Given f(x): find the average rate of change of f(x) on the interval 8, 8+ h. Your answer x + 8 will be an expression involving h. Submit Question

Q: Determine wheather the series con verges or diverges. S tate which +est of Convergence/divergence…

A: We have to find if the given series converges or diverges.

Q: An object moves along a coordinate line with velocity v(t) = 1(6 - 1) units per second. Its initial…

A: Solution:  To find the position of the object at a point, we must find the position function, which…

Q: dr 2.

A: Use simple integration formula.

Q: Find c 0 such that the area of the region enclosed by the parabolas y z? -c² and y= c² – a?is 200.

A: Solution: we are given curves and firstly, we find bounds and for finding bounds, we set them…

Q: Without using a calculator evaluate the definite integral. | (10x - 6x +6) dx = Σ

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Q: In 7 years Harry and Sally would like to have $20,000 for a down payment on a house. How much should…

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Q: 3. Which of the following is always true for any real numbers x, y? For real e > 0, if Ix-yl se,…

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Q: Jackie wants to design a cylinder shaped container to hold popcorn. Each container will be made from…

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Q: Question 4 Solve the initial value problem: y' = – 0.03y + 6 y(0) = 50 - y(t) =

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Q: Provide

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Q: a. Prove that (A'B*)-1= (A-B-1)* and B are 3 x 3 matrices and %3D b. If |A| = 4 |B|= -1 compute…

A: I have used the property of  transpose and inverse of product of two matrices and then show the…

Q: 2x and y 2x. Decide whether to integrate with respect to a or y. Sketch the region enclosed by y…

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Q: Jan paid Php 9,250 on a loan made 6 months before at 12% simple interest. Find the interest…

A: Amount Paid after 6 months= 9250 rate of interest=12%=0.12 Recall: Amount after time t years…

Q: 1. Find the area bounded by the graphs of y = 6 + x, y = x', and y breaking the region into two…

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Q: Show that the limit does not exist. xy? - 1 lim (Ky)→(1,1) y-1

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Q: e cos-1x 5. S V1-x2 dx

A: To evaluate the given integral.

Q: dy Find dx of æ³ – y? = 5 by implicit - differentiation and evaluate the derivative at this point:…

A: According to our guidelines, we can answer only one question or three subparts of a question, other…

Q: t) Determine an antiderivative, y, of the given derivative, y. Then use the given condition on y to…

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Q: Set up the definite integral required to find the area of the region between the graph of y 20-z and…

A: Set up the integral

Q: Find the length of the spiraling polar curve 2e 40 From 0 to 27. The length is

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Q: Consider the curve C with parametric equations Ja(t) = t° – 3t +1 lu(t) = t(t +1) defined for t e R.…

A: Given

Q: 7. Find the area of the region bounded above by the line y 3, below by the graph of y VT, between…

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Q: (a) f(x) = (6x² –8x + 4)4 2х -5 (b). у 3D 2.x2 – - 10 2. The population of a city grows from a…

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Q: There is a line through the origin that divides the region bounded by the parabola y 7z 5x and the x…

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Q: :Q1 Solve the second order differential equation Y" – 5Y' + 9Y = 0

A: Here we have to solve second order differential equation.

Q: Given a derivative transform of s³Y (s) – s²y (0) – sy (0) – y" (0) – 382Y (s)- 3sy (0) - 3y (0) +Y…

A: We will use the formulae of Laplace transform of derivatives of a function.

Q: x²y' + 2xy – 2y = 0

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Q: Find the critical point and determine if the function is increasing or decreasing on the given…

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Q: (a) Express du / ax, du/ ay, and du / az as functions of x, y, and z both by using the chain rule…

A: Solving

Q: 1. f(x) = 4x + 7 3. f(x) = 2x -r + 5x %3D

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Q: Let C1 be the curve with parametric equations x = cos t, y = sint – t, where t e [0, ). (a) Find the…

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Q: point C on land such than ZCAB = 44.2°. Find the distance across the lake from A to B. В 506 ft…

A: Given the query is to find the distance between A and B.

Q: 12)List the first five berms of Ehe regence a,=6, aan= 5a -4 as=3 a=? asz?

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Q: 1) Evaluate the integral dy dx using polar coordinate

A: Explanation of the answer is as follows

Q: Q4) Find for the following functions (choose five only): dx 1. у %3D 2** + е2х-1 2. y = sec x tan x…

A: 1) y=2x2+e2x-1Differentiatey'=2x2ln(2).2x+2e2x-1dydx=2x2+1.xln(2)+2e2x-12)…

Q: The tangent plane and the normal line of the surface y = x² + z – 6 at the point (2, -1, 1) have the…

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Q: Write the 4 x 4 elementary matrix which accomplishes the row operation R3 - 5 R2 ---> R3 when you…

A: let  I be the 4×4  identity matrix I=1000010000100001

Q: Find the area of the region bounded by the given curve:r = 5e 2 on the interval

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Q: Directions: Evaluate the following integrai. Show your complete solution. 1. 1 2. dt 3. (3x? – 1)(x+…

A: 1. ∫x2x dx2. ∫1t2+1t3+1t4+1t5dt3. ∫3x2-1x+1 dx Note:     Multiple questions with multiple subpart…

Q: 439) Use the matrix capabilities of a graphing utility to solvecif possible) the systems of linedr…

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Q: (3) (E) - (a) - () 2. 2. 는 (v) 1 1 1. (B) 1 1 = xP (x)fj fx+1 for x<0, 9. Given f(x)= cos nx for…

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Q: xsin x dx

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Q: Find the divergence of the field. F = (2x+7y-8z)i + (5x +3y+6z)j + (-6x-y+2z)H div F =

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Q: Suppose that z = x/y, where x and y are differentiable functions of u and v such that x = dx/dv 3, у…

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Q: Use the nth-term test for divergence to show that the series is divergent, or state that the test is…

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Q: 2. a) Determine the coordinates of all point(s) on the graph of y = 2x In x where the tangent line…

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Q: 14) Test the secies for convergane divergence or 2. (-1)"

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Q: Find the limit of f as (x,y)→(0,0) or show that the limit does not exist. Consider converting the…

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Q: Use Newton's method to approximate the solution to the equation 4 = x+ 2. Use xo = -1 as your…

A: This question can be solved using the concept of methods of approximation of roots.

Q: Determine an expression, in simplified form, for the slope of the secant PQ with P(1, 2) and Q(1 +…

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