A piece of cardboard measuring 14 inches by 9 inches is formed into an open-top box by cutting squares with side length x from each corner and folding up the sides. Find a formula for the volume of the box in terms of x V(x) = Find the value for x that will maximize the volume of the box X =

Q: The graphs of f and g are given. Use them to evaluate each limit, if it exists. (If an answer does…

A:

Q: 7. Thirty two teams join a beach volleyball league. The league is split into four divisions where…

A: How many games should be scheduled in total for the league??

Q: Given F(x) below, find F'(x). et -1₁° 0 F(x) = (1³ + 7) dt

A:

Q: 2√ty' =√1-y²

A:

Q: Find the first four derivatives of the following functions: 1. y = 4x³ + 12x² + 7x 2. y = 2x5 + 6x²…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: T Express the surface area of the surface obtained by rotating the graph of y = 4 sin (x) for 0 ≤ x…

A: Recall: Surface area SA=∫ab2πy1+dydx2dx We have, y=4sin(x), a=0, b=π6

Q: Given the function f(x)= = Find the difference quotient Find f'(x) by determining lim f(x +h)-f(x) h…

A:

Q: Differentiate f(x) = (a-x)(a + x) with respect to x. Assume that a is a positive constant. f'(x) =

A: Solving the problem by finding the value of the differentiation.

Q: Let f(x) = 2x² -5x - 7. Expand and simplify: f(x +h)-f(x) h =

A: The answer is given below:

Q: Find the area of the region enclosed by the curves y=2 sin x y = 2 sin x and y=2 sin 2x for 0≤x≤ T.…

A:

Q: Let h(x) = tan(3x + 4). Then h' (2) is and h'' (2) is

A: The function is given by hx = tan3x+4 To evaluate: The values of h'2 and h''(2)

Q: Find the constant a such that the function is continuous on the entire real line. f(x) = √5x², x ≥ 1…

A: We need to find a.

Q: - x² - 6x - 1. Suppose that f is a function given as f(x) Simplify the expression f(x + h). f(x + h)…

A: see below the answer and calculation

Q: 1. (x+y)dy +(x-y)dx=0

A: Given: (x+y)dy+(x−y)dx=0 ⇒dydx = -x+yx+y   ...(1) To prove: Given differential equation is…

Q: Given the equation y The amplitude is: The period is: The horizontal shift is: The midline is: y = =…

A:

Q: Find F(s). ℒ{e−8t cos(6t)}

A: To find the laplace transform of the given function.

Q: rodal Multiple Choice Questions 1. Using all the letters in the word CANDYCANE, determine the number…

A: We have to find out solution

Q: Find the derivative: y = ln (3x + 1) O y = O y = Oj = 2 y = = 2ln(3 + 1) (3x + 1) 6 (3x + 1) 3 (3æ +…

A:

Q: ormation to answer the next question. The graph y = f(x) has undergone one reflection and one…

A: The given function y=f(x) undergoes 2 transformations to map the graph of y=f(x) on to the graph of…

Q: Find the transition points. y = 3x - 3x² In(x) (Use symbolic notation and fractions where needed.…

A:

Q: A street light is at the top of a 13 ft tall pole. A woman 5.75 ft tall walks toward the pole with a…

A: Given problem:- street light is at the top of a 13 ft tall pole. A woman 5.75 ft tall walks toward…

Q: Find dy/dx for: y cosy = xy Y O -y sin y+cos y-x Y cos y-x Y -y sin y-x 1 cos y-x O O O

A: Given :y cosy= xy

Q: Determine if the function f(x) is continuous and/or differentiable at x = 5? x+5 for 5≤x≤5 f(x)= 2x…

A:

Q: Solve the equation |2x - 3| = 0 Rewrite |2x - 3| using the definition of absolute v

A: Topic:- algebra

Q: Evaluate lim 00 0-1/1/201 O None of the choices ¹ 0-1/201 O 14 tan z 1 x cos x

A:

Q: along the line AM WI a magnitude of midpoint of the vertical side OB of the parallelepipe Express F…

A:

Q: Given that f(x) = x³h(x) h(1)=2 h'(-1)=5 Calculate f'(-1).

A:

Q: Find f(t). ℒ−1{9s / (s - 4)2}

A:

Q: Verify that the indicated function y = p(x) is an explicit solution of the given first-order…

A:

Q: Prove lim x-a 4x 4a, using the ɛ, 8 definitions of limit.

A: The given limit,   limx→a4x=4a

Q: A graphing calculator is recommended. (a) Find the vertical asymptotes of the function y = X = (b)…

A: Explanation of the answer is as follows

Q: Use a graphing utility to graph the equation. Use a standard setting. y = x2 + x − 12   Approximate…

A: The given function y=x2+x-12

Q: Use a linearization to approximate tan(π/100).

A:

Q: Evaluate the integral. (Use C for the constant of integration.) x² - 16 dx +8

A: We have to find the integral

Q: xample following flow field: Find the acceleration u= 2x² + 3y, v=-2xy + 3y² + 3zy, w= at a point…

A:

Q: Find f'(x): f(x) = sin(2x) O 4sin (2a) (2 ln 4) cos(2x) O 4sin (2x) (2 cos(2x)) O 4sin (2x) (In 2)…

A:

Q: Use a graph of the function to estimate the slope of the tangent line at P. (This slope represents…

A: It

Q: What function do you know from calculus is such that its first derivative is itself? (Do not use the…

A:

Q: 1) (4x + xy²)dx + (y + x²y)dy = 0_2) y' - 2y = 5 3)xxx + y = x

A:

Q: f5(x³ + x)⁹ (3x² + 1)dx O 5(x³+x) ¹0+C 10 (x²³+x) ¹0 10 +C O 45(x³ + x) +C O(x³ + x)¹0+C

A:

Q: f(x+h)-f(x) h Use f'(x) = lim h-0 s(x) = 6x+7 to find the derivative at x for the given function.

A:

Q: en the following total revenue (TR) and total cost (TC) functions for a firm, TR = 5820Q +4Q² − 2Q³…

A:

Q: Solve the following equations for a a. az+b cx+d = A b. √₁+x+√₁+z=0 ar c. a²x² - 6² = 0

A:

Q: x and y are functions of a third variable t. If √√x + √= 5 and dt = 2, find when = dt 1

A:

Q: What is the area bounded by the curves y=x2+5 and y=−x2, the line x=3, and the y axis.

A: Topic:- application of integration

Q: Given z=x²y+3xy, x=sin(2t), y=cos(t), find dz/dt when t=0

A: ddxcosx=-sinx

Q: Show that a right triangle is formed by points ?(3,1,-1), ?(5,3,6), and ?(3,-5,0). If it does not…

A:

Q: Its tot as TR = 300q - 6q² and its total costs as TC = 4q². a) Determine the optimal quantity and…

A: Given

Q: Convert the angle 270° to radians. Give the exact value and use pi for .

A:

Q: Show that the operators T and T₂ from 2 R² into R² de fined by T₁: (F₁) √₂ ) → (9₂9₁) and T2=…

A: