a) to estimate the…

A: Solve the following

Q: 2. Maximise f = x-y² subject to x? + y² < 4, where x, y 2 0 i) Write the Lagrangian function. ii)…

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Q: x* +2 has a unique fixed point in 0,1 and find an approximation to 9 2. Show that g(x) = the point…

A: Fixed point: A fixed point of a function g:[a, b]→[a, b] is a real number p such that g(p)=p.…

Q: f(x) = Ae (x-b)2 2a2 - f(x) z e° ze-x²

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Q: (x²-9 A) f(x) = x + -3 x+3 -6 x = -3 Is f cont. at x =-3 ? x2-8 x< 6 B) f(x) = x+3 -6 , 6 <x < 1 Is…

A: 1. (A) To find the continuity of the function we need to find the limit of the function f(x) near…

Q: 2 - x The function y= x² – 5x +6 has vertical asymptote/s at

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Q: 3. Example 3. Determine how large the number a has to be so that the 1 z dx is less than or area…

A: We have given

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.