Suppose the derivative of a function f is f'(x) = (x + 1)4(x − 3)(x - 5)6. On what interval is f increasing? (Enter your answer in interval notation.)

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A: Given : rate = 5% time = 4 year  d = $ 200   formula :

Q: Find the dot product and the angle between the vectors, ū and v. 2. (3,-5), (7,4) 3. (-3,0), (5,7)…

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Q: Approximate the derivative of the function f(x) = sin (x²) on the interval [0, 2] in steps 0.25…

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Q: C [² (₁²- Jo (u² - 2u) du

A: Solution : Given that integral is

Q: The marks scored by 10 students out of 75 are given as 3, 30, 10, 13.9, 41, 56, 30, 71, 30, 13.9,…

A: The marks scored by 10 students out of 75 are given as 3, 30, 10, 13.9, 41, 56, 30, 71, 30, 13.9,…

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Q: Evaluate the following integrals analytically: Cπ/2 #1 #2 #3 (8 + 4 cos x) dx 3 [² (1 - e²^x) dx [²₂…

A: The given integrals, 1. ∫0π28+4 cosxdx 2. ∫031-e-xdx 3. ∫-241-x-4x3+2x5dx We have to solve these…

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Q: 4. Use the table in the book to find the Taylor series for the function, centered at the specified c…

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Q: Evaluate the integral 27 fa² (2³ – 3)" dx, by making the appropriate substitution: u = 27 fa" (x³ −…

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Q: The fox population in a certain region has an annual growth rate of 5 percent per year. It is…

A: Given: Fox population in year 2000, P1=13200  Annual growth rate, r=5%

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A: We have to solve  thegiven   First order linear differential equation  which is linear in r.

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A: Given query is to find indicated limit.

Q: -3x² 2√√8-³ (a) Show that f'(x)=- for x < 2. The graph of y = f(x) is shown in Figure 9, along with…

A: Given a function f(x)

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the functions  b)…

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Q: 95. Hours of daylight in Boston. The number H of hours of daylight in Boston t days after the vernal…

A: iven H = 12 + 3 sin2πt365where H = numbers of hours of daylight

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A: The given equation is; (D2 + 2D + 1)(D2 + 4)y = 0

Q: Evaluate 4²+² r2y dxdy S² √²4 Ο π/12 Ο π/6 Ο π/16

A: NOTE: Refresh your page if you can't see any equations. .

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A: we need to graph the polar coordinates and have to label them.

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A: Given query is to find the computer usage for first 14 weeks.

Q: Find the equation of the tangent line to the parabola y 2x2x+3 at x = 2. Circle your final answer

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Q: 1 The vector field F = is conservative. Find a potential function for F compute SF dr, where C is…

A: To find the given line integral.

Q: ind the area between y = 12 sin (x) and y = = 12 cos (x) over the interval [0, π] Jse decimal…

A: Point of intersection⇒12sinx=12cosx⇒tanx=1⇒tanx=tanπ4⇒x=π4

Q: Find a function f such that the slope of the tangent line at a point (x, y) on the curve y = f(x) is…

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Q: suppose gradient f(a,b) =4i + 3j. find a unit vector u such that a) Du f(a,b)=0 b) Du f(a,b) is a…

A: Please see the below picture for detailed solution.

Q: Problem 5. the Ratio Test. (a) M18 πη n! n=1 State whether each of the following series converges or…

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Q: If the sales tax 4% and the purchase price is $263, what is the amount of tax?

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Q: d. f(x) = (2x-3)5 (2x²- e²x)-3

A: Given query is to find the derivative of the expression.

Q: a. a₁ = 1, a2 = 2, an=2an 1+3an 2

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Calculate the integral approximation S6 for 1 Så 21 dx. zº+1

A: we have to calculate the integral ∫4911+x6dx  using S6 here   a = 4   and  b = 9  and n = 6    here…

Q: f(x) -x³-2x² -5x+2. Use calculus and show work. Use exact values only. Find all intervals of…

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Q: 4. Complete the table of values (to five decimal places), and use the table to estimate the value of…

A: Ans= 0.25 For detail..go through the solution I have solved step by step in detail

Q: 4. y(2xy² − 3) dx + (3x²y² − 3x + 4y) dy = 0

A: Given differential equation y( 2xy2 - 3 )dx + ( 3x2y2 - 3x + 4y )dy = 0 standard form Mdx + Ndy = 0

Q: Find the Laplace transform of the following functions. (a) S6 0 < t ≤ 3 = 2 t≥ 3 {{ f(t)

A: according to bartleby guideline we do only first part of muktiple questions f(t)=6  0≤t≤32   t≥3from…

Q: Evaluate the integral 20 fx³² (x³ – 5) 2⁰ da by making the substitution u = x = x³ – 5. + C NOTE:…

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Q: Consider the following initial value problem, defined for t > 0: y² – 2y = f* (t- a. Find the…

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Q: 3. The region in the first quadrant bounded by the curve y = cos x and the axes is rotated about the…

A: To find:- Volume of solid bounded by curve y=cos(x) in first quadrant about x axis

Q: Use properties of a right triangle, trigonometry, and implicit differentiation to determine the…

A: By using the properties of a right triangle, trignometry, and implicit differentiation to determine…

Q: The height (in meters) at time t (in hours) of a balloon is given the formula h(t) = -20tª + 80t.…

A: The height (in meters) of a balloon at time t (in hours) is given by ht = -20t4+80t…

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Q: The figure below shows the derivative f' of f. f ' (x) 4 10 + x मुंह 2 6 8 12 (a) Choose all…

A: We know Function increasing when f'x≥0Function decreasing when f'x≤0

Q: Problem 7. series converges or diverges and mention the test you are using. Show all work. 00 (2) Σ…

A: To solve this problem we can use p-test , comparison test and root test

Q: Write the composite function in the form f(g(x)). [Identify the inner function u= g(x) y = √e*+…

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Q: The integral ₁ |102² – 2³ – 24x| da MUST be evaluated by breaking it up into a sum of three…

A: The given integral is:∫-15 10x2-x3-24x dx

Q: Find the indefinite integrals of the following. Answer is already given. Show step by step on both…

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Q: The figure below shows the derivative F' of F. Let F (0) = 0. F'(1) ਜਿਹ 8 + 2 4 6 Of the four…

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Q: 8 If f(x) = 14 +₁ 7 0 O f(x) 14+ f(r) x", then f"(x) is co

A: Please refer to the image below

Q: Using Integral test, determine convergence or divergence for Σn (Inn)³3 * n=3

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Q: Compute the flux of the vector field F(x, y, z) = 3i + 23 + 2k through the rectangular region with…

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