For the following, problems, find the volume generated when the region between the two curve is rotated around the given axis. Use both the shell method and the washer method. 5. Bounded by curves y = 3x, y = 0, and x = 3 rotated around the x - axis.

Q: For f (x) = x2 −2x + 5, find its derivative by using the formal (limit) definition of the derivative

A: We have to find derivative using definition

Q: (a) Given the curve of y=x -x(x+3)(x-2)(x-5) i) Sketch the graph for -4<x<6 ii) Find the area of the…

A: Given curve y=110x(x+3)(x-2)(x-5) First we find point of intersection with X-axis, Therefore put y=0…

Q: Q.1B) Prove that: Iff, Cos) dxdy - = sin (1) where R the region bounded by x + y = 1, x = 0, y = 0

A: We use the change of variable to prive the given equality

Q: Consider the initial value problem x' = 4x², x(0) = x0. For what value(s) of co will the solution…

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Q: 1505 152 mxa 081 dial 3a. Find the coordinates of the relative maximum and relative minimum of the…

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Q: 2.1 Calculate the value of C.   2.2 Use your answer in question 2.1 to determine the total of…

A: We have to find the value of C and calculate her change.

Q: Set up the the integral to find surface area for f(x)=x^4+1 over [1,3] show all steps for setting up…

A: The solution is given below

Q: Use Integration by parts to solve: Sxe cosxdx

A:

Q: 9. Find the indicated roots. Sketch the roots in the complex plane: a) The fifth roots of 32 b) The…

A: According to Bartleby guidelines I can only answer the first question of the given problems

Q: Test the convergence and divergence of the following series, find the sum of convergent series.…

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Q: WHich of the following represents the shell height if the shell method will be used to find the…

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Q: Mark heard that he could triple his money in 13 years if he invested it in a large business. What…

A: This question is related to compound interest, we will solve it using given information.

Q: s) Calculate the indefinite integral using Trigonometric Substitution. X [ dx +x²

A: This is a problem related to integral. Based on the trigonometric substitution we will answer the…

Q: 1. Write the equation with the smallest possible shift for: a) a positive sine function b) a…

A: Let's find sine and cosine  equation from the given  graph.

Q: c- Show that the following limit does not exist (x² - y²) lim (x,y)-(0,0) x2 + y² 2

A: Given ; lim(x, y) -(0,0)[(x2-y2)/(x2+y2)]2.

Q: How about number 2?

A: Let's solve two parallel diffrential equation problem.

Q: Compute the limit of the function at −1 AND determine if the function is continous at 1. f (x) = {…

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Q: If f(x,y,z)=z In(x²ycosz), then fz is O 2z X OZ y O2z y O In(x²ycosz) - ztanz <|N

A: This question is related to partial differentiation, We will solve it using given information.

Q: 11. The point (9, 16- A. (3,4)

A: y=f(x)after transformation y=f(x)(x,y)→(x , y)(9,16)→(9 , 16)=(9,4)

Q: What function will you differentiate to get each function? 2. f(x) = 8x7 - 4x³ + 2x - 3

A: dxndx =n.xn-1

Q: e the graph of f(x) is given. Describe verbally how the graphs of the following functions can be…

A: Graphical transformation

Q: A kite 100 ft above the ground moves horizontally at a speed of 5 ft/s. At what rate is the angle…

A: This question can be solved using the concept of rate of change of quantities.

Q: (2x² - x - 1) x³ - x² ; 2 dx

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Q: . Evaluate Jo So fixy³ dydx

A:

Q: 6. 7. 8. Determine the derivative of the curve with equation y = 4²x a) 4²x ln4 b) 42x In2 c) 4* In2…

A: We have to find out derivative

Q: Test the convergence and divergence of the following series, find the sum of convergent series. b)…

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Q: The total charge in an electrical circuit as a function of time is given by q = t 1+t² Find the…

A: Given:        q=t1+t2,C        q=t·1+t2-1 The derivative of this expression is      dqdt=ddtt·1+t2-1…

Q: H.W 1. Test the convergence and divergence of the following series, find the sum of convergent…

A: This is a problem related to series and sum calculation. Based on the general formula and concept we…

Q: A stone is dropped into a still pond. Concentric circular ripples spread out and radius of disturbed…

A: Here we have to use the concept of the derivatives

Q: 2. For the following problems, determine the area of the region between the two curves in the given…

A: The simple integration..

Q: Consider the Initial Value Problem (IVT) dy = Axy, y(0) = 1, da where A is a positive constant. The…

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Q: f cos² x dx

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Q: Calculate the indefinite integral using Partial Fraction Decomposition. X √(x − 2)(x + 1) dx - galmi…

A: We can evaluate the given indefinite integral by using the partial fraction method.

Q: Solve the following equations for x: a) 2e6x = 18 b) c) d) e) In x²: In x f) Inx² - In 25 2 And…

A: (a) 2e6x=18 e6x=9 Taking ln both side we get lne6x=ln9 6x=ln9 6x=2ln3 x=(1/3)ln3 x=0.36620…

Q: Sy² sin(3y³ + 4) dy

A:

Q: find y dy dx 2x-1 x-3 for the following functions b) y = x³e-x

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Q: 1) In medieval times there were 10,000 people living in a city that was struck by a plague so that…

A: This is a problem related to differential equation. based on the general formula of decay law we…

Q: Calculate the discount on one bike if they decide to buy 10 bikes at the same time.   1.3.2…

A: This is basic algebra problem

Q: For the following, problems, find the volume generated when the region between the two curve is…

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Q: EXAMPLE 2 Consider again our analysis of a heavy rock blown straight up from the ground by a…

A: Given problem:- Consider again our analysis of a heavy rock blown straight up from the ground by a…

Q: Factor the difference an+1-an to show that the given sequence {a} is strictly increasing or strictly…

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Q: Use the formula Py_ PM 71−(1+i)~* | PV=

A: We have to find out pv

Q: H. Evaluate coordinates. 4-y² 4-x²-y² 1 x²+y²+z² So dzdxdy by using spherical or cylindrical

A:

Q: Using rectangles each of whose height is given by the value of the function at the midpoint of the…

A: Here we need to estimate the area under the curve using two and four rectangles.

Q: How long did it take for an investment of $21,250 to grow to at least $24,000 at 2.50% compounded…

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Q: Using rectangles whose height is given by the value of the function at the midpoint of the…

A: Let's find area under the curve by using two rectangles.

Q: Use spherical coordinates. Evaluate SSS √x² + y² + z² dv, where E lies above the cone z = √√x² + y2…

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Q: Calculate the derivative of the function below using the quotient rule. y = 2-10 √x + 5x8 f(x) = and…

A: Use quotient rules

Q: Compute the approximate value using differentials. √272 √234 The final answer should be in fractions…

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Q: QI\ A\ Find Domain and Range for this function y √x²+2

A: