10 Find the derivative of: -4x/4_ 5x Do not simplify negative exponents

Q: a. y'=-20x (3– 5x')" 32. Suppose that x and y are both differentiable functions of t and are related…

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Q: Find a general solution. Check your answer by substitution. ODES of this kind have important…

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Q: dy in terms of a da Use the Chain Rule to find y = (u – 2)3 and 1 27 + 1 u%3D

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Q: Consider the given: х3 — 4х2 x(х + 8)(х — 2) (x + 2)3 8(7x – 4) f(x) = ;f"(x) (x + 2)2 i f (x) : (x…

A: The given functions and their derivatives are: f(x)=x3-4x2(x+2)2=x2(x-4)(x+2)2,…

Q: 1 f(æ) = 10x + 29 - a) Give the domain of f (in interval notation) b) Find the critical numbers of…

A: There are more than 3 sub-parts, as per the Q&A guidelines we are answering the 1st 3 sub-parts.…

Q: If f(x) = 6 + 5x – 5a, find f'(- 3).

A: Topic = Derivative

Q: Think of four random integers q, r, s, and t selected from 0 through 9. Let a1 = 0.qrst, where q, r,…

A: let as consider four integers q,r,s,t from 0 to 9 then we get a1=0.qrst=0 now if we select four more…

Q: For the series below calculate find the number of terms n that must be added in order the indicated…

A: The solution is given below

Q: Water flows into an empty reservoir at a rate of 2200 + 15t gal/hour . What is the quantity of water…

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Q: determine the area of the region bounded. show complete solutions.

A: We have to find the area of the region bounded.

Q: 1. Which of the following is equal to the first derivative of a function? A) point of tangency B)…

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Q: A rock is thrown upward from a bridge that is 53 feet above a road. The rock reaches its maximum…

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Q: Test the series below for convergence using the Root Test. n2n (In(n))" n=2 The limit of the root…

A: To solve thsi question we will apply the concept of root test and limit.

Q: [x* sin 3.xdx

A: Note that, according to Bartleby guidelines, we can answer only the first question in the case of…

Q: 1. Determine whether the function ƒ(x) = x² + 6x +9 is continuous at x = -2. Sketch its graph…

A: Here, the given function is: f(x)=x2+6x+9 which is a polynomial function. To determine the…

Q: 2. Find f(2.6) by interpolating the following table of values. Using Lagrange interpolation. i xi yi…

A: I am attaching image so that you understand each and every step.

Q: Use the Chain Rule to find the derivative of the function. y = (4x2 − 5)3 y' =

A: Solved below

Q: 2. Using partial fractions, show that 4 Σ n² – 1 n=2 converges.

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Q: Below is the graph of the derivative f'(x) of a function defined on the interval (0,8). You can…

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Q: 4. S V tan x sectx dx

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Q: Verify that f has an inverse function. Then use the function f and the given real number a to find…

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Q: a) obtained by rotating the curve Sketch and find the area of the surface y =/2x + 3 for x E [2,4].…

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Q: 2. Find the equation of the tangent line to the curve y = x2 - 2x -3 that is parallel to the line x…

A: Note: As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Given: 3a – 6x + 2y + 8y- 1= 0. Identify the conic and give its foci.

A: Follow the procedure given below.

Q: 2.34 Let f(x) = cos x – x – sin x. Prove: There exists a solution to the equation f(x) continuous on…

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Q: -2n f) S“ cos 2x dx g) S et² t dt h) S x sin(x²) dx

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Q: Test the series below for convergence using the Root Test. 3n 6n + 2 n=1 The limit of the root test…

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Q: Use the Root Test to determine the convergence or divergence of the series. (If you need to use co…

A: Root Test : Consider the positive term series ∑ an . Define,         L= limn→∞  ann= limn→∞ an1n ,…

Q: determine the area of the region bounded. show complete solutions.

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Q: Find an equation of the hyperbola having foci at (1,-2-/25) and (1, -2+25) and asymptotes at 3 r- 4.…

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Q: The functions y1 = ex and y2 = e-3x solutions for the homogeneous DE: are both y" – 9y = 0. Then,…

A: y''-9y'=0Since y1=e3x  , y2=e-3x are the solutions of homogeneous DE  Then complementary function is…

Q: A particle moves in a straight line with velocity t-2 – * ft/s. Find the total displacement and…

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Q: Solve for x. Record solution using boxes below. Then answer graph questions. (Given solution in…

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Q: 3-8 (a) Sketch the plane curve with the given vector equation. (b) Find r'(t). (c) Sketch the…

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Q: Find an equation of the ellipse having a major axis of length 6 and foci at (-5, 3) and (-5, -1).…

A: Given problem:- Find an equation of the ellipse having a major axis of length 6 and foci at (-5, 3)…

Q: Use the Root Test to determine If the following series converges absolutely or diverges. Σ ne1 (3n +…

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Q: 20-21) What is the equation of the tangent line to y = x3 at x=2? A) y = x - 12 B) y = 12x C) y = x-…

A: Use derivative for finding the  equation of tangent line .

Q: 1. Determine whether the function ƒ(x) = x² + 6x +9 is continuous at x = -2. Sketch its graph…

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Q: 8 x2 + 16 dx x2 The integral is equal to ...

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Q: Use the General Power Rule to find the derivative of the function. y = 12 3 4x2 + 7 y' =

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Q: Evaluate A Se-* dx by Simpson's 1/3 rule with n=10, work for six digit

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Q: (a) Find an equation of the tangent plane to the surface at the given point. x² + y2 + z? = 33, (1,…

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Q: Determine the point(s) (if any) at which the graph of the function has a horizontal tangent line.…

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Q: Graph the curve and find its length. (Do this on paper. Your instructor may ask you to turn in this…

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Q: Sketch the curve. a) r=-2 sin 0

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Q: %24 3 To test this series for convergence 4" 1 7" n=1 You could use the Limit Comparison Test,…

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Q: The function f has a continuous second derivative, and it satisfies f(9) = -4, f'(9) = 0 and f"(9) =…

A: If a  function f(x) is defined on an interval [a,b] and it's second derivative exists at x=c, then…

Q: Find the second derivative of the function. g(t) =  7 8t6

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Q: Which one is the arc-length of the curve y =2V12x + 14, x E [12, 14]? 14 126x+219 dx 12 6x+7 14 18x2…

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Q: 3 ų (Vector Q.2 For the twJo Vectors: A=i-3j-2k B= 31 +5j +7K Find Ahe fallowing O BA Å+2B %3D…

A: Solution of question is written in below steps.