Find the points at which the following polar curve has a horizontal or a vertical tangent line. r=1-sin 9

Q: Prob. 6 (a) 3) Find the critical numbers of the function y = x³/2 - 4x¹/2 3

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Q: Evaluate the following integral: [²√²+² (cos(x² + y² S - y²)) dydx

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Q: 8 i) 이름을 . dx ii) f xel+x2 dx

A: This question can be solved using the concept of definite integrals.

Q: For u(x, t) = f (x + ct) + g (x – ct), where c is a constant, find ux, ut, uxt . Show your work…

A: Given, u(x, t) = f (x + ct) + g (x – ct)

Q: Prob. 4 (a) (6 pciats) If h(x) = (1 + f(x))³, where f(1) = −2 and ƒ'(1) = 3, find h'(1).

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Q: Use the Laplace transform to solve the given initial-value problem. y" + 8y' + 7y = 0, y(0) = 1,…

A: Let's solve initial value problem by using laplace transform.

Q: Find f'(x) and f'(c). f'(x) f'(c) || 11 Function x²-9 X-9 Value of c c = 1

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Q: find the angle between the pair of vectors to the nearest tenth degree 7i-5j,2i-8j

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Q: 68 3 (x + yz) dx + 2x dy + xyz dz, C consists of line segments (1, 0, 1) to (2, 3, 1) and from (2,…

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Q: Use the Laplace transform to solve the given initial-value problem. y' + 2y = e-2t, y(0) = 4 y(t) =

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Q: Find the sum. 6 Σ k k = 2

A: Here we have to find the sum.

Q: -4 -2 12- -8 -4 0 2 -N What is the equation of the graph shown here? 4

A: Let's find equation of given graph.

Q: i) f si sin 3x cos 3x dx ii) [ cos³x dx

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Q: Evaluate: L{cos8t} = Blank 1 Blank 1 Add your answer

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Q: # (u²-1)4 (u² + 1)4 du

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Q: -6 -4 -2 -6 y 2 4 The graph of f(x) is given above. Determine the domain and range of f-¹(x) using…

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Q: 1. (a) First find the following indefinite integral A. e666 B. 2e667 (e - 1) e√x+666 [= √x dx = (b)…

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Q: Find the critical numbers of the function. (Enter your answers as a comma-separated list.) g(t) =…

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Q: Use Theorem 7.1.1 to find L{f(t)}. (Write your answer as a function of s.) f(t) = (et-e-t)² L{f(t)}:…

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Q: Use Definition 7.1.1. DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t≥ 0. Then…

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Q: Consider the following. (Round your answers to four decimal places.) f(x, y) = x cos(y) (a) Find…

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Q: Consider the function f(x) = 2x³ - 6x² - 18x + 54. a. Find the first derivative. f'(x) = b. List any…

A: As per our guidelines we only solve three sub parts of given question and rest of the sub parts of…

Q: (1) f (1) x²(x³ +1)5 (x³ − 1)5 dx -

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Q: Find the slope of the tangent line to the graph of the function at the given point. g(x) = 20-x²;…

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Q: Consider the following initial-value problem. y" 5y' = 8e4t4e-t, y(0) = 1, y'(0) = -1 Find L{f(t)},…

A: We need to fill in the blanks

Q: 29. a) 5) The displacement of a particle is given by the equation s = 1³-152² + 63t, where s is…

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Q: What is the magnitude of an earthquake 600 times as intense as a standard earthquak

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Q: 2. Demonstrate that the double angle formula for sin2x is derived from the compound angle formula…

A: Double angle formula for sin2x is sin2x=2sinxcosx. and compound angle formula for sin(a+b) is…

Q: dr Let A be the area of a circle with radius r. If dt = 2, find dA dt when r = 1.

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Q: 3 A merry-go-round has a radius of 4 m and is spinning at a rate of 0.5π radians/s. Bill is standing…

A: Formula used: Circumference of circle = 2π×radius of circle  velocity =  angular velocity × radius

Q: (b)(is) Verify that the function satisfies the hypotheses of Rolle's Theorem on the given interval.…

A: Explanation of the answer is as follows

Q: Find an equation of the plane with the given characteristics. The plane contains the y-axis and…

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Q: Use Theorem 7.1.1 to find L{f(t)}. (Write your answer as a function of s.) f(t) = et cosh t L{f(t)}:…

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Q: Three sides of a rectangular playing field are to be fenced with 400 m of fencing. Determine the…

A: Application of derivative

Q: y = √√2x, x=2 yaxis 17 x-axis

A: Given that y= √(2x) and x= 2 and we find equation of tangent line and normal line at the given…

Q: Find the indefinite integral. (Remember to use absolute values where appropriate.) sec x tan x sec x…

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Q: Find the nth term of a sequence whose first several terms are given. 11 17 23 29 4 9 16' 25' an = II…

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Q: 6.0 and a are each acute angles in standard 12 13 position. sin0 = and cosa = 3 5 a. Determine cos(a…

A: We need to determine given angles.

Q: x4 x² x² + 1 - 1 dx ii) Š 1+ Inx

A: Please refer to the image below

Q: Step 3 At x = 4 + Δx, the value of the function is g(4 + Δx) = 20 – Hence, Step 4 m = lim Δx=0…

A: Here we have to find the limit in step 4.

Q: f Find f+g, f-g, fg and - Determine the domain for each function. g . f(x) = 3x² - 17x + 10,…

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Q: 8. Prove: 2 1-tan x 1+tan²x cox2x.

A: (1-tan2x )/(1 +tan2x ) = cos2x here we have to compare the left hand side and right hand side apply…

Q: The velocity of an object is v(t) = 29t²,0 ≤t≤6 where v is measured in meters per second and t is…

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Q: Find the unit tangent vector T, the principal unit normal vector N, and the unit binormal vector B…

A: Consider the curve     Ct: rt =cost,sint,t (i) unit tangent vector                  The unit tangent…

Q: Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded on…

A: The given data is: gy=8y To find: the volume of the solid obtained by rotating the region bounded on…

Q: 17. Find the linear function f(x) that is parallel to 4x + 3y = 6, such that f(0) = 7.

A: Given function, 4x+3y=6, That is 3y=-4x+6 y=-43x+2 compare to y=mx+c Therefore m=-43

Q: Use the Laplace transform to solve the given initial-value problem. y" + 7y' + 6y = 0, y(0) = 1,…

A: Use Laplace transform

Q: Evaluate the following integral: sos X 1 +1 d dydx

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Q: Find the tangent to y = cotx at x = - T O A. y = - 2x + 2 π +1 +1 OB. y=2x-- OC. y=2x+1 OD. y=-2x +…

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Q: Consider the following. u = (-2, -7, -5), V = = (-8, 3, -6) (a) Find the projection of u onto v. (b)…

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