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Q: Using the concept of the derivative of sin x, what is the antiderivative of sin x? -2 cos x + C 2…

A: We know that: ddx(cos x)=-sin x...(1)

Q: Write the first five terms of the sequence: +∞ {√n² + n n n=1 Determine whether the sequence…

A: The given sequence is;  (sqrt(n2+n) -n).

Q: Let f denote a piece-wise defined function whose graph on the closed interval [-3,3] is shown below:…

A: we have given the graphf will be decreasing in itervals where its slope is negativewe can observe…

Q: If the graph of f has a horizontal tangent line at x = c and f" (c) is negative, which of the…

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Q: Whatis the derivative of y = sin (2x − 1)?

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Q: Instruction: Evaluate the following Integrals. Write your COMPLETE solutions neatly and organized.…

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Q: 2 X * sin² Lys y dy d

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Q: 24 The following limit gives the derivative of a function f(x) at a point zo: lim h→0 √8+h 2 h Which…

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Q: Which of the following is equivalent to the expression a) √√³² Ob)-20 h³ d) h² • ?

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Q: Find the area under the graph y = x 3 on the interval [1, 8]. 1 2 3 4 5 6 7 8 9 -NW 01 5- 4 3 2 क्त…

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Q: e ☺ x +9 x² + 9x + 18 -dz

A: You have asked multiple questions and not mentioned which question answer you need so according to…

Q: Find y' 1. 3x − y + (3x-y)5 = 100

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Q: Given: f(x, y) = ln[1 + x siny] Find: g² f(x,y) 8x² 2 sin y (1+xsin y)² sin² (1+2 sin y)² 1+2 sin…

A: In this question, we need to find the second partial derivative of the given function.

Q: Given f(x, y, z) = ze™" - a sin none of the choices 02-1/ 02²/ 0 01- ¹(), what is fax (0,2,1)?

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Q: 15. Yogurt containers can be shaped like frustums. Rotate the line y = x around the y- axis to find…

A: 15.   yougurt containers can be shaped like frustrums.Rotate the line y=1mx around the y-axis…

Q: Question 7a. Zombies have invaded campus! They recruit more of the undead at the rate: dz 10 f(x) =…

A: For Equilibrium value , derivative is zero .

Q: What is the derivative of y = sin (x³ sin (x³ – 3x)?

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Q: 3. | rV3 – adr -

A: We have to find out solutions

Q: The percentages of police officers who are women are listed in the table for various city…

A: Solution: a. We use Desmos to graph the data points given, plotting the city population n along the…

Q: Evaluate: lim-0 (cos 2x) 2²

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Q: Given the graph below, what can you say about the function at x = -2? Not Continuous Continuous

A: A function f(x) is continuous at x=a if and only if limx→a f(x) = f(a).

Q: If c is a constant, what is the limit of c as x approaches a? 0 C a X

A: A detailed solution is given below.

Q: Use a table of integrals to evaluate the following indefinite integral. The integrals may require…

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Q: Given the graph below, what can you say about the function at x = 1? 10 Continuous Not Continuous

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Q: Find y' tan³ (5x - y) + cos ¹(5x - y) = 100

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Q: Evaluate: Express your answer in three decimal places. 3x-2 limx→8 2-8

A: limx→ 8x3-2x-8       00 formApply L'Hopital's rule,=limx→ 813x231Plug in the value x=8=13·…

Q: ** asin I sin²Lys y X IT 3- 2 จา

A: Use change of order of integration.

Q: The graph of f is given below. -2.5 -2 -1.5 Why is f not differentiable at = -1? Of has no tangent…

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Q: Given the graph below, what can you say about the function at x = -1? Continuous Not Continuous

A: Explanation of the answer is as follows

Q: Given the differential equation y'' − 3y' – 4y = - 2 sin(2t), y(0) = 0, y'(0) = - = - 1 Apply the…

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Q: What is S (x² + 2x)² dx? + x³ + ³x² + C 4 S (x² + 2x)²dx = ¹x¹ + x³ + 4 f (x² + 2x)²dx = (x² + 2x)¹…

A: We know, ∫xndx= xn+1/(n+1)

Q: what is the lim f(x)9(x) if lim g(x) ln f(x) = +∞ x→a x→a

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Q: The derivative of sec22x(cos2x−sin2x) with respect to x is?

A: I have appended the formula used in the solution part of the question

Q: Question 13 Given: ez + xy = 1 dz Find: dr zey te O dz 8x 8x dz 8x Za zerx Ty IZ ce¹² ze Ty

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Q: PROBLEM: Integral of sin²x cos²x dx is equal to A. X+C B. cos2x/16-x/8+C C. x/8-(sin 4x)/32+C D.…

A: We need to find integral.

Q: find the derivative:  c(x)=(x2)500x (the choices are in the image bellow)

A: This question is based on Chain rule differentiation. d/dx {f(x).g(x)} = g(x).d/dx{f(x)} +…

Q: 10 5(5+10) a/n A ナ B 5+10

A: See the details solution in below

Q: olve the differential equation y"+4y=sec(2t).

A: To solve the following differential equation  y''+4y=sec(2t).

Q: What is the derivative of y = √x? 1 1 X 2 2 1 √x X 2 1 2 X 22

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Q: Which of the following represents the symbol for the indefinite integral? S dx dy b a Σ

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Q: xcsc {( 2 ) - »]dx + y y dx+xdy=0 X (x² − xy + y²)dx−xydy=0

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Q: 2x³ is an antiderivative of what function? y = 6x² y = -6x² X y = y = - 2 X 2

A: 2x3 is an antiderivative of what function.

Q: Solve for fazy for f(x, y, z) = 4x³y²z - e²zy¹ + + 4y - x¹6

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Q: 3. A point P(3,0,5) lies on a plane that can be defined by the scalar equation Ax+By+Cz+ D = 0. A…

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Q: Consider the initial-value problem y' + exy = f(x), y(0) = 1. Express the solution of the IVP for…

A: Given:- y'+ex y =f(x) , y(0) =1  Find:- Express the solution of the IVF for x>0 as a non…

Q: ii. Given g(x)= √x²+5 if x<-2 3-3x if x2-2 Find the following: d. g(-2)= e. Determine with an…

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Q: (a) Does the point P(1, 2, -1) lie on the line & given by the vector equation (x, y, z) = (2, 1, -2)…

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Q: The domain for the function ex y = x ln(3 - x) is {x/x 3} O

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Q: 28 Which one of the following is the co-ordinates of the y-intercept of the tangent line to the…

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Q: Convert ₁(4-4x²-y2)dyda into a triple integral with dV = dydzdx.

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