If cos(t) = 1. cos(2t) 4 = 2. sin(4t) = || || = where t = [0, 90], determine

Q: Evaluate the integral using the indicated trigonometric substitution. S dx, 6x³ √x²+36 X = 6 tan(0)

A: The integral is ∫6x3x2+36dx   ; x=6 tanθ

Q: Let z = f(x,y) = 6x² - 4xy +9y². Find the following using the formal definition of the partial…

A: z=f(x,y)=6x2-4xy+9y2.

Q: Solve for 0: ❍ O # Ꮎ O Ꭿ O = = = 2 ᏗᏓ 6 " -1 3 6 51 6 -1 2 3 " 2 3 3 -1 4cos-(0) - 3 sin(0) - 1 t[…

A:

Q: A11. Given the following cost and price per unit functions below: C(x) = 149.79x² + 13722.22x…

A:

Q: Find the derivative of f(x) = ln x² sin x 2x+1

A: fx=lnx2sinx2x+1

Q: determine the absolute maxima and minima for following interval f(x) = 2x3 - 3x2 - 12x + 2 -6≤x≤5

A:

Q: Evaluate the indefinite integral. Then check your answer by differentiation. (b) √x (x² + 3) dx ()…

A: We are required to find: a. ∫1xxdxb. ∫x(x2+3)dxc. ∫2sinx+3cosxdxand then check the answer by…

Q: d d Calculate[ri(t) r₂(t)] and [r₁(t) × r₂(t)] first by differentiating dt dt the product directly…

A: We need to perform differentiation.

Q: What is the exact value of tan 5 T 12 /?

A: → let  H=tan(5π12)

Q: lim (t+Δt)2–4(t+Δt)+2-(t2–4t+2) Δt-0 ΔΕ

A: Consider,

Q: Find the exact area between y = x² and y = x for x ≥ 0.

A:

Q: III. 2. Consider the function x<0 0SAS1 (1) At what points is this function continues? (2) For each…

A: fx=1+x2, x&lt;0ex2,      0≤x≤11+x2, x&gt;1

Q: Please describe the answers step by step since it is difficult to figure it out since the answers…

A:

Q: Write the following expression as an algebraic expression. sin(arcsin x + arccos x) O z√1-z²+z √2+1…

A:

Q: Find f if f"(t) = 2et + 3 sin(t), ƒ(0) = 2, ƒ(π) = 5. f(t) = = 2e^t-3sint+ (2e^(pi) - 5)/(pi)t

A:

Q: Find the total area of the shaded region shown to the right given by the curve y=2(sin x)√1+ cosx.…

A: The curve equation y=2sinx1+cosx Graph

Q: Use the figure below to find the exact value of the following trigonometric expression. cos O cos ○…

A: we know the formula is→cos(θ2)=1+cos(θ)2

Q: Consider the function Evaluate the definite integral. f(x) = X x 3 L²₂ f(² -3 if x < 1 if x ≥ 1 f(x)…

A: Given: x     ifx&lt;11x    if x≥1 We are required to find: ∫-33f(x)dx

Q: Calculate the definite integral. 2 0 2 0 7e - 5x 7e - 5x dx = dx (Type (Type an exact answ

A:

Q: For the following vector field, compute (a) the circulation on and (b) the outward flux across the…

A: The solution is shown in step-2

Q: The expression 5 tan(x) sin(x) + 4 sec(x) simplifies to A sec(r) - B cos(x), determine A and B. A =…

A:

Q: A) The Marginal Cost function: MC(q) = B) The Marginal Revenue function: MR(q) = C) The Marginal…

A: According to bartleby guidelines we supposed to do the first three subparts of multiple subparts…

Q: Suppose that f(x, y) = x² - xy + y² - 3x + 3y with D = {(x, y) |0 ≤ y ≤ x ≤ 3}. 1. The critical…

A:

Q: Find the volume of the pyramid with base in the plane z = −7 and sides formed by the three planes y…

A: Here we have to use the concept of triple integration

Q: Cost of Producing Guitars Carlota Music Company estimates that the marginal cost of manufacturing…

A: The marginal cost C'x=0.004x+110

Q: Evaluate the integral. 3 19-x² √9-x² 19-x²-2² -√9-x²-2² 1 (x² + y² + z²)1/2 dy dz dx =

A:

Q: A The graph of the piecewise linear function f is shown above. What is the value of B -8 O -1- -2-…

A:

Q: he given vector functions are solutions to the system x'(t)= Ax(t).

A:

Q: Evaluate the definite integral. 1 S 0 30x5dx

A: let  D=∫0130x5dxformula of integration is→(i) ∫xndx=xn+1n+1+c

Q: Determine the area bounded by the curve: y=x^2-4x-5, y=0, between x=3 and x=6 y=1/4 (x^2-16), y=0,…

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

Q: For the point (r, 0), r is the [Select] [Select] [Select] directed distance directed angle from O to…

A: For the point r,0, r is the __________ from O to P and 0 is the _________ counterclockwise from the…

Q: Write the repeating decimal as a fraction. 4.17326326326...

A: We know that the formula 0.326326326......  =326/999

Q: Find the reference angle for the given angle. (a) (b) (c) -7A 9 14π 13 0.5

A:

Q: 2 A particle moves along a line with a velocity v(t) = - the particle from time t = 2 to time t = 4.…

A: Displacement equal to Integral of velocity

Q: 9. The demand equation for a certain product is p demanded for the product. =√-0.04x+8 where p is…

A: We have to find the elasticity.

Q: Find the vector equation that represents the curve of intersection of the cylinder x² + y² = 1 and…

A: The equation of the Cylinder : x2 + y2 = 1 and the equation of the Surface : z = xy We have to find…

Q: I-up-1 + u^ з (ы

A:

Q: 5. The graph shows the derivative, f'(x), of a function f(x). What do you know about f(x)? YA 8…

A:

Q: 1 dx -1 (tan¯¹ x)(1+x²)

A: We have to evaluate the integral…

Q: 1 3 rgence, using each test once. assume that all conditions to perform this test are met. Σ n=1 (a)…

A: Using one of the given test, identify which test needs to be used. “Since you have posted a question…

Q: πχ ¹ (727) ln x 37. lim tan x → 1

A: Limit of 0*inf form  We have to apply L' Hospital rule to solve the limit....go through the solution…

Q: Write the following expression as the tangent of an angle. tan 7a-tan a 1+tan 7 tan a

A: Before solving the problem , first I have written a note in which a formula has written.Just use…

Q: (d) 9 f(x) dx = = 11

A: From the given figure

Q: uestion Completion Status: If the cost of selling y yards of fabric is given by C (y) = O O 10 3y 3…

A:

Q: Let y'=2xy²; y=- 24 16-x²1 y(2)=2 Then by considering y=(x) as a solution of the differential…

A: y'=2xy2 Then y=2416-x2,y2=2

Q: 7 Use geometry to evalute S (|x-1|-3) dx 0 This solution must include. a graph of the function on…

A:

Q: The quadric surface 3z = √√x² + y² and the plane x+y=0.5 intersect in a curve. Parametrize this…

A: The quadric surface 3z=x2+y2 and the plane x+y=0 intersects in a curve

Q: The equation y= 2e65 is a particular solution to which of the following differential equations? B D…

A: An equation,

Q: Consider the graph of the function f(x): YA (a) -2 0 2 f(x) dx : = 4 5 (0) ["f(x) de = [ Evaluate…

A: To evaluate the following integrals by interpreting in terms of areas. (a) ∫02fx dx (b) ∫05fx dx (c)…

Q: What are the rectangular coordinates of the point whose spherical coordinates are (5, 7,)? X Y || ||…

A: