Evaluate the improper integral and state whether it converges or diverges. Show limit notation and all integration

Q: lim 21-2 A) 1 √√2x+5-1 x+2 || B) 0 C) ∞ D) -∞ E) does not exist

A: given limit to find

Q: 2/ Lift all 5 Possible -6x² +12x²-3x +2 Zeros (make list and Stop)

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Q: exponential model, shown below. In this model, P is the population of bacteria (total count,…

A: The objective of this question is to linearize the given exponential model P(t) = 5e^(t/8) around t…

Q: Suppose that y is a differentiable function of x andw = cos(y6).Express the derivative of w with…

A: The objective of the question is to find the derivative of w with respect to x, where w = cos(y^6),…

Q: (a) (xy² + nx²y)dx + (x³ + x²y)dy = 0,

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: Given: x-2, if x #-2 |3kx+5, if x=-2 Calculate k so h(x) is continuous. h(x)=

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Q: continue D, E and F

A: Given that,f and h are continuous and differentiable functions that satisfy the followings,

Q: Find if the series converges or diverges.

A: Given series converges, detailed explanation given belowExplanation:

Q: Find the area of the region under the given curve from 1 to 2. x² + 7 3x - x² y =

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Q: Test for convergence or divergence with the Direct Comparison Test.

A: Refer to explanation section Explanation:

Q: 17. The following function describes the motion of an arrow shot upwards. The height h in meters…

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Q: Find the arclength of the curve r(t) = (2√2t, e²,e-2t), 0 ≤ t ≤ 1

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Q: Determine whether the statement is true or false. True O False 1 '00 7 xvž dx is convergent.

A: To determine whether the following statement is true or false. is convergent.

Q: xy√x + y lim (x,y) →(0,0) x² + y²

A: To determine whether the following limit exists or not by using polar coordinates.

Q: The graphs of the function F (left, in blue) and G (right, in red) are below. Let P(x) = F(x)G(x)…

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Q: For the function f(x) = simplify the difference quotient: f(x+h)-f(x) h

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Q: A Ferris wheel has a radius of 31.2 feet. The bottom of the Ferris wheel sits 0.8 feet above the…

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Q: A point is moving along the graph of the given function at the rate dx/dt. Find dy/dt for the…

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Q: The total cost (in dollars) of manufacturing x auto body frames is C(x) = 60,000+ 900x. (A) Find the…

A: Let  c(x) be the total cost .Average cost , =

Q: Find f'(1) if f(x) = √√√x + )=√x+ +2

A: We are given,

Q: Please help me with this thanks! full detailed solution

A: The objective of this question is to find the derivative of the function f(x) = sqrt(x) + 2 at the…

Q: Let f(x) = 8 + 7- 6 5 4- 3 2 H S ૨૨ 4 2 In(x) 1 2 3 4 5 6 7 8 Find the arc length of f(x) on the…

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Q: Evaluater(g(t)) using the Chain Rule: =(t) = (e¹, eº¹, −8), g(t) = 5t - 5 dr(g(t)) = { >

A: \)" data-mce-style="cursor: default;">r(t)=<et,e6t,−8> and g(t)=5t−5We have to find the…

Q: 1+x² What is the slope of the tangent to the curve y=- 2x when x = 3?

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Q: Suppose that the weekly sales volume y (in thousands of units sold) depends on the price per unit…

A: The objective of this question is to find the rate of change in sales volume with respect to the…

Q: Q/ Find the Integral of the following: 1- fx sin x dx 2- ((1+tan²x) dx 3- [cos 2x dx

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Q: For the circle x² + y² = 25, a. find y when x = 3. Enter your answer as a list of numbers separated…

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Q: Find the value of the constant c that makes the following function continuous on (-∞, ∞). x² { x = 1…

A: The given function is If function continuous at

Q: Please don't provide handwritten solution .....

A: The answer is written below:Explanation:

Q: Use cylindrical shells to find the volume of the solid generated by rotating the curve y = 2 ln(x)…

A: By using the cylindrical shells, to find the volume of the solid generated by rotating the curve…

Q: lim x-0 1 - cos x sin x

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Q: 2) Find the volume of the solid generated by revolving the region bounded by the parabola y² = 4x…

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Q: Let R be the region bounded by y = 2√x, x = 5.75 and the x axis. 4.5 4- 3.5 3 2.5- 2 1.5 1 0.5 1 2 3…

A: Given that the region is bounded by the curve  , and the x-axis

Q: Find a basis for the following ODE. y" - 2y" - y' + 2y = 0

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Q: Find all functions whose derivative is −11sin (x). Your computer is able to provide a hint that…

A: The given derivative of thenfunction is

Q: Find the relative maxima and relative minima, if any, of the function. Use the First Derivative Test…

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Q: Find the converges or diverges.

A: Here I attached the detailed explanation to the questionExplanation:Solution:

Q: Factor the polynomial and use the factored form to find the zeros. P(x) = x5 − 4x3

A: The objective of this question is to factor the given polynomial and then use the factored form to…

Q: Topic: Chinese Remainder Theorem

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Q: Use the graph to find the limit L (if it exists). If the limit does not exist, explain why. (If an…

A: We can say that L=limx→af(x) iff for every 0 \)" data-mce-style="cursor: default;">ϵ>0 there…

Q: Given fex, y) = sin (x+y) where x = 3445 Find f(x (st), y (s, t)) ft (x (st), y(s, t)) 1y = 45-5t.

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Q: Find the period, amplitude, and phase shift of the function. y=-3-2 sin (2лx+x) πχ+ Give the exact…

A: The sine function of the form

Q: f Determine the general tangent slope to the curve X = √x +3.

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Q: Find dy: dx y = x sin6x

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Q: Use cylindrical shells to find the volume of the solid formed by rotating the area between the graph…

A: By using cylindrical shells to find the volume of the solid formed by rotating the area between the…

Q: A toy race car travels along a circular race track that has a radius 29 meters long. The race car…

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Q: 10 First Number: (−2 ƒ (x) – 3 g (x)) dx. -7 -7 10 Second Number: ƒ (−2 ƒ (x) − 3 g (x)) dx + ƒ ƒ(x)…

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Q: The graphs of x = 8, y = f(x) (solid) and y = g(x) (dashed) are shown; the graph is not drawn to…

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Q: Evaluate the definite integral. Use a graphing utility to verify your results. 64 104 √5 dx X

A: .

Q: 1. Prove that for n € Z (any integer n), n²n+5 is an odd number.

A: To proveFor  (any integer n),  is an odd number.