Derivation of a formula of volume cylinder (using Calculus, in two different ways).

Q: Let w = f(x, t) where a depends on r and t. That is, æ = x(r, t) and w = w(r, t) = f(x(r, t), t). As...

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Q: Write the first five terms of the sequence: {Vn²+n – n}1 n=1 Determine whether the sequence converge...

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Q: Find the Taylor polynomial of orders 0, 1, 2, and 3 generated by f at a. 5x f(x) = cos x, a = 6 Po(x...

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Q: The count of a bacteria in a culture was 5 initially and doubles every 30 minutes. Find the size of ...

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Q: Find the inverse for the following function f(x), and find the domain and rang for f(x): x+2 f(x) = ...

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Q: Evaluate the improper integral. 9. 3x²e* dx (Express numbers in exact form. Use symbolic notation an...

A:     ∫-∞9 3x2ex=3·∫-∞9 x2exdx=3x2ex-∫ 2xexdx-∞9=3x2ex-2exx-ex-∞9=195e9

Q: Find the derivative of the function. y = a6 + cos6 x y'(x) =

A: Given

Q: Given the function: f(x,y, z) = x°y2² + æy° +y°z Find а. fazy: (x, y, z) b. fazyz(1, –1, 1) -

A: Given the function :  f(x,y,z) = x3y5z7 + xy2 + y3z

Q: 2y" – 3y" – 3y' + 2y = (e" + e¬²)²

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Q: Write the equation of a sine function that has the given characteristics. The graph of y = x2, shift...

A: Given that: y=x2

Q: 2000 A television camera at ground levell is 2000 feet away from the launching pad of a space rocket...

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Q: 6 and its graph, use the graph to determine the following. r(x) 10 하 6 4 2 -4 -3 -2 -1 -2 1 2 3 4 -8...

A: where f'(x) is positive f(x) will increase and f'(x) is negative then f will decrease , observe the ...

Q: Perform the following operation with the vectors а3(2. о, з>. ь-(з. 1, 2) %D |2a– 3b|

A: Given that: a=<2, 0, 3> and b=<3, 1, 2>

Q: Use the Integral Test to determine whether the infinite series E 41 is convergent. (Use symbolic not...

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Q: Consider the following sequence: {a,) = {n – n²} Sn=1 Use an+1 - An to show that the given sequence ...

A: Calculus   sequence 

Q: 4. y=ysin 2xcos 5x + 3

A: Find your answer below 

Q: 8) For this problem, consider the function f(x) = e". (a) Find P3(x), the third-degree Maclaurin pol...

A: Find your answer below 

Q: Given the function: f(x, y, z) = æ²y*z³ + xy+ ² + 1. %3D Find a. f,(x, y, z) b. f:(x, y, z)

A: Topic:- partial derivatives

Q: Evaluate the limit lim CSC X

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Q: A time study showed that, on average, the productivity of a worker after t hours on the job can be m...

A: The productivity of the worker after t hours is given by: P(t)=21t+6t2-t3, 0≤t≤8 where P is the numb...

Q: popsicle is taken out of the freezer with an internal temperature of 32◦F and is allowed to warm in ...

A: Given problem:- A popsicle is taken out of the freezer with an internal temperature of 32◦F and is a...

Q: Let y be the part of the curve y = x² running from (-1,1) to (2,4). Calculate xy dx + (x + y) dy.

A: (1)

Q: 28.lf a flash of lightning is observed in a cloud 2640 m away and the speed of sound in air is 330 m...

A: Given that: Distance between the observer and cloud=2640 mSpeed of sound=330 m/s

Q: Given the side length b = 9 and the angle B = 43° on the triangle below, find the lengths of a and c...

A: Given that:                              

Q: Use the formula for the sum of a geometric series to find the sum or state that the series diverges....

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Q: Of an initial amount of 7000 g of lead-210, how much will remain in 180 years? Lead-210 decays at a ...

A: Given that: Initial amount of lead, P0=7000gRate of decay, k=3.15%per year.

Q: Suppose you were given $500 from your uncle. You deposited that money in a bank and added $10 per mo...

A: Topic:- algebra

Q: 3. If T(x) = Ax+b is a linear transformation where A is an mxn matrix and x is an n dimensional vect...

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Q: (x – 2)(x + 2)(x +1) (x+ 3)(x+1)

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Q: cos (0) = -0.115 Round your answer to the nearest thousandth. Provide your answer below:

A: follow next step

Q: Express w as a linear combination of u and v: ? = (4,1), ? = (−2, −1), ? = (2, −2)

A: Let w = (4,1) u = (-2,-1) v=(2,-2) we can write this as: u-21 + v2-2 = 41   -2u + 2v = 4 u - 2v = 1 ...

Q: The graph of f(x) is given by 3 Determine the following limits. Write your 2 answer in the form lim ...

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Q: A) What is the point of intersection between the plane x – 2 y +3 z +1 = 0 and the line r = + t? B)...

A: Use substitution method

Q: Find y' : In(cos² 3x) = e*+y + sin-1 y

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Q: (a) Find the series' radius and interval of convergence. Find the values of x for which the series c...

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Q: Use substitution to find the Taylor series at x = 0 of the function 15 sin (-x). ... What is the gen...

A: This question is based on Taylor series expansion of sinx .

Q: 7. уз y =/x³ – 1/1+ vx

A:

Q: Given the function: f(x,y) = x cos (xy) – x²e*Y - Find fa(x, y) а. b. fy(x, y) a fzy(T, y) C.

A: As per our guideline we are supposed to answer 3 sub parts of a question please repost the other que...

Q: Let f(x, y)= Jxy +x+xcosy. (a) Find fxy-

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Q: You are designing a poster which has a border around th printed portion. The border is 2 inches wide...

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Q: 6. The limit of that constant is that constant. 7. The limit of a constantc times a function is equa...

A: Since we are given with the multiple number of questions and our guideline is solve the problem only...

Q: ACTIVITY 1 onl Direction: solve and analyze each of the following problem in neat and orderly manner...

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Q: Determine convergence or divergence by any method. 00 (-1)"n n=0 Vn2 + 9 The series diverges. conver...

A: The given series,       ∑n=0∞(-1)nnn2+9

Q: Determine the general solution for each given higher-order differential equation or particular solut...

A: Given that: (D2+8D+25)3(D2-4D-5)2(D2-2D-15)4z=0,   Dz=dzdx

Q: Suppose it is known that for a given differentiable function y = f(æ), its local linearization at th...

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Q: Express the repeating decimal as a fraction. 0.685828282828... 0.685828282828...

A: This question is based on conversion from repeating decimal to fraction.

Q: A moving truck rental company charges $20.95 to rent a truck, plus $0.62 per mile. Suppose the funct...

A: Given:- A moving truck rental company charges $20.95 to rent a truck, plus 50.62 per mile. Suppose t...

Q: 137 What is the value of cos-(cos d) where d = 15T radians? If undefined, enter Ø. 2 Provide your an...

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Q: Find the Taylor series generated by fat x = a. 3 f(x) = a = 1

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Q: equations. 1. (D2 + D)y = sin x %3D 2. (D2- 4D+ 4)y = e* 3. (D2 – 3D+ 2)y = 2x3 - 9x2 + 6x 4. (D2 + ...

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