If y = sin(6x), then dy is equal to which of the following? dx -6cos(6x) O-1-cos(6x) O cos(6x) O 6cos(6x)

Q: (b) A water tank is shaped like an inverted cone with height 8 m and base radius 1 m. If the tank is…

A:

Q: Complete the square and find the indefinite integral. (Remember the constant of integrati √…

A: The given integral is

Q: 1. Evaluate the given integrals. d. S₁x²99 dx √₁ (3x² - ¹) dx f. ³₂ (x³ - 2x + 3)dx e.

A: To evaluate the following integral.

Q: Sketch the graph of the following functions. State the domain and range. y = 2√√x+3

A:

Q: Find the Maclaurin series for the function. (Use the table of power series for elementary…

A: To find the Maclaurin series for the following function.

Q: f(x) = Cos (3x) as a 6th degree polynomial centered at x = 0. Hint use the following: P₂(x) = ƒ(0) +…

A:

Q: Determine each feature of the graph of the given function. ƒ(x): 2x² + 8x + 8 x + 2 Answer Attempt 1…

A: To determine the features of the graph of the following function.

Q: Find the series solution first 8 terms. about an appropriate point. Write down the

A:

Q: c. (18,-11,9,8) d. (18,11,9,-8) 2. x = (-1, -2,-2), u = (0, 1, 4), v = (-1, 1, 2), and w = (3, 1,…

A: since you have posted multiple question in this question which are not interlinked so i have solved…

Q: A random variable has CDF given by F₁ = JA i = 0, 1, 2 1 i = 3 if A = 0.81, then what is p3? Round…

A:

Q: 1. Find the Taylor polynomials of orders 0, 1, 2, and 3 generated by f at a. a) f(x) = e²x, a = 0 b)…

A:

Q: Find the volumes of the solids generated by revolving the regions bounded by the graphs of the…

A:

Q: 4) Decide whether the following sequences converge or diverge and why a) {1, 0, 1, 0, 1,....}

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: 2sin ¹(x + 1) + C

A:

Q: Let z = tan² (3x²y2²). Find Vz. O Vz= 12xy² tan (3x²y²)sec² (3x²y²)i + 12x²y tan (3x²y²)sec²…

A:

Q: The number of different mammal species observed along a transect through a forest is a random…

A: We have been given -We have to find the expected value of the random variable X.

Q: Question Find ∫−2xlnxdx using integration by parts with u=−2lnx and dv=xdx. Give only the…

A: The objective of the question is to find the integral of the function -2xlnx using the method of…

Q: Find the arclingth of A) r(6) = 4cos (0) OS OS T ... B) / X (²) = +²+1 2 y(t) = 2³² +2 1≤t≤ 3

A:

Q: Evaluate: ΣΣ 1041

A:

Q: The temperature at point (x,y) on a metal plate is T(x,y)=400x² - 400xy+100y². An ant on the plate…

A:

Q: Determine the total charge transferred Over the time interval of o≤t ≤2 see when i(t) = 4e-0.3t че…

A:

Q: The region R is a triangle with vertices (-1,0), (0,1) and (1,0). Draw the region then set up the…

A: The region R is a triangle with vertices (−1,0),(0,1) and…

Q: What is the present value of a savings bond with a 7.8 percent APR compounded continuously if it is…

A: The objective of this question is to find the present value of a savings bond that is compounded…

Q: -3 -2 -1 y (-2.0) and (2.4) 2- 1- O 1 2 3 t X Graph of f' The graph of f', the derivative of the…

A: Consider

Q: d (cot x) = da A) B C D - tan x - sec²x tan x -csc²x

A:

Q: 3. Use the limit definition of the derivative to find the derivative of the functic a) f(x) = 2x² +3

A: The given function is The limit definition of derivative

Q: Determine whether the following series converges or diverges. Hint, write as a sum of rational…

A: The given series

Q: Use Lagrange multipliers to find the maximum and minimum values of f(x, y, z) = xyz subject to the…

A: The given function is Let

Q: Which of the following are Taylor series representations of f(x): Check ALL that apply 0 Σ(-1)" n=0…

A: ,

Q: Find dy dx given that y = x¹-x

A:

Q: Find the interval of convergence of the series. (x - 2)n (-1)" (n+1)².57 n=0 O [-1,5) O (-1,5] O…

A:

Q: Let R be the relation on the set of ordered pairs of positive integers such that (a, b)R(c,d) if and…

A:

Q: Assume f(3) = 0, f'(3) = 6, g(3) = 1, and g'(3) = 3 f(x) g(x)* Find h'(3) given h(x) = A. -2 B. 2/2…

A: Given,

Q: Graph the following function: 3π ( 2 ( x + ³/4)). y = 3 sec 2 - 2 -

A:

Q: Set up an integral to find the area of the region above y = x² - 4x and below y = 2x ○ ſ₁¹ (2x − (x²…

A:

Q: y = 4 (x + 2)²¹ (0, 1)

A: Given that the expression

Q: Let g be the function given by g(x) = lim cos(a+h)-cos. What is the instantaneous rate of change of…

A: The given function is

Q: [s sin x cos x esin²x+dx = A B C D - sin x cos x esin²x+ esin²+ + C 1/2 (sin ²x + 7) + C e -…

A:

Q: Use the law of sines to find the indicated angle(theta). Assume c=30. A=120(degrees),…

A: Given some values of angles and the length of a triangle.

Q: 12 Find equations of all lines having slope - 3 that are tangent to the curve y = X-7

A:

Q: Use the intermediate value theorem to determine whether the function f(x)=x²+2x-4 has a root or not…

A:

Q: 9. Evaluate the integrals. a) f(3x² + sec² 2x) dx

A:

Q: 2. Use l'Hôpital's Rule to evaluate the following limit. a) x→∞0 d) lim f) g) h) x³-1 x-1 4x²-x-3…

A:

Q: Use the approximate doubling time formula for the case described below. Discuss whether the formula…

A: Gasoline prices rise at 0.5% p.m

Q: For what value of a is the following function continuous at every x? a²x+8a, x≥2 10, X<2 f(x) =…

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

Q: 12. Find the Taylor polynomial of degree 3 for the given function, centered at the given number a:…

A:

Q: Find a formula for the general term an of the sequence assuming the pattern of the first few terms…

A:

Q: c) y = sin 53x e) — (In|sin x) d) Find s" (t) for the function. s(t) = 3t² + 5e f) y = sin-¹(x² - 1)

A: To differentiate the following and to simplify.(c) To find .(d) To find  for the function.(e) To…

Q: valuate ∫10xlnxdx using integration by parts with u=10lnx and dv=xdx. Give only the function as your…

A: The given integral is

Q: √3 j. (t+1)(t² + 4)dt 1/2 (27-12) du k. 1. 1v5-2y dy y3

A: Since you have posted multiple subparts question in this question and as per company guidelines i…