2. Create your own example of convergent series containing 5 terms. Explain what makes it convergent. Calculate the sum if it exists.

Q: Find the horizontal and vertical components of the vector with the given length and direction, and…

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Q: 1. Consider A = (0, 4, 2) , B =, (6, –1,0) and C = (3,0, 1). 1 (a) Find the unit vector having the…

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Q: dx J (x² + 2x – 10)²

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Q: The New River Gorge Bridge is 880 feet above the water below. A bottle rocket is launched upward off…

A: To find out the velocity and acceleration.

Q: s) Find the equation of the tangent line to the curve y = x Vx´ +5 at the point (2,6).

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Q: . Identify and sketch the graph of the following equations (a) a2 + 2y? + z² – 8x + 12y – 2z + 35 =…

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Q: I = 3 sin(60?t) + cos(120?t)

A: answer is in next step

Q: C) = (" † ')- (,",) 'n + n _1. Show that :

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Q: A. Evaluate the following integrals: 3 | tan°x dx 1.

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Q: fosc 4 2. csc* xdx

A: I =∫ cosec4x dxI =∫ cosec2x cosec2x dxI =∫ (cot2x+1) cosec2x dxcot x = t-cosec2x dx = dtcosec2x dx =…

Q: 1(x) (х+1)* II

A: follow the procedure given below.

Q: Write the integral that would be used to find the area bounded by y = x2 + 1, y = x - 2, x = -2 and…

A: Given y=x2+1,  y=x-2, x=-2 and x=2

Q: Find all the antiderivatives for the following function. Check your work by taking the derivative.…

A: Consider the function  f(y)=-24y25

Q: . Using the vectors in the previous item, which of the following vectors makes an angle of 90° with…

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Q: i an arithmetic series is 38. irst 40 terms of the series is 1250. the common difference of this…

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Q: dy and d'y of the parametric equations Determine da da 1. a (t) = t - 4t and y (t) = 2t – 6t %3D

A: 1)x(t)=t2-4tDifferentiate w.r.t 't'dxdt=2t-4 --->1dtdx=12t-4…

Q: 19. Evaluate the given integral, ſe*1+ ex dx: A.(1 + e*) + c B. (1 + e*)} + e c. (1 + e*)* + D. (1+…

A: Evaluate the given integral,

Q: Suppose z = x? sin y, x = –2s² + 2tť², y = 2st. A. Use the chain rule to find and dz as functions of…

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Q: Consider the parametric equations: x = 2t2, y =t³. Find at the point t = dx? 8 without eliminating…

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Q: Write the quotient in standard form. 11 1-i

A: Topic = Complex number

Q: find (a) (f + g)(x), (b) (f - g)(x), (c) (fg)(x), and (d) (f /g)(x). What is the domain of f /g? i.…

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Q: 11. Find the definite integral of S, 2 sinx 1+cos x dx : A. In (1+ cos x) В. 2 In 1 C. In 1 D. In 2

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Q: Convert the polar equation r² = 2tan 0 to a Cartesian equation. x3 + y3 = 2 y x3 + xy² = 2 y x² + y²…

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Q: The pencil holder is to have a base that has the same sides and a surface area of 100 cm. What…

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Q: Find the solution. y'+=J5. y(1) = o у, у(1 х - 2 A y 9x 1 x+ 3x 2 - 3 9x 3 x2 – 3x +2 y 9x x3 – 2x 2…

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Q: Find all the antiderivatives of the following function. Check your work by taking the derivative.…

A: f(x)=13exIntegrate on both sides:∫f(x) dx=∫13ex dxF(x)=13ex+C

Q: I. Write 2 – 7i in polar coordinates on the complex plane. - II. Find (1+ i)° using DeMoivre's…

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Q: TT sin 5. Approximate dx by Simpson's rule with seventh ordinates?

A: Simpson's Rule:    ∫abf(x)dx=∆x3f(x0)+4f(x1)+2f(x2)+...+2f(xn-2)+4(fn-1)+f(xn) Where, ∆x=b-an We…

Q: y =x, 4x + y =12

A: Let's find.

Q: Choose the point which shows the correct location for the polar coordinate (3, –-45°). 90° 2 WIN…

A: Option D

Q: If y = 5u² + 1; u= 2 , find dy %3D do O 21 O 20 O 11 O 10

A: Given : y=5u2+1 ; u=2x   To Find : dydx

Q: Find an equation of the tangent line to the graph of y = ln(x2) at the point (3, ln(9)). y=_____

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Q: the area of the region enclosed by y = 2 – x´ and y = -x, identify the "a" and "b"

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Q: If f(x, y) = 7xey + 7y Inx, then is given by: дудх O 49e5y + 7/x 35eby + 7/x O 25e5y + 7/x O 35e5y +…

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Q: M. Vx? N. xe* O. 4 Р. cot x Q. cot?x R. 2 cot x

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Q: Find real numbers a and b such that the equation is true. a + bi = 2+6i a = 3,6 = 2 a = 5,6 = 9 a =…

A: To find the values of a and b.

Q: Select the answer option that corresponds with polar coordinates (-1,-210\degree). 90° WIN 150° 4…

A: The given polar coordinates is (-1, -210°)

Q: Find the derivative of each function defined as follows: 1. y (2x3 + 9x)5 2. f(x) = -7(3x* + 2)-3 3.…

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Q: Consider the following. t = − 4?/3 (a) Find the reference number t for the value of t. t =    (b)…

A: We have to find the reference no t and terminal point determined by t.

Q: Find the centroid of the region. NOTE: Enter the exact answers. (7, 9) (?, ?) %3D y = 23

A: The expression for the centroid is: x¯=1A∬xdydx & y¯=1A∬ydydx   Where; Area=A=∬dydx   From the…

Q: What is the area of the region between the graphs of y = x – 1 and y : -X – 1

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Q: 4. Sketch the function Ax) = 2xª – 16x², indicating any extrema, points of inflection,

A: follows the procedure given below.

Q: Find the exact area of the surface obtained by rotating the curve x = 2t² +÷,y = 8/t,1<t<3, about…

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Q: sẽ the point which shows the correct location for the polar coordinate (-2, 180°). 90° 2 4/2 135° 7…

A: point (-2,180) here -2 show radius of circle  180 is angle with x axis here one circle is 1 unit…

Q: Find the critical points of the following function. 14x f(x) x2 + 49 Select the correct choice below…

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Q: 16. Evaluate the given integral, ," x sin x² dx coS 16 coS 4 A. 2 2 cos 16 cOS 4 В. + 2 cos 16 coS 4…

A: We have to find the solution

Q: 1) Sketch the curve. a) r=-2 sin O Show All Work

A: Here we have to sketch the given curve.

Q: Find the angle in radians between the planes -2x + z = 1 and -ly+ z = 1.

A: See the answer below

Q: Determine the intervals on which the following function is concave up or concave down. Identify any…

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Q: Find the arc length of the parametric curve. x = e', y = e, z = /2t; 0<t<7 L=

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