Solve the equation by first using a Sum-to-Product Formula. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate.) cos(4theta) − cos(2theta) = sin(theta) theta =

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Q: Consider the given function and the given interval. f(x) = (x-4)², [2, 5] (a) Find the average value…

A: a)    favg=1 b)   c=3  (smaller value)       c=5  (larger value)

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Q: Find the general solution (and particular solution, whenever possible) for the given differential…

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Q: The height, h, in meters of a dropped object after t seconds can be represented by h(t) = dropped?…

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Q: Regarding y as the independent variable and x as the dependent variable, find the slope of the…

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Q: Determine the domain of the function algebraically (use algebraic methods, not a graph). Give your…

A: The function is given by fx = 29-4x+1 To evaluate: The domain of the function algebraically.

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Q: a₁ = 3 4 r = -in 2 a₁ = ?

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Q: Find the limit, if it exists, or type 'DNE' if it does not exist. lim e√4x²+1y2 (x,y)→(4,3) =

A: limx, y→4, 3e4x2+y2Plug in the value x, y=4, 3=e4· 42+32=e73

Q: Suppose that the position of a particle is given by s = f(t) = 4t³ + 5t + 9. (a) Find the velocity…

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Q: Equations of Order One: Separation of Variables Instructions: Obtain the general solution of the…

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Q: √r 9. lim r→9 (r - 9)4

A: Concept: The definition of a limit is the value at which a function approaches the output for the…

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Q: Suppose that the dollar cost of producing x appliances is c(x) = 1200+70x-0.1x². a. Find the average…

A: Topic- Functions and application of derivatives We are given

Q: 3. Using the triangle below, if sin 0 = x then 0 = sinx. Fill in the missing side using the…

A: Pythagoras Theorem ⇒Hypotenuse2=perpendicular2+Base2

Q: Lim 6 (os (cos) 0-0 Sec O

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Q: The height of a cylinder is increasing at a constant rate of 3 inches per minute. The volume remains…

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Q: The mass of the part of a metal rod that lies between its left end and a point x meters to the right…

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Q: Suppose a² = 8, F(x) = f(x³), G(x) = (f(x))³ and: f(a) = 2, f'(a) = 6, f'(a³) = 2.

A: Topic = Functions

Q: Consider the following polynomial. g(x)= x³ + 3x² - 6x8 Step 1 of 3: Use Descartes' Rule of Signs to…

A: Given function is g(x)=x3+3x2-6x-8 We have to determine number of positive of negative real zeros…

Q: 4 Find the slope of the tangent to the curve f(x)= √√x at the point where x = The slope of the…

A: We have to find slope of tangent of curve at point x= 1/9 Topic :- Application of derivative.

Q: 1. Given a function f, (a) show (by a suitable computation, not by viewing the graph) that f is…

A: One-to-One function:- A function is said to be one-to-one if it is one-one and onto.One-one function…

Q: Let f(x, y, z) = 4xy – z², x = 5r cos(0), y = Use the Chain Rule to calculate the partial…

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Q: Evaluate the indefinite integral. (Use symbolic notation and fractions where needed.) S cos(2x)…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Find the directional derivative of f(x, y) = ln(xy) at (,) in the direction of .

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Q: Use the limit definition of the derivative to find the slope of the tangent line to the curve f(x) =…

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Q: ay Use implicit differentiation to determine given the equation x5y + cos(x) = e". dx dy dx

A: The given equation is: x5·y4+cosx=ey   As we know that; The Sum/Difference rule: f±g'=f'±g' The…

Q: In each of Problems 8 through 19, find the general solution of the given differential equation. 8. y…

A: Solution: y"' -y"-y'+y=0 The Auxiliary equation can be written as m3-m2-m+1=0

Q: III. Find the equation of the tangent line to at the point (7,0). ㅠ ye* + cos x = sin x +sinh(2 . −…

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Q: Use the method of cylindrical shells to find the volume V generated by rotating the region bounded…

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Q: Solve the seperable differential equation 5yy' = x. Use the following initial condition: y(5) = 9.…

A: Q1)  y14=14{ln(x)+x}+(614-14)   Q2)  X2=5y2-380

Q: 3 cot2 0-4 csc 0 = 1

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Q: 2.1/(x²-3x¹) dx

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Q: Write the equation. Equation of degree 5. Roots at x = 3 and x= 1 both of multiplicity of 2 and  x =…

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Q: ग Calculate the partial derivatives and using implicit differentiation of (TU-V)² In (W - UV) = ln…

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Q: IV. Given the functions f(x) = 2x + 5, g(x) = -x² - 6x + 7, and h(x) = the following. Show complete…

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Q: Find the indefinite integral. (Use C for the constant of integration.) / (8 cos(x) + 7 sin(x)) dx

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Q: Begin with the graph of y= ex. Use transformations to graph the function. Then determine its domain,…

A: giveny=ex

Q: Using the expanded series of cos 2x, evaluate the given limit. (Non-anonymous question) lim X →0…

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Q: Construct a polynomial function with the following properties: fifth degree, 2 is a zero of…

A: we will find the required.

Q: Consider the function f whose graph is shown below. This function is given by f(x, y) {* 0, 5xy…

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Q: Gravel is being dumped from a conveyor belt at a rate of 20 ft/min, and its coarseness is such that…

A: The height is increasing at the rate of =45π  ftmin

Q: Take a derivative. 1. f(x)=(x²+2x)√x 2. f(x) = (x+1) 4x+7 3. f(x) = (x+1)(√x-D(²+4)

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Q: 3C. The equation of the parabola is f(x) = = x^2-x-2. Calculate the derivative f'(x). Evaluate f'(1)…

A: We need to find the solution to the problem 3C and 3D   Given data÷ fx=x2-x-2 Now we need to find…

Q: Find two unit vectors orthogonal to a = (-1, -3, -1) and b = (5,0,4) Enter your answer so that the…

A: Here is the solution:

Q: 3.y = 2√x -1; x-axis; x = 5; x = 17

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Q: 1 In the equation y = -x + 2, if x = 6, y = ?

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Q: Example 8: Find the vector v of the length √5 extend along the line through A(0,0,4) to B(2,5,0).

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Q: 37. F(t) = tan√1 + ²

A: Given query is to find the derivative of the function.