Find the exact values of the following expressions. sin (630°) and cos (630°)

Q: Find the arc length of the graph of (y − 1)3 = x2 on the interval [0, 8]

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Q: 6. Determine whether the following series converges or diverges. 1 Σ tan (√) n=1

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Q: The input value x = a is in the domain of the function g'. Explain the meaning of g'(a). Write an…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Determine if the following function is continuous and differentiable at x = 0. ex - sin x f(x) = {…

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Q: Suppose a dog jumps in the air and that its height (in feet above the ground is given by h = -16t² +…

A: Given suppose a dog jumps in the air and that its height (in feet) above the ground is given by

Q: g(t) = t³+ t².

A: g(t)=t3+t2

Q: Consider the following. f(x) = -3x² + 36x Find the critical numbers. (Enter your answers as a…

A: The objective of this question is to find the critical numbers of the function f(x) = -3x^2 + 36x…

Q: 10. Find a function f such that F = Vf and evaluate ScFdr along the given curve C • F(x, y, z) =…

A: If there are two functions, a vector function and a scalar function that satisfies the following…

Q: Let g(x, y, z) = 0.03x + 0.04y - 0.01z - 0.05. Complete the following sentences. (a) The variable g…

A: Given function

Q: x+6 (x + 2)2 dx

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Q: Build the tangent line approximation (linear approximation) to 6 -5 0 2 3 4 5 6 7 8 9 10 11 12 f(x)…

A: To build the tangent line approximation (linear approximation) to .

Q: Please do part a)

A: The objective of this question is to find the general solution of the given linear nonhomogeneous…

Q: for Integrals Find or approximate all points a which the given function equals its average value on…

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

Q: Suppose your newspaper is trying to decide between two competing desktop publishing software…

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Q: Find the area bounded by curves y = -4 + √x and y = -16 + x 4 (Round your answer to two decimal…

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Q: Suppose f(x) = 3x -2. Find f (x+²) 3 (x+2) 3 (Simplify your answer.)

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Q: Use the Ratio Test to determine the convergence of the following series. 8 Σ(-1)n+1 n=1 5 nn n!

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Q: (4) Find the maximum and minimum values of f(x, y) = xy on the ellipse x² - xy + y² = 1.

A: The given equation of function  Let

Q: 2. f(x) = = 1 1+72) [0,4], n = 4 , 1+x²¹

A: The given curve .The aim is to find the area under the curve using right-hand approximation in the…

Q: Determine the polynomial function, f(x), with the smallest possible integer co- efficients that has…

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Q: Find the domain of the function. f(x) = -5x + 3

A: f(x)=-5x+3

Q: Use a familiar formula from geometry to find the length of the curve described and then confirm…

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Q: (i) Find the derivative of the function. esin x COS X In(1+2v) dv.

A: To find the derivative of the following function.

Q: (a) Eliminate the parameter to find a Cartesian equation of the curve.

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Q: What is the second derivative x³ - 5x² + x = 0? A. 3x² - 5x B. 10x-5 C. 3x + 10 D. 6x-10

A: The given equation is Let

Q: Find the critical numbers and the open intervals on which the function is increasing or decreasing.…

A: The objective of this question is to find the critical numbers and the open intervals on which the…

Q: The function f(x) = 6(1.2) is an exponential function. Af(x) Ax a. Determine the value of the ratio…

A: The given function .The aim is to find the value of the ratio  over the given intervals.

Q: 4. When an infectious disease is introduced into a city of fixed population N, the rate of change of…

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Q: Find the solution of 4x²y" - 6x²y + y = 0, x > 0 of the form Y₁ = x¹(1+₁x + €₂x² + 3x³ + ...) Enter…

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Q: To find an antiderivative of f(x) = arctan(3x) you used integration by parts, and obtained…

A: The integration by part formula is:                             ..(1)

Q: Identify domain and range and determine it it’s a function

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

Q: NASA launches a rocket at t=0 seconds. Suppose its height, in meters above sea-level, as a function…

A: The height function of the rocket is h=−4.9t2+205t+108 Here the objective is to find the peak of the…

Q: At time t, the position of a body moving along the s-axis is s=13-1512+72t m. Find the body's…

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Q: 31. 3 1-25x2 dx

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

Q: Determine lim f(x) given the definition of f(x) below. (If the limit does not exist, enter DNE.)…

A: For finding, if f(x) is a polynomial, then for finding limit, we need to substitute a in f(x) and…

Q: Use the zero, 5+ i, to write P(x) as a product of linear and irreducible quadratic factors.…

A: we need to write P(x) as a product of linear and irreducible quadratic factors

Q: Use l'Hôpital's rule to find the limit. Use -∞o or ∞o when appropriate. 3x²+5 lim x→∞04x³ +2 Select…

A: The objective of this question is to find the limit of the expression (3x²+5)/(4x³ +2) as x…

Q: d) Write an expression that represents the approximate value of g(x) for a generic value x in the…

A: The graph of the function g'(x) is shown as,

Q: Question 1 (i) Determine dy/dx in the following: (ii) y = cos(x³ - 2x) y = x²-2 sin x y² −2(x+y)+x²…

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Q: Use complex number operations to determine the solution to the expression below. The final solution…

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Q: Find the vertex, focus, and directrix of the parabola with the given equation. Graph the equation.…

A: The given equation of parabola is The vertex form of parabola with the vertex  is

Q: When Abraham jumps into the air, his height in feet above the surface of the water is given by h =…

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Q: Find the value of (f o g)' at the given value of x. Assume that f'(3) = 6, g'(4) = -5, g(4) = 3, and…

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Q: √3x + 16-5 x-3 18. lim- x 3

A: we need to find out the limit.

Q: •3 L₂(³- -2 - (3 - x) dx

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Q: Consider the following function. f(x) = -5x Complete the table.

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Q: Find the value of (fog)' at the given value of x. Assume that f'(3)=8, g'(4) = -6, g(4)=3, and y =…

A: The chain rule of differentiation is given by

Q: 7. Determine where fis discontinuous. Justify your answers. √=x if x < 0 3-x if 0<x<3 (3-x)² if x ≥…

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Q: Air freshener A has a mass of 42 grams when opened and its mass decreases by 4.2 grams each day. Air…

A: The mass of the Freshener a=42 gmIf opened in the air decreases to  4.2% per dayThis means the decay…

Q: Suppose the height of this motorbike's jump is given by h = -16t² +32.1t+5.7 where h is the height…

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