n open rectangular box with a volume of 12m^3 has a length that is 5 times the width. Express the surface area of the box as a function of the length of the side of the base, x.

Q: (b) Evaluate [x² sin(x³) dx using substitution technique.

A: Substituting t as

Q: Write each of the following principal values in Cartesian form (i.e., in the form a + ib where a, b…

A:

Q: 24. f² (2x − x³) dx

A:

Q: Given u (2) = 6, u' (2) = 4, v(2) = −3, v' (2) = −5. Find d (u(x). dxv(x) Evaluated at x = 2.

A: Use the quotient rules of the derivative

Q: The derivative of y = 4cosxsinx is: ○ a) yl= 4(1 — 2 sin² x) b) y/= -4 sin x cos x c) dy = 4 sin x…

A: To determine the derivative of the following function.

Q: 2. Determine the derivative with respect to x of: a) f(x)=12* - 60

A:

Q: x - 27 lim x 7x + 4

A:

Q: S dx x√16x²-5

A: Let I is the value of given integration.Therefore I=∫1x16x2-5dx

Q: Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve.…

A:

Q: 19.) Find the indicated of 0. exact value of the trigonometric function CSC =-9/8, is in quad III 7…

A:

Q: Find the exact length of the polar curve described by r = 6e-0 32 -π ≤ 0 ≤ 5π. on the interval 2"

A:

Q: Sketch the curve given by the pair of parametric equations over the given interval x = 4 cost, y = 2…

A:

Q: what type of a calculus calculation is this?

A:

Q: Find the limit of the Limit: sequence an = (4n+ 1)! If the limit does not exist, type "Diverges" or…

A:

Q: h³ - 27 lim h-3 h-3

A:

Q: Question 4 a. Let f(x,y) = x² + 2x + 2xy + y² Find f(1, 2) and f(0,0)

A: Note:-Since you asked multiple question, according to our policy we can solve only first question…

Q: Consider the following limit. lim Ax+0+ 8 x + Ax Ax 8 X Simplify the rational expression as much as…

A: This question is related to right hand side limit

Q: Express the set in interval notation. 3 Select one: O a. [3,9) O b. (3,9] O c. [3,9] O d. (-∞,3) 9

A: The number line represents the solution  the aim is to find the solution in interval notation

Q: √x f(x) = {3-x b) lim f(x) = Evaluate the following limits without graphing the function. a) lim…

A:

Q: 1. 3 [x² x³√x² + 1 dx

A: 1. Given thathere need to substitute

Q: Consider the equation 4x - 9y = 18 A line parallel to the above line would have a slope of A line…

A:

Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

A:

Q: What is the area of the region bounded to the right by x = -y²+2 and to the left by x = y²? 5432-…

A:

Q: Find the annual percentage yield for an investment at the following rates. (a) 7.1% compounded…

A:

Q: X Sketch of f(x)= ƒ(x) = -√²-4

A:

Q: 22. √₁² (x² – (2 (x² - 4x + 2) dx

A:

Q: A region bounded by f(y) = √y, y = 4, and x = 0 is shown. What is the volume of the solid formed by…

A:

Q: Q3: Solve the differential equation by the Laplace: (choose one) 1. y" - 3y' + 2y = 16e³t 2. y" +…

A: Note : as per guidelines we support only first question.kindly repost next question.

Q: Explain why the function is discontinuous at the given number a. (Select all that apply.) x2 - 2x x2…

A:

Q: A region bounded by f(x) = x + 3, y = 1, x = -1, and x = 2 is shown. What is the volume of the solid…

A:

Q: Determine the Cartesian equation of each of the following planes: a. through the point P(0, 1, −2),…

A: Solving the problem

Q: Determine the Cartesian equation of each of the following planes: a. through the point P(0, 1, −2),…

A:

Q: You reach the communication device and are alerted by your computer that the communication device is…

A: Let's consider a curve  y=f(x), such that point P(xi,yi) satisfy the curve, then slope of tangent at…

Q: Applying implicit differentiation, find the derivative of the function 1/x + 1/y = 1

A: Given :  1/x + 1/y = 1

Q: 3 = (2x³ + 4). 3. Find the equation of the tangent line when x = -3 for the function f(x) =

A: given f(x)=(2x3+4)3

Q: If $17700 is invested at an interest rate of 6 percent per year, find the value of the investment at…

A: The compound interest formula A=P1+r100tA= final amountP=principle valuer=the rate of interestt=time…

Q: Given the geometric sequence: 36, 4, 0.444444444444444,... Find an explicit formula for an. an =…

A: We have,Sequence: 36 , 4 , 0.4444

Q: The Ninth Gate You arrive at the final gate, which leads into a building-like structure. You hope…

A: We need to find derivative and rearrange then in order.

Q: Upload a picture of your full solution in one file and attach it to this question. Determine the…

A: "Since you have posted multiple questions, we will provide the solution only to the first question…

Q: 2 7 sin 8-cos 0 Enter your answer in slope-intercept form by filling in the boxes. Enter values so…

A: The equation in polar coordinates isTo determine: The equation in rectangular form.Relation between…

Q: b. through the points (3, 0, 1) and (0, 1, -1), and perpendicular to the plane with equation…

A: (B) we can use the cross product of the direction vector…

Q: -x + y -z = −17 2xy + z = 3x + 2y + z = (x, y, z) =

A: -x+y-z=-17......(1)2x-y+z=24......(2)3x+2y+z=16......(3)

Q: A particle that moves along a straight line has velocity v(t) = t²e-8tm/s after t seconds. This…

A:

Q: Suppose that a savings account pays an effective rate of interest of 10.2 percent. What is the…

A:

Q: Graph the function and find the limit (if it exists) when x approaches 2. [2x + 1, x < 2 x + 3, x ≥…

A:

Q: Let f (x) = ln (1 + x + x² + x³) and ∞ n=0 Cnxn be the Taylor series of f at x = 0. Then the value…

A: Taylor series:- Taylor series or Taylor expansion of a function is an infinite sum of terms that are…

Q: If an object's position over time is given by the function d(t) = (t² + 2)e on what interval is the…

A:

Q: Given the region bounded by the graphs of y = In x, y = 0, and x = e, find the following. (Round…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Find the area of the region under the given curve from 1 to 6. x² + 5 7x - x² y =

A: The given curve is

Q: Determine whether the improper integral diverges or converges. 3 √x(x + 5) 1.0⁰ dx

A: