Question#4: A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 14×22 inches by cutting out equal squares of side x at each corner and then folding up the sides as in the figure. Express the volume V of the box as a function of x.

Q: calculate following values:   f(-2) =  f(1) =  f(2) =

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Q: Question 2: Check whether the given functions have at least one solution over the given intervals by…

A: Intermediate value theorem Theorem States that if function is continuous on the interval [a,b] and…

Q: Question 5. Show that the function f(x) = x5 + 3x3 + 2x +1 is one-to-one.

A: Please rate

Q: Question 3 Evaluate the functions at the given values of x. f(x) = -x, g(x) = |x+4, h(x) = x-3 1 %3D…

A: The objective of the question is evaluating the function at given value of x

Q: Question 3 Given F(x) = VVx – 1, find functions f, g,h such that F = f °go h.

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Q: Question 11: Determine if the function f(x) = 8x2 + 4x + 2 is even, odd, or neither.

A: Given function is,

Q: Question 15 Given the function f(x) =4x- 39x2+90x +2 which of the following describes its absolute…

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Q: Question 2 Consider the Function f (x) = ||x – 3| – 2| What is one of the roots of this function?

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Q: QUESTION 1 Determine the symmetry of the function. f(x): to x² + 2 O Even О odd O Neither О Both

A: If f(-x)=f(x), even If f(-x)=-f(x), odd

Q: Question 16: Determine if the function 1 f(x) = x* + x² + is even, odd, or neither. Show work.

A: The given function is,

Q: Question 5 The following function is homogenous of degree what? Vx?y²+x²+y² f(x,y) = х, у ху 1 3 4…

A: We have to find the degree of function.

Q: Question (3): Determine the absolute extrema of the function f(x) = x² + 2x - 4 in the interval…

A: Given :f(x)=x2+2x-4   [-1, 2]

Q: Question 14 Express the hypotenuse h of a right triangle with an area of 25 m2 as a function of its…

A: The area of the right triangle is 25 m2 and hypotenuse is h

Q: Question 1 (10 Marks): Calculate of given function f(x,y) = ye**. əx²əy³

A: Definition used -       Partial derivative -             In partial derivative, we differentiate…

Q: Problem 4: The volume of a cylinder is known to be 20. Express the total surface area S of the…

A: The piecewise function is defined as the function for which the function is combination of different…

Q: Question No3: Find fogoh where f (x) = lx-4|, g(x) = 2%, h(x) = Vx. %3D

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Q: QUESTION 13 For the pair of functions, find the indicated composition. f(x) = 5x + 7, g(x) = 4x - 1…

A: In mathematics, function composition is an operation that takes two functions f and g and produces a…

Q: QUESTION 4 Find the domain of the function. f(x) O [9, = -4x + 9 *) (0, ) O (*, *) O (*, 0) U (0, *)

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Q: Question 22 For the function f(x), find the simplified form of the difference quotient, f(x + h) –…

A: Consider the following function: fx=x3-3x Consider the following formula of difference quotient:…

Q: Question 7 <. Let f(x) = 5 – 8x + 3x. Calculate the following values: f(a) = %3D f(a + h) = f(a + h)…

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Q: Question 6 The following function is homogenous of degree what? Vx++x²+y? x+y other/not possible 2 4…

A: For the detailed solution of the problem follow the next step.

Q: • Question 5 Given the function ( 4x -6 4x - 12 0 f(1) = Calculate the following values: f(- 1) =…

A: our objective is to find f(-1) , f(0), f(2).

Q: Question 5 elect the equation that represents the function given in the table below. |-2|16 |-111 11…

A: Given: Equation of line passing through the point (x1, y1) and (x2, y2) is (y-y1)=m(x-x1) Where…

Q: • Question 14 Given the function f(x) = 5 + 7x², calculate the following %3D f(a) = f(a + h) = f(a +…

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Q: Question 6 Given the function f(x) = - 5 + 3x², calculate the following values: %3D f(a) = f(a + h)…

A: For f(a) ,we put x=a in f(x)  For f(a+h), we put x=a+h in f(x)

Q: Question 2: Illustrated below are two tangent lines drawn at 2 different points on the curve whose…

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Q: Question 3 Find two functions f(x) and g(x) so that h(x) = (fog)(x) a) h(x) = (2x +3)². %3D

A: The function h(x) is defined as hx=fοgx

Q: Question 11. 4x – 3 Given that f(x) = find f'(x) as a function of z. 7x – 2 Enter the answer as a…

A: ddx(u(x)v(x)) = [v(x)× ddx(u(x))] - [u(x)×ddx(v(x))](v(x))2

Q: Question 1 The domain of the following function f(x.v) = In(x-v+1) is given by the equation:

A:

Q: Question 8 Suppose f: [a , b] → R is a function with no absolute maximum on [a , b] Which of the…

A: Given that: f:[a, b]→R is a function with no absolute maximum on [a, b].

Q: Question 3 Find two functions f(x) and g(x) so that h(x) = (fog)(x) a) h(x) = (2x + 3)². 1 b) h(x) =…

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Q: Question: 2 Find the absolute maximum and minimum values of function f(x) = 3x - 2 - 2x over the…

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Q: Question 4 Consider :(-x, 2] → R, where f(x)=(x– 2)² +1. a. Define the function " x = 1,x = 5-V5 „*…

A: Since you have posted the different questions of parts. I am answering the first one. Please post…

Q: Question 25 Use the slopes of tangents to determine whether the function f(x) = -6x² + 36x is…

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Q: Question No 1: Using the quotient rule to differentiate the x3+1 following function y = Vx2+1

A: As per our company guidelines, we are supposed to answer only the first question. Kindly repost…

Q: Question 32- of 33 Step 1 of 1 Given the following function, what is u' (x)? Treat F. Q, and W as…

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Q: Problem 7: Sketch the domain for the function f(x, y) = In((x – 1)0+1))

A: Given function: f(x,y)=lnx-1y+1

Q: Question 5 Given the function: 5x 6 x < 0 ƒ(z) = { 5x 12 x 20 Calculate the following values: f(-1)…

A:

Q: Question 8 Suppose that H is a function of r satisfying H'(0) (1+-). N H" (r) – aH'(r) = 0, H'(0) =…

A: Given second order homogeneous differential equation : H''r-aH'r=0, where H is a function of r. To…

Q: QUESTION 7 State the domain of the function 15x f(x) = %3D x2-4x -21

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Q: Question 4 f (x) = = +1 is an odd function. O True False

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Q: Question#5: Consider the point (x, y) lying on the graph of y = vx – 3. Let L be the distance…

A: From the given data:

Q: Question 1 Which of the following functions passes through the point(0,12) and satisfiesf"(x)=8?

A: step 2 complete solution

Q: hat instead of having a box with square ends, you have a box with square sides so that its…

A: Introduction: The volume of the cuboid with length l, width b and height h is given by, V=lbh

Q: Question 6 Determine the domain of the function. f(x) = x3 %3D All real numbers O No solution Ox<0…

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Q: Question 2. Given that f'(x) = 4x(x² + 8)-1/3 and f(0) = 0, find the function f

A: In this question we will use basic of calculus i.e concept of integration. We will simply integrate…

Q: Question 7 Find all points of discontinuity of the function: f (z)= 324 (A) -2,-2i (C) -2+2i z4-16…

A: The function is given by fz = 3z2+4z4-16 To evaluate : The point of discontinuity.

Q: Question 1 Consider the function f (x, y, z) = x² + y² – xyz %3D | Find grad

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Question 1: Differentiate the functions. a) f(x) = 2 – 5cosx +x4 + 3* b) f(«) = +

A: I am attaching image so that you understand each and every step.

Q: Question 15 Given the function f(x) = - 6+ 3x, calculate the following values: f(a) = f(a + h) = f(a…

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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.