Set up, but do not evaluate, an integral for the length of the curve. ST 2 x = 4 sin(y), Osys (C dy

Q: Use a double integral to find the area of the cardioid r = 6 - 6 cos 0.

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Q: Let f(x) = Then f'(x) = 4 sin x 2 sin x + 6 cos a π The equation of the tangent line to y = f(x) at…

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Q: or problems 1-3, prove the given identity. 1. tan(-x) cos x + cscx sinx = 1 - sin x

A: Prove the Identity

Q: radius=100mm radius=100mm

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Q: The graph of the derivative of f(x) is shown below: 7+ 6 5 4 3 2 -7 -6 -5 #4 -3 -2 -1 -1 -2 -3 -4 -5…

A: Topic = Functions

Q: Use the Squeeze Theorem to show that lim x² cos(22xx) = 0. x-0 Illustrate by graphing the functions…

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Q: Let f(x) = 8x². (a) Find f(x)-f(-2) X+2 (b) Find f(x) = f(a) x-a

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Q: Calculate the derivative of the following functions. Use the rules for derivatives. a. w(x) = x² +…

A: Note:As per our guidelines we are supposed to answer only 3 subparts if there are multiple subpart…

Q: The function f(x) has a domain of (-∞, -1) u (-1, ∞) and a second derivative given by the following.…

A: Topic = Functions

Q: Find parametric equations of the line through (−2, 1, 3) that is parallel to 3i - 7j+k. x(t) = 5 t -…

A: Given query is to find the equation of the line.

Q: Find an equation of the plane containing points P(-2, -3,1), Q(-1, 2, -3) and R(1, -2,-4).

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Q: Given the function f(x) = -x^6 - x^2 + 10x + 6, find the equation of the tangent line at the point…

A: See this solution in below.

Q: Explain why Rolle's theorem does not apply to the function even though there exist a and b such that…

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Q: Evaluate the improper integrals or show that they diverge. Make careful use of limit notation. (a)…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: What is the expansion of the series Σ 3*+1? n=1 9+27+81 +243 9+12+15+18 3+9+27+81 3+6+9+12

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Q: Find dx 11 for y = 9x2 sin x + 18x cos x – 18 sin x. dx

A: Finding the derivative of y

Q: What is the exponential function of the graph shown below? Provide your answer below: f(x) = -2. -2…

A: Given graph

Q: A country's postal service will accept a package if its length plus its girth (the distance all the…

A: Let x be the a side of the square base and y be the length of the package.

Q: Use Fubini's Theorem to evaluate the double integral ſƒ ƒ(x, y) dA, where f(x, y) = 8x² − 4x²y²-y…

A: Answer: The solution is given below:

Q: state the axioms that define a group.

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Q: Find ST (x + y) dydx. 5 4

A: To evaluate the iterated integral.

Q: Consider the function f(x) = 5(x - 2)2/3. For this function there are two important intervals: (-∞,…

A: As nothing is mentioned, we will be answering by the method of the graph. Thus, the critical number…

Q: Find the derivative of the function f(x) = f'(x) = sin x 1 + cos x 2

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Q: For the demand equation, use implicit differentiation to find dx p² + p + 9x = 120

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Q: Find the arc length of y= 2x sqrt(x), from x=0 to x=1

A: Given: y=2xx We need to find the arc length of the above function from x=0 to x=1.

Q: Find the domain of the vector-valued function. (Enter your answer using interval notation r(t) =…

A: To determine the domain of the given function

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

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Q: Sketch the graph of a function f such that f is always decreasing and f(x)>0 for all real numbers x.…

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Q: Suppose that the radius r and volume V = πr3 of a sphere are differentiable functions of t. Write an…

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Q: A The equation below gives the position s= f(t) of a body moving on a coordinate line (s in meters,…

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Q: Find the intercepts and asymptotes. (If an answer does not exist, enter DNE. Enter your asymptotes…

A: solution:-r(x)=x-1x+3x+1x-7x-interceptr(x)=0x-1x+3x+1x-7=0x-1x+3=0,   x+1≠0, x-7≠0x=-3, 1x-intercept…

Q: 4. Find an equation of tangent line at the point (-1, 1) to the curve x¹y² + 1 = x² + y³. 5. The…

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Q: Evaluate each expression using the values given in the table below. -7 -5 -3 -1 -5 9 -3 3 -5 X f(x)…

A: here is table given  we find the function value from the table  a) f(g(-1)) = ? g(-1) = -5 f(g(-1))…

Q: The domain of the function f(x) = √e-4-elx-3|—x is O(A) the empty set (B) a half-line of the form…

A: The given function is  f(x)=e-4-ex-3-x

Q: logarithmic differentiation to find the derivative of f (x) = (cos x)x

A: Given is to find the derivative.

Q: Find the equations of the lines tangent to the curve: 2e^x = y^2 − x, at x = 0.

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Q: Sketch the region of integration and evaluate by changing to polar coordinates: 1/2 1,x² ¹/² √¹-2²…

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Q: Find dy/dx where: tan (x+y)=cos x+cos y

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Q: A company produces a special new type of TV. The company has fixed costs of $489,000, and it costs…

A: Given that demand (sales) verses price is linear. That means it have two points we can find the…

Q: Evaluate the following indefinite integral by making the appropriate trigonometric substitution. Be…

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Q: 11 x ² D the top half of the disc with center the origin and radius 3, by changing to polar…

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Q: Find the intercepts and asymptotes. (If an answer does not exist, enter DNE. Enter your asymptotes…

A: The given function rx=3x2-30x+76x2-10x+25 We have to find the domain, range, horizontal and vertical…

Q: Classify each differential equation as separable, exact, linear, homogeneous, or Bernoulli. Some…

A: A Differential Equation of the form dydx+h(x)y=g(x)yn is called a Bernoulli differential equation in…

Q: Analyze the following rational function: f(x) 5+2x² 2 x -x - Include the following: 2 • Identify the…

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Q: 2. A thermometer reading 18°F is brought into a room, the temperature of which is 70°F. One minute…

A: Given: The temperature of the room (T)= 70°F The initial temperature of the thermometer (To) = 18°F…

Q: For the given function, find all values of c over the interval (4, 8) stipulated by Rolle's Theorem…

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Q: KW. Solve the following 3....2 X... DX. + Xdy - where you... ************

A: By using exact diffential equation

Q: Find all complex z that solve the equation z^12 = −1. Which of these solutions also solve z^4 = −1?

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Q: Find an arc length parameterization of a helix of height 20cm that makes 4 full roations over a…

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Q: d = -1 The region R is bounded by the x-axis, y-axis, and the line in the graph and has a constant…

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