A rectangular box with an open top has a square bottom and a volume of 4 m³. Find the dimensions of the box that will result in it having the smallest possible surface area. Width of Box: m Height of Box: m

Q: Find the indefinite integral. J. x cos 107Tx2 dx

A:

Q: Find the derivative of the trigonometric function. Re) = e® sin(e) f (e) = -1

A:

Q: Practice: Find the volume of the solids generated by rotating the area bounded with the given functi...

A:

Q: Find the exact value of each expression, if it is defined. Express your answer in radians. (If an an...

A: Given query is to find the value of indicated angles.

Q: An+1 to determine if the sequence An is strictly increasing or strictly decreasing. Use the ratio 5n...

A:

Q: Find the derivative of the function. f(t) = 8r2/3 - 4t/3 + 8 f '(t)=

A:

Q: A Complete the table. du formula answer 24x+2 1. (2x-1)(3x+2) 2. -dx de 3. 4-S 4-3inin2r 4. xp- sin ...

A:

Q: Use sigma notation to write the Taylor series about x = xo for the function. 10 In x; xo = 1 k =

A:

Q: find the function y(x) satisfying dx/dy=5x ^(-6/7) and y(-1)=-2

A:

Q: Make a 1 rational equation problem involving 3 rational expressions with binomial term with solution...

A: We have to form a rational equation problem such that it contains 3 rational expressions and each ex...

Q: cot 2x J Vcot 2x – 15

A: Given,           ∫cot2xcot22x-15dx

Q: Determine the following equation if it is Homogeneous IVP, First, second, higher order equations and...

A:

Q: 3. Is the function given by Sx-4x-5, メ<5 X-5 2. continccus at x =52 Why ar whynot ?

A:

Q: Solve using the U-Technique Question 12 Consider ) x(1+v) dx and using u-substitution in rewriting t...

A:

Q: Write the first five terms of the sequence: +00 {Vn² + 10n – n}-1 n=1 Determine whether the sequence...

A:

Q: (х + 2) dx (x + 3) sin y cos y dy In(x + 3) sin? y + C - ans. 2 2.

A:

Q: (x – h)? + y? = r² O y " +(y')² + 1 = 0 O y" +(y')² = 0

A:

Q: #1 only

A: Topic:- differential equations

Q: Given: ((x)dx Evaluate f(v2). There is a function f(x) such that when u = -x³, the resulting integra...

A:

Q: m+2m Consider J dm. If we letu = m+ 1, what will be the resulting integral as a function of u? In(u)...

A:

Q: Q9

A:

Q: Find each limit in Problems 37-60. Note that L'Hôpital 's rule does not apply to every problem, and ...

A:

Q: x² + y? = r2 O y = - y' = - y

A: topic - differential equation

Q: Consider the integral 2h* g(x) dx. There is a function g(x) such that when Inx the resulting integra...

A:

Q: asap

A: We will verify the differential equation 

Q: Find the indefinite integral. (Use C for the constant of integration.) 4 cos(0) – 1 OP

A:

Q: Find the indefinite integral. (Use C for the constant of integration.) xp J xV81 - (In x)²

A: topic ,- indefinite integral

Q: 19. A rock thrown into a still pond causes a circular ripple. If the radius of the ripple is increas...

A: Given :Radius of thr ripple increasing by 2 feet per secondCircumference = 2πr

Q: e solution to fe2* sec?(e2x+1)dx is equal to k tan(e2*+1) + C , find the exact value of k.

A: Given query is to find the value of K.

Q: Find the derivative of the function at Po in the direction of u. x- 5y g(x,y) = Ро(1, - 1), и%3 3і +...

A: To find the derivative of the function  g(x,y)=x-5y5xy+7 at P0(1,-1)in the direction of u=3i+4j=&lt;...

Q: Q4) Find dy /dx for the following functions: a) e*y = x – y b) y = (cos x)Vx

A:

Q: Q1) Evaluate the following integral using By Parts Method: y = х.In(x3 + x) dx

A:

Q: 4. If x - xy + y = 1, find y 3x a.) x-3y2 c.) d.) ay b.) 1-3y2 3y2. 5. If 3x? +2xy + y? = 1, then y ...

A:

Q: Express the repeating decimal as a fraction. 0.451141 41 41.

A: Given data

Q: ew PollCies Current Attempt in Progress Find the general term of the sequence, starting with n = 1, ...

A: Topic:- sequence and series

Q: I. Identify the elements for the following set expressions given the sets below: (Explain your answe...

A:

Q: Q5) Use the Chain Rule to express dy /dx in terms of x and y: y = csc t аnd x = sec-1t

A:

Q: 1. If x - y = 25, then y" = c.) d.) - a.) b.) 2. If y = cos(3x+1), find y a.) 3 sin(3x+1) b.) -3 sin...

A: Authoring guideline: As per the authoring guidelines, we can solve only the first three parts. Repos...

Q: When the linear differential equation is multiplied by an integrating factor the equation will becom...

A: Answer of given question is written in below steps.

Q: A Plane flies 320km due West and then 240km due North. W- ►E 320 km 240 km

A:

Q: メ+

A:

Q: Questióh 2 of 9 View Policies Show Attempt History Use the formula for the binomial series: (1 + x)"...

A:

Q: = t?y – y + t? – 1, y (0) = 1 dt dy Solve the differential equation

A: Given: dydt=t2y-y+t2-1   We know that; ∫1ax+bdx=1alnax+b+C And The Power rule: ∫xndx=xn+1n+1+C ; n≠-...

Q: Q3) Find the limit for the following function by using L'Hopital's Rule: x2. e* lim x→0 tan2 x

A:

Q: Find the indefinite integral. (Use C for the constant of integration.) 2 cosh(x) dx

A: Evaluate the integral∫2coshxxdx

Q: on 3 of 9 cies empt History Correct. y method to determine whet

A:

Q: dx 2. The linear differential equation dy r = y' has the integrating factor equal to_ 3. When the li...

A: To answer questions 2 and 4 related to the first-order differential equation. The standard form of t...

Q: If the solution to fe sec (ex**)dx is equal to k tan(e**) + C, find the exact value of k 1. 2e 2e (0...

A:

Q: Solve the initial value problem. d²y = 2 e -X, y(0) = 0, y'(0) = 4 dx

A: ∫ d2ydx2 =∫ 2 e-x dxdydx=2e-x(-1)+Bdydx=-2e-x+B ...(1)

Q: Use sigma notation to write the Taylor series about x = xo for the function. 4 In x; xo = 1

A: Taylor series of function fx at a is defined as:       fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+…=0+ddx...