1-12 For each of the following power series, find the interval of convergence and radius of conver- gence. 14. (-1) 8"(x – 3)" (n +1)! n=0

Q: A. Solve the following problem involving derivatives 1. The position of a particle is given by the…

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Q: II. Find the equations of the tangent and normal lines at the point indicated. a. 7x - 6V3ry + 13y -…

A: Solution is given below:

Q: 1. A soccer ball is kicked with a speed of 75 mph at an angle of 30° from the horizontal. Write the…

A: Given query is to find the velocity components.

Q: y cos x+sin y+y 0. Solve the following dx sin x+x cos y+x differntail equation 1.

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Q: If f(x) = sin (a*), find f (x) Find f'(5)

A: Given function is f(x) = sinx3 we have to find the first derivative of f(x) that is f'(x).

Q: Use the integral test to determine the convergence or divergence of the series. 1 20) E k = 1 6k- 1

A: Let's find.

Q: Let E be the region that lies inside the cylinder x2 + y2 = 64 and outside the cylinder (x- 4)2 +y2…

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Q: how does csc x/ cos x is equal to sec^2 x/ tan x

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Q: Find the general solution of the given ODE: dy _ x²y – 4y dx x + 2 (x² y = Ce2 = ce) (x² = Ce2…

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Q: Evaluate the definite integral 9 6x² + 6 dx 35 X o 588.65298705274 3

A: We know, ∫xndx=xn+1n+1+C, C is a constant for any real number n.

Q: A company produces two types of solar panels per year: x thousand of type A and y thousand of type…

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Q: P6: x2 x² – 1

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Q: dy Differentiate implicitly to find dx e**y = 8x + 3y +8 Evaluate the derivative of the each side of…

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Q: Eliminate

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Q: Eliminate the arbitrary constants on the given equation: y= Ae" + Bre 2y +y=0 O y =-y" + 2g

A: To eliminate the arbitrary constant.

Q: (zxャy)dx->xy dy =。 2-

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Q: cos(xy) + secy = 5

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Q: Differentiate Зх — 6 y = csc 5x2 + 9 A. Зх — 6 Зх — 6 - y' = cot csc 5x2 + 9 5x² + 9 ) В. Зх — 6 Зх…

A: Differentiation

Q: is a factor of 2 + 5z2 – 5x +1. - O I+1 O 2z +1 O +2 O 2x -1

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Q: -3 -8- -

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Q: Let f(x) = log2(x) and g(x) = cosx. Give the composite fog and go f, and determine their domains.

A: The given functions are: f(x)=log2(x) & g(x)=cos x

Q: P1:

A: Solving

Q: For which value of x is the function f(x) = X - 4 undefined? 2х - 8 O.4 04 1/2

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Q: 7/2 SAT sin" x cos3 x dx

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Q: X = -y A y 2Fx = 2- y² -2

A: Recall: Formula Area=∫abf(y)-g(y)dy  We have,  f(y)=2-y2, g(y)=-y

Q: 0 14 (x² + 4y) dæ dy 4

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Q: Find the equation of the tangent line at the given point on the curve. 2y - Vx = 4. (16,2) y =U

A: We need to find equation of tangent line.

Q: dy Suppose that x and y are related by the equation 2x - y = 1 and use implicit differentiation to…

A: The given equation 2x2-y2=1

Q: L,x²(x³ + 8)²dx 19. Use the Fundamental Theorem of Calculus to evaluate:

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Q: Consider the circle in the ay-plane given by the parametrization x = 2 cos t, y = 1+2 sin t, 0<t<…

A: Let's find.

Q: Find the angle of the largest right circular cone which can be inscribed in a sphere of radius 9…

A: Given problem:- Find the angle of the largest right circular cone which can be inscribed in a sphere…

Q: 1 dv 5 3 v 2 –8v² +24v 2 –32v+16v 2

A: solution:-∫1v52-8v2-24v32-32v+16v12 dvlet v=t2dv=2t dt=∫2tt5-8t4-24t3-32t2+16t…

Q: Solve the second derivative(y") of the following function and simplify the final results. Show your…

A: We need to find second derivative.

Q: Given: a = 22, c= 24.1, zB = 6T C a A Solve the triangle. (Do not round until the final answer.…

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Q: 1. Calculate the area of the graph enclosed by the curve y = sec(2x)tan (2x), the x-axis, and the…

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Q: y=x nd y=x+2 Revolve the area about the x-axis. Using circular ring method, the volume of the solid…

A: The given curves are; y=x2 and y=x+2. And the bounded region is as shown below; Apply the circular…

Q: 1) Use the Integral Test to determine whether the series 1 is convergent or divergent. (Зп — 1)? c)…

A: The given series ∑n=1∞1(3n-1)2

Q: Find the surface area of the plane ( 15x- 5z+20y=35) if it is in the first octant

A: Given problem:-   Find the surface area of the plane ( 15x 5z+20y=35) if it is in the first octant

Q: 4 Find f(x) dx if if x< 2 f(x) if x 2 2.

A: To evaluate the given integral

Q: Solve the equation (2xy - tan y)dx + (x^2 - x (sec y)^2))dy = 0

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Q: dy 3) y = u5 and u = 3x – 1; 2 Ans: 2 = 15(3x – 1)* %3D dx dx

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Q: Exercises: Find the derivatives of: 1- sin(x?y?) = x, 2- xy + y? = 2

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Q: At what point on the line y = b does the line segment from (0,0) to ( a,0) subtend the greatest…

A: We have to find the point where the angle is greatest

Q: Choose the values that are in the range of y= arccot x Select all that apply. NEXT QUESTION O ASK…

A: Given query is to find the values which are in the range of the function.

Q: What type of DE is the following? xydx + (x2 – 3y)dy=0 O Bernoulli in x Bernoulli in y O Linear in x…

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Q: X- Consider the function f(x) = x2 -1 Please explain all steps (a) Find the intercepts of the graph…

A: This is a problem related to function. Based on the general formula and concepts we will answer the…

Q: Integration of (sin(x) + cos(x)) e^x is ______________.

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Q: provide a step by step solution to the following bernoulli equation (y⁴ - 2xy)dx + 3x²dy = 0 ; when…

A: Let's find.

Q: 2) z= (1+t²)(3 - 2y); z' Ans: z' = -2(3t? + 3t + 1)

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Q: Use the properties of the derivative to find the following. r(t) = ti + 5tj + t²k, u(t) = 5ti + tj +…

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