The average value of a function f(x, y) over a region R is the value 1 AV (f, R) //. f(x, y) dA. Area(R) Find the average value of f(x, y) = x sin xy over the region R = [0, 1] × [0, 1]. %3D

Q: 10203040-10102030405060-10 You are a lifeguard and spot a drowning child 40 meters along the shore ...

A: Follow step 2 and 3.

Q: The profit in dollars from the sale of x expensive watches is P(x) = 0.06x – 3x + 7x° -5000. 0.7 Fin...

A:

Q: Write the equation of the sphere if (1, – 2, – 5) and (– 1, – 2, 7) are the end points of a diamter ...

A:

Q: the ratio d/dx 8csc(x)/csc(x)cot(x) is a constant number. Its value is

A:

Q: Given revenue and cost functions R(q) = 90q - 0.4q and C(q) = 15q + 600, find the maximum profit tha...

A:

Q: 8. Find the value of p for which the series 2n Inn (In (In n))" is convergent. n=3

A: the given series,        ∑n=3∞1n ln n.lnln n p

Q: dx (25 – x2)3/2

A:

Q: The position of a car traveling along a highway is given by the function s(t) = 21² – 2t where t is ...

A: Position function iss(t)=2t2-2tThen acceleration is given  bya(t)=s''(t)

Q: Given: B 2 30° V3 A AC = O1 O 1/2 O V3/2

A:

Q: p. Based on your table in part (a), complete the following statements. i. As x → – x, f(x) → - Previ...

A: b) i) As x tends to -infinity , f(x) tends to 0 .  as 1/-infinity =0

Q: Determine the derivative of f(x) = In(18 x4+4 sin(5 x5)) with respect to x. f '(x) =

A:

Q: Consider the function on the Interval (0, 2x). f(x) = 4 sin? x + 4 sin x (a) Find the open interval(...

A: We will have relative maxima when the derivative changes sign from positive to negative. And for rel...

Q: 7.2. +4 7.2. 1- 'y'+ 16

A: Using integration formula,

Q: Consider the function on the interval (0, 2x). (x) = 4 sin? x + 4 sin x

A:

Q: Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answ...

A:

Q: Find the limit of the sequence, using L'Hôpital's rule when appropriate. n2 8n

A:

Q: 2. Find five arithmetic means between 12 and 21-6.

A: let a1=12 the five arithmetic means be named as a2,a3,a4,a5 & a6 a7=21.6since it is arithmatic s...

Q: The height of a cone is decreasing at a constant rate of 3 centimeters per minute. The volume remain...

A: V=13πr2hSubstitute V=52 and r=6 into the above equation52=13π(6)2h h=52×336πh=133π cm

Q: Question dy dy du dy by using Leibniz's notation for the chain rule: dx Given y = f(u) and u = g(x),...

A: We will find the derivative of y by using Leibniz's notation as shown below

Q: Sketch the parametric equations by eliminating the parameter. x = sec(t), y = tan(t) y y 4 4 2 X -4 ...

A:

Q: 3) The volume under z = xy and over [0, 1] X [0,1]. 2 decimal places

A:

Q: 5 cos(30). curve r = Set up an integral for finding the area that it encloses. de

A: We have to find the area of the curve

Q: Suppose f(x) = – 0.5 · x² + 3 graphing calculator (like Desmos function f. a. Determine the interval...

A:

Q: Use the formula for the binomial series: m(m–1)---(m-k+1),★ + k! m(m-1) 2! m(m-1)--(m-k+1) „k if k=1...

A: expansion through maclaurin series .

Q: Determine whether the series converges, and if so find its sum. If the series diverges, indicate tha...

A:

Q: 9. Evaluate W(1 +a, r, r?) (a) -2 (b) -2r (c) 2r (d) 2

A:

Q: Determine if the graph can represent a polynomial function. If so, assume that the end behavior and ...

A: topic- polynomials

Q: emine whether the series is convegent or divergent. If it an=lo00,evaluate lim Can) Cos M8

A: We have to find the value of the given limit according to the given information

Q: Find the midpoint of the line segment with the given endpoints (-7,- 1)and (- 3,- 2) The midpoint is...

A: The midpoint of the line segment with the endpoints (x1,y1) & (x2,y2)is given by: x1+x22,y1+y22 

Q: Given cost and price (demand) functions C(q) = 110g + 41,000 and p(g) = - 2g + 870, what is the maxi...

A: Basic application of derivative problem

Q: 4) Verify the identity using the definitions of hyperbolic functions. e2x + 1 e2x – 1 coth x

A:

Q: Answer the question below: A gift from an organization is wrapped in a box provided that the sum of ...

A: This is the problem of maxima and minima of the function. By using lagrange multipliers we will solv...

Q: 9. What is the parent function of f (2)? What transformations have taken place, to get from this par...

A:

Q: Let f(x) = 2tan(x)/x. Find the following: f'(x)= f'(4)

A: We have to find the derivative and its value at x=4.

Q: Use the ratio Un+1 to determine if the sequence an is strictly increasing or strictly decreasing. 2n...

A:

Q: Let M = y? + xy³ and N = 5y² – ry+ y³ sin y ƏM =? 9. dy (a) 2y+3ry? (b) 2у — Згу? (c) y²x+y³ (d) y²r...

A: Given:   To determine:

Q: c. Let h(x) 5x2. Determine the roots of h, as well as the x-value of the vertex of the graph of h. i...

A:

Q: Answer the given DE below: x (dy/dx) +y=y^2

A:

Q: 6. Which of the following equations is an exact differential equation? (a) (x² +1)dx – xydy = 0 (b) ...

A:

Q: 2. The equation y² = cx is the general solution of which of the following differential equ tion? dy ...

A: y2 = cx ...(1)c=y2x ...(2)differentiating w.r.t.  x;2y dydx= c (1)dydx=c2ydydx =12yy2xdydx =(y2x)

Q: Determine the end behavior of the graph of the function. m (x) = -2(x-2)(3x+1)°(x+4)* As x→-00, m (x...

A:

Q: b. Suppose g(x) = 969 – 0.9x³. - i. What monomial expression best estimates g(x) for very large valu...

A:

Q: Use sigma notation to write the Taylor series about r = xo for the function. In x; xo = 1 %3D Σ k =

A:

Q: Find the Taylor polynomials of orders n = 0,1, 2, 3, and 4 about x = x0 and then find the nth Taylor...

A:

Q: Suppose the function g is defined as g(x) = Fill in the following blanks. f(x) (Note: if g(x) increa...

A: The g(x) function is defined as g(x)=-5f(x) ........................................... (1) and the ...

Q: | tan x sec* x dx

A:

Q: 1 we, ON =? - м ду dx 3 (a) 3 (b) (c) 3y (d) —Зу - --

A: Topic = Derivative

Q: Given Cost and Revenue functions C(g) = g° - 9g + 56g + 5000 and R(g) = - 3g + 2500g, what is the mi...

A:

Q: 4. Which of the following represents the differential equation of the family of parabola having thei...

A: Follow the procedure given below.

Q: Given f(x) = 3x+22x-3x-70, answer the following. Part: 0/2 Part 1 of 2 Factor f (x), given that -2 i...

A: