If a box with a square cross section is to be sent by a delivery service, there are restrictions on its size such that its volume is given by V = x2(54 − 2x), where x is the length of each side of the cross section (in inches). What restrictions must be placed on x (the domain) so that the problem makes physical sense? (Enter your answer using interval notation. If V is not a function of x, enter DNE.)

Q: How can I explain what it means for a function f(x) to be O(1)?

A: The 'f(x) to be O(1)' is to be read as function f(x) is of the order of 1.  Now refer to step two to…

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

A:

Q: Find the local and absolute extremum for the functions over their domain: x²+2x-3 4. f(x) : x-2 ||

A:

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

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

Q: Suppose that f(x) is a differentiable function and g(x)=(x+2)/f\x). If f(0)= 22 and f(0)=5, then…

A:

Q: Suppose that f is a function given as f(x)=x3+bx2+cx−4 Find the exact values of b and c if we know…

A: Given: fx=x3+bx2+cx-4   and tangent line y=36x+68

Q: It was determined that the number of prey consumed by a predator over a period of time was a…

A:

Q: The graph of f (x) = |x| is reflected over the x-axis, shifted vertically up 1 unit, horizontally 3…

A: This question is based on transformation of graph.

Q: When a function is discontinuous at x=2, does that necessarily mean that 2 is not in the domain of…

A:

Q: It was determined that the number of prey consumed by a predator over a period of time was a…

A:

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

A:

Q: Juanita wishes to have a rectangular garden in her backyard with an area of 64 ft2. Letting x denote…

A: we know that area of rectangle =  length × width

Q: On what domain is the function f(x) = – 4+ V3x – 6 continuous? %3D

A: The function is a square root function and hence, the function is continuous in the domain.

Q: Find the tangent line of the function f(x) =16/x− 4√x at x = 4, and the point at which the tangent…

A:

Q: Find the local and absolute extremum for the functions over their domain: 5. f(x) = vx2 + 8x + 20

A:

Q: Find the local and absolute extremum for the functions over their domain: 1. f(x) = x2 – 6x + 8

A: Given

Q: Find a function f such that  f '(x) = 5x3  and the line  135x + y = 0  is tangent to the graph of…

A: Consider the given derivative function f'x=5x3

Q: Find k such that the line is tangent to the graph of the function.

A: The function is given as fx=kx......(1) The line is given as y=x+4......(2)

Q: Which of the following is the x-coordinate of a relative extremum of the function f(x) = = Arct…

A: We will use first derivative test to determine the extremum of the function.

Q: For the function f(x), defined graphically, state the value(s) of x where the function is not…

A:

Q: 2. Use the graph of the function f(x) to estimate where (a) f'(x)= 0, y f(x) (b) f'(x) 0.

A: (a) f'(x) =0   => the slope is zero, it means when the graph is parallel to x-axis  i.e. at…

Q: For this function Y=x^3 + 15x^2 -225x prove that we have a point of inflection at x=-5

A:

Q: A major car company analyzes its revenue, Ríz), and costs Cx), in millions of dollars over a…

A: The revenue function and the cost function is given as:…

Q: 5. Determine the area of the largest triangle that can be formed in the first quadrant by the…

A: The area is found by making a function of area into a variable and finding the values at which…

Q: 1 Find the distance between the two values of x at which the function is discontinuous. x²-3x + 2

A: The function given is ,f(x) = 1x2-3x+2f(x) is discontinous when,x2-3x+2 = 0Using quadratic formula,x…

Q: Find the global extrema of the function f(x)=x4−2x2−1 on [0,+∞).

A: Given function is Differentiating both sides with respect to x, we get Now, we will find critical…

Q: Show that the function is discontinuous on R. f(x) = { 1; 0; for x € Q for a Q

A:

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

A:

Q: On what domain is the function f(x) = 3x + 5x + 6 continuous?

A: The given function is, fx=3x2+5x+6

Q: What happens to the function f (x) = 1 + as x approaches to zero.

A: The definition of the function gx=x is given by, gx=x for x≥0=-x for x<0 Thus, the left hand…

Q: given that the graph of f(x) passes through the point (10,9) and the slope of its tangent line…

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Q: Find the function whose tangent line has the slope 3x² + 1 for each value of x and whose graph…

A:

Q: If x is large, which function grows faster, f(x) = 2x or g(x) = x2 ?

A: Given,            fx=2x or gx=x2To find : if x is large, then which function grows faster.

Q: X+1 5) Is the function given by f(x) x2 - 8x + 15 continuous at x = 3? Why or why not?

A: f(x)=x+1x2-8x+15

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

A:

Q: Determine whether the function is differentiable at x = 2.

A: The given function is fx=x2+1,x≤24x-3, x>2. Sketch the graph of the above function as shown…

Q: Find the slope of the tangent line to the graph of the given function f (x) = 4x³ at the point (2,…

A:

Q: Determine an equation for the line tangent to the graph of the given function at the indicated point…

A:

Q: Consider the function f(x)=(x+1)(x–1)2, At what value of x will the graph of f cross the y-axis?…

A:

Q: There is a bacteria cell in a Petri dish that is reproducing at a rate of              r(t) = 2t^2+1…

A: Solution:

Q: Determine if the following piecewise-defined function is differentiable at the origin. 4x - 4x° -…

A: Solve the following

Q: Differentiate the following function with respect to x for y=2e^3x + 8e^9-2x .

A: Given equation is y=2e3x+8e9-2x Differentiate with respect to x.  then,

Q: Find all the values of x where the graph of f(x) = 2x³-36x2 + 192x 9 has a horizontal tangent line.…

A: topic - derivative of a function and point of horizontal tangent line

Q: Find the equation of the tangent line to the graph of the function f(2)=√1026 +26 at the point…

A:

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

A:

Q: Express the area A of a right triangle as a function of the height h if the base of the triangle is…

A:

Q: Find the line tangent to the function at the indicated point: f(x) = v8x² – 4x ;x = 1 ОУ-12х-10 o…

A: Since there are multiple questions present and you have not specified which question to answer,…

Q: 3 Show that the function f(x) = Vx – 5 is one to one function.

A: The given function is: fx=x-53

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

A: Given:  From a 12‐cm by 12‐cm piece of cardboard, square corners are cut out so that the sides can…

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.