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Q: 1 4) Find the exact area of the surface obtained by rotating the curve x = + on the interval 6 2y <y...

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Q: In(x³) Compute lim x²

A: Given: The limit limx→∞lnx5x2, To find: The value of given limit.

Q: I'm trying to solve this using u-substitution.

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Q: Choose the letter of the correct answer:

A: We need to choose the correct answer, limt→0et-1t A. -1 B. 0 C. 1 D. e

Q: Solve for x accurate to three decimal places.

A: Solve for x accurate to three decimal places. 50001+e2x=2

Q: Find the length of the curve. x = 413. y = 612. 0 sts v8 %3D The length of the curve x = 4t°, y = 6t...

A: Given curve x=4t3, y=6t2 0≤t≤8

Q: 22. Per capita income. In 2009, U.S. per capita personal income I was $48,040. In 2012, it was $52,4...

A: It is given that the growth of US per capita income follows an exponential model. An exponential mod...

Q: find the area of the region please

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Q: 12.5.3 Answer the following questions about F(x) = 6x + 150. (A) Calculate the change in F(x) from x...

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Q: Calculate the area of the shaded rectangles in Figure. Which approximation do these rectangles repre...

A: Given: y=fx=4-x1+x2 In the picture given above, the midpoints of the intervals are used to define t...

Q: I need help with the question below A water tank has the shape of an inverted circular cone (point d...

A: Given an inverted circular cone with base of radius = 3 ft depth of cone = 8 ft Water is pumped into...

Q: 1. Use the definition of the definite integral as the limit of a sum to evaluate -3 (4.r – r) dr.

A: Definite integral Definition The definite integral of a real-valued function f(x) with respect to a...

Q: Exercise 7. Let f(2)=4Re(z) and C be the line segment connecting 1+i to 0. The integral of f over C ...

A: Solve complex line integral

Q: (iv) Solve the differential equation dy/dt + 4y 12, with the initial condition %3D y(0) = 2 and brie...

A: Given differential equation is : dydt+4y=12 y0=2

Q: Fill in the blank with a number to make the expression a perfect square. y +18y +

A: To make the expression a perfect square, we use formula of (a+b)² We know that ...

Q: Consider the equation below: f(x)=x^4-32x^2+3. Find the interval on which f is increasing and decrea...

A: Here we have; f(x)=x4-32x2+3 ............(1) differentiate with respect to x f'(x)=ddxx4-32x2+3

Q: Find the general solution of the first order differential equation 2xy(dy/dx)=x2-y2

A: The given differential equation is a homogeneous. See attached file for a step by step explanation.

Q: 3. Evaluate cach of the following integrals using any suitable technique (or com- bination of techni...

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Q: Find the positive values of p for which the series converges. (Enter your answer using interval nota...

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Q: Let h(t) = tan t. Find the maximum and minimum values of h on the interval I = [0, z/4]. Then use th...

A: To find the bounds for the area

Q: Let f(x) = x5 + 5x4 + 6x + 3. a. Conduct a sign analysis of f''. That is, determine the sign ...

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Q: Find a power series representation for the function. (Give your power series representation centered...

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Q: help

A: According to the properties of integration we have: ∫[f(x)±g(x)] dx=∫f(x) dx ± ∫g(x) dx

Q: A man wants to set up a 529 college savings account for his granddaughter. How much would he need to...

A: Given: Future value required 17 years=60,000

Q: Answer b and c

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Q: B) find the Domain and Range f(x) = Vx – 3x²

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Q: A business sets up a sinking fund so they will have a $66,000.00 to pay for a replacement piece of e...

A: An annuity is a contract between you and an insurance company in which you make a lump-sum payment o...

Q: Consider the following. y X (a) Determine the interval(s) on which f'(x) is positive and negative, a...

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Q: Part d only

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Q: Calculus Question

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Q: Evaluate the definite integral. '16 9e V x dx

A: Topic- Definite integration

Q: An equation whose variables are polar coordinates is called a(n)............... .......................

A: given, An equation whose variables are polar coordinates is called a(n). . . . . . . . . ...

Q: Calculus Question

A: Given, ∫022 x21-x2dx We have to integrate by using trigonometric substitution.

Q: Evaluate the following limit. Use lHôpital's Rule when it is convenient and applicable. y? + 2y - 3 ...

A: Here we use L Hospitals Rule to determine the limit of function.

Q: Let f (x) = | x |. The mean value of f on the interval [-4, 3] is

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Q: Which of the following is the solution of the differential equation y^(4)-10000y=0 ? a) y=(x^2)(10+e...

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Q: help

A: The explanation of answer as follows

Q: In Problem,the letters r and represent polar coordinates.Write each equation using rectangular coord...

A: To Determine: Write each equation using rectangular coordinates (x, y). Given: we have r=33-cosθ Exp...

Q: Showing and justifying all work, find: lim (2 – r)tan(52) Hint: Take logs and use properties. You ne...

A: Topic- limits

Q: A test requires that you answer first Part A and then either Part B or Part C. Part A consists of 6 ...

A: part A can be filled in 2C1*2C1*2C1*2C1*2C1*2C1= 2^6 ways= 64 ways part B can be filled in 5C1*5C1*5...

Q: Evaluate cach of the following integrals using any suitable technique (or com- bination of technique...

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Q: Part a only

A: Integrate

Q: Q 4. Use ab-initio method and find the derivative of 3x +5x² – 2x-12.

A: ab-initio method is nothing but differentiating the function using basic principle of differentiatio...

Q: help

A: Given:fx=x2-3x-10To find Riemann sum ,S5 on the interval -3,7, by partitioning the interval-3,7 int...

Q: What is an increasing function?

A: What is an increasing function?

Q: help

A: We have to estimate the e0.02 Use equation of tangent line to the curve y=ex at x=0 Substitute x=0 i...

Q: 4.8· 12...(4 k) Σ Determine whether the series converges or diverges. (4k)! a) Oconverges b) Odiverg...

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Q: Graph the following function using information from the first and sec- ond derivatives. Label all ke...

A: From 1st derivative test we can find out the critical points.

Q: ах + b Using a Function Let f(x) сх + d' (a) Show that f is one-to-one if and only if bc ad + 0. (b)...

A: Given function is f(x)=ax+bcx+d

Q: Calculus Question

A: Splve intregal