(a) Show that the sequence is strictly decreasing and downward bounded. (b) Show that the sequence converges and find the limit value limn→∞ an.

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Q: Differentiate f(x) = (5x² - 2x + 3) (3x³ + 8x² − 5x + 1) - Show all work.

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Q: Consider the parametric curve r(t) = (t³, -t²). Determine which of the following graphs is the…

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Q: v. an = vi. an = (10/11) (9/10)n + (11/12)" 1 tan-¹ n √n n² +3 3n² + 2n + 1 vii. an (-1)";

A: The given nth terms of sequences(v) (vi) (vii)

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A: Answer:-  2313 peoplesExplanation:Diseases tend to spread according to the exponential growth model.…

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Q: Graph. f(x)= 3, for xs-2 |x²₁ for x>-2 Choose the correct graph. O A. A Q C OB. Q Q OC. N Q Q ✔ O D.…

A: To graph the following function.

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A: The objective of the question is to find the interval of convergence for the given series and…

Q: (BC Topic) Which of the following statements about the series below is true? (-1)" Ž n=11+√√n²³…

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Q: Please use Differential equation or intergral equation to solve thanks

A: Done.Explanation:Done

Q: In a survey of 270 college students, it is found that 64 like brussels sprouts, 94 like broccoli, 58…

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Q: x4k =0 k-256 * The radius of convergence of the power series Σ Select one: O a. 4 O b. 6 O c. 5 O d.…

A: To find the radius of convergence of the following power series.

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Q: Fill in the equation for this function. -21 -3π/2 -TI F -TT/2 n 2 -3 (1 TT/2 TU f(x) = [ ? ]sin(-×-)…

A: To find the equation of the following graph.

Q: Please solve the following calc 3 problwm

A: The objective of this problem is to find the equation of the plane that passes through the three…

Q: 5. Find the linear approximation of f (x, y, z) = x³y² + 22 at the point (2, 3,4). Use this to…

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Q: Find one value of x that solves the equation by using the inverse sine or cosine function on your…

A: Ques 1 : (a) -0.253 (b) 1.328   Ques 2 : 1→b2→c3→e4→a5→fExplanation:

Q: Evaluate the following integral. 5 x(x² + 2)² dx 5 In x² +2 In|x²| 1 √ + 0 = 0 _ _ _ ) - 0 dx 5 + +…

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Q: X y = y 77 225 471 877 3 1480 1.5 2 2.5 Paste the table into Desmos and fit the requested type of…

A: (a). Exponential function: The exponential function that best fits the data is :…

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Q: If f'(x) = 10x⁹, what is f(x)? (Remember the constant of integration.) f(x) = X

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Q: Use the graph of F, shown on the right, to find the given limit. When necessary, state that the…

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Q: Please help evaluate each sum knowing that f(x) = x2, g(x) = 3x , & h(x) = 2/x

A: f(x) = x2, g(x) = 3x , & h(x) = 2/x

Q: ƒ(x) = −2x² + 3x – 1

A: f(x)=−2x2+3x−1

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Q: an = (-1)" η2 + 3 3η2 + 2n + 1

A: To determine if the sequence is convergent or divergent, we can examine its behavior as n approaches…

Q: 3. Graph y = 4 sin(3x) over the interval 0 ≤ x ≤ Find the surface area of revolution about the…

A: Given: To Find: To draw the graph of the above function.To find the surface area of revolution about…

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Q: (BC Topic) Which of the following infinite series converge? 2 1. Ž n = 1 II. n = 1 n ΣΕ Σ III. Σ n=1…

A: We have to check which series are convergent

Q: Use the Divergence Theorem to calculate the surface integral F(x, y, z) = 3xy²i + xe²j + z³k, S is…

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Q: 2. Find the velocity, acceleration, and speed of a particle with the given position function. (a)…

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Q: Consider following relations on the set of positive integer: R₁ = {(a,b) | a> b} R₂ = {(a,b) | a = b…

A: The objective of the question is to determine which of the given relations are symmetric and which…

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A: f(x)=16x2+x4Using the power ruleddxxn=nxn−1

Q: Problem #2: Evaluate and determine whether the function is continuous at (0,0). Provide…

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Q: The Maclaurin series Σ (16) Select one: O a. cos(4x2) O b. e-4x² O c. sin(4x²) O d. cos(16x4) (2k)!…

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Q: Find the interval of convergence and radius of convergence of the series Σ(5x)". n=1

A: S=∑n=1∞(5x)nUsing geometric series test,∑n=1∞arn−1=a1−r,|r|<1

Q: Write an equation for the transformed logarithm shown below, that passes through (3,0) and (-1,3) 3+…

A: To write an equation for the following transformed logarithm shown below, that passes through .

Q: Which of the following limits does not yield an indeterminate form? 4x3 x0 cos(x)-1 (A) lim (B) lim-…

A: The indeterminate form:

Q: 6. Find the derivative of the following. *SIMPLIFY your answer: 2x a) f(x) = (√2/² 4x-x 2 b) f(x) =…

A: The given functions (a) (b)

Q: let f(x) = (x-3)^-2. find all values of c in (1, 7) such that f(7)-f(1) = f1(c)(7-1)

A: There is no number c in (1,7) such that  f(7) - f(1) = f'(c) (7 - 1)    If you face any problem in…

Q: 2. Find the solution of Yn+2 = -4Yn with yo = 1, y1 = 4. Write the answer without using imaginary…

A: THE ANSWER IS IN THE EXPLANATION PART.FEEL FREE TO ASK ANY OF YOUR DOUBTS AND COMMENT IF YOU FACE…

Q: The formula for wind chill C (in degrees Fahrenheit) is given by C = 35.74 +0.62157-35.750.16+…

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Q: f'(x) = Let f(x)= = I cos ³

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Q: (5.) Let u(x, y) = ln(x² + y²) (a (b. (c. State the domain of u: Determine lim f(x,y) (x,y) →(0,e)…

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Q: Find the difference quotient f(x) = f(2) x-2 when f(x) = 4 - 5x + 5x². Simplify the expression fully…

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Q: Use the graph of H shown to the right to find the limit. If necessary, state that the limit does not…

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