Consider a rectangle with perimeter 28 (units). Let the width of the rectangle be w (units) and let the Area of the region enclossed by the rectangle be A ( square units). Express A as a function of w and state the domain and range of the function

Q: Compute the difference quotient  f(x+h)-f(x)/h    , for the function below.…

A:

Q: Let f(x) be the function 12x – 2x + 12. f(9 + h) – f(9) - can be simplified to ah h a =

A: We have to find

Q: Consider the function defined on the indicated interval. f(x) = 2x – 30x + 144x – 220, [5, 8] %3D…

A: To find maximum and minimum of the given function in interval [5, 8] fx=2x3−30x2+144x−220

Q: Show that the function has a removable discontinuity at x = 4.

A: A function is continuous at a point x=a if limx→af(x)=f(a). For limit at a point to exist both…

Q: From a 18-cm by 18-cm piece of cardboard, square corners are cut out so that the sides can be folded…

A: From a 18 cm by 18 cm piece of cardboard, square corners are cut so that the sides can be folded up…

Q: Sketch the given function and find its domain and range 1 z = x² + y2

A: Consider a real valued function z=f(x,y) Then the domain of z = {(x,y): f(x,y) exists} and Range of…

Q: Express the function in the form f°g. H(x)= / 4 + /x %3D

A:

Q: Express the function h(x) = (x +7)° in the formfog. If f(x) = 1°,fi 6 %3D

A:

Q: An open box is to be made from a square piece of cardboard of side 12 inches by cutting out squares…

A: To find the size of squares cut out of the box for maximum volume.

Q: Differentiate the expression with respect to x, assuming that y is implicitly a function of x. ( x2…

A: It is given that y is implicitly a function of x. =x2+y23/2 differentiate with respect to x

Q: Show that the function f(x) = x' + 3x² is continuous at every real number a.

A: fx=x3+3x2

Q: Determine whether the function f is one-to-one.

A: Given function is fx=4-x2. To determine whether the function is one-to-one. Solution: A function is…

Q: From a 24-cm by 24-cm piece of cardboard, square corners are cut out so that the sides can be folded…

A: in this first we will find side of the box and then  Volume of the box = length × breath× height

Q: From a 12-cm by 12-cm piece of cardboard, square corners are cut out so that the sides can be folded…

A: Given, Cardboard of size 12 cm  by 12 cm in which square corner of sides x cm is cut out. We have to…

Q: A rectangle has a length of 16 inches and a width of 9 inches. If the length is increased by x…

A:

Q: From a 27-cm by 27-cm piece of cardboard, square corners are cut out so that the sides can be folded…

A:

Q: h(x) = In(v2x +4) %3D

A:

Q: A pool measuring 20 meters by 10 meters is surrounded by a path of uniform width, as shown in the…

A: Given information: A pool of rectangle size of length 20 m and breadth 10 m, Surrounded by a path of…

Q: Find the open intervals where the function is concave up, concave down

A:

Q: Let f and g be the functions, their sum and difference are denoted by ____________ and ____________…

A: In this question, we have given two functions given as f and g To find their sum and difference

Q: Given f(x) = Vx and g(x) = |x – 2|, find 9. Determine the domain of the function in interval…

A: Given function :

Q: a box with a square base and no top has a volume of 100cubic cm. If the material for the 4 sides…

A: Given that, the volume of the box is 100 cubic cm, the material cost for the 4 sides is 8 cents per…

Q: A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 36…

A: Given that:   (1)                                                (2)

Q: A closed rectangular box with a square base has a volume of 8000 cubic centimeters. Express the…

A:

Q: what valu e shouled be assigneed to a to make the function fex)= %3D 2ax

A: For the function to be continuous, the necessary condition is LHL=RHL=f(3) Here,  LHL=limx→3-f(x)…

Q: 2. Determine whether the function is one-to-one. (a) y = 4x2 + 3 %3D (b) y = Vx + 3 – 5

A:

Q: III. Verify if the function is continous at the point. 1. f(x) = x³ – 2x² + x – 5 at x = 0

A: f(x) is continuous at x=0 if- limx→0-f(x)=limx→0+f(x)=f(0)

Q: A rancher has 4,648 feet of fencing available to enclose a rectangular area bordering a river. He…

A: Let the figure of the fencing be:

Q: Determine if the following piecewise defined function is differentiable at x= 0. 4x- 3, x20 f(x) = x…

A: Given,           fx=4x-3x≥0x2+5x-3x<0

Q: Suppose that f(x) is a function with f(85) = 76 and f'(85) = 1. Estimate f(84). %3D f(84) =

A: f(85) = 76 f'(85) = 1 f(84)  = ?

Q: From a 18-cm by 18-cm piece of cardboard, square corners are cut out so that the sides can be folded…

A: A square card board is of 18cm by 18cm side of a card board is 18cm find the volume of the box

Q: Find the domain of the function in interval notation: f(x) = V + 17 %3D

A: Domain is the set of x values for which the function is defined We know that square root (negative…

Q: Explain if the function is continuous or not for the given number a. if x>1 if x = 1 ,a=1 if x<1…

A: we have given function     we need to determine the continuity at a=1

Q: Construct a function that is undefined at points 2,3 and T.

A:

Q: Use this information to answer parts a and b. - express N as a function of t.

A:

Q: From a 12-cm by 12-cm piece of cardboard, square corners are cut out so that the sides can be folded…

A: Please refer the attached image for complete solution.

Q: please solve it and show yor work

A:

Q: From a 12-cm by 12-cm piece of cardboard, square comers are cut out so that the sides can be folded…

A: The length side of the box is 12-x-x =12-2x cm So the area of the box is (12-2x)2 cm2 Here height of…

Q: Find the domain of the function.

A: Consider a function fx. The domain of the function is the set of all values of x for which fx is…

Q: In what degree of homogeneity is the function x + 4y

A: The given function is x+4y To find: degree of homogeneity of the given function.

Q: Differentiate the following function with respect to X : F(X,Y) = x8 y9 In (6 x4 Y + 5 x2 + 9 X + 6)…

A: Given,           FX,Y=X8Y9ln6X4Y+5X2+9X+6+9X8

Q: Evaluate the piecewise function at the given values of the independent variable. x2-4 if x#2 h(x) =…

A:

Q: Given the function f(x) = -, calculate the difference quotient X f(x) = f(a) x - a

A:

Q: Evaluate the piecewise-defined function. f(x) =    x − 4   if  x &lt; 1 x2   if  x ≥ 1…

A:

Q: Compute the difference quotient f(x+h)−f(x)h for the function given below. f(x)=−2x2−3x+1

A:

Q: Evaluate the given piecewise function at the given points 2x +1, x 2 1 f(x) = %3D x2 +3, x< 1 at…

A: We need to find value of f(-2) and f(6) for piecewise function

Q: A function is defined as: (-1 for - 3<x< 0 %3D +1 for 0 < x < 3

A: Given, f(x)=-1    for  -3≤x&lt;0+1    for    0&lt;x≤3 Given function is a piecewise defined…

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.