Use (1+x)™ = 1+[ m(m− 1) ···(m− k +1) k=1 k! Maclaurin series for (a) 1 1+x if |x| <1, to obtain the

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Q: For what value of X does the function f(x)=x³9x² 120x+6 have a relative minimum?

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Q: Find the limit algebraically. lim h→0 f(-6+h)-f(-6) h where f(x) = - 8x² + 8x - 7

A: see below the answer and calculation

Q: Find the length s of the circular arc.

A: We will find the required  length of arc.

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Q: Let A = Then a = 5 0. 24], -4 B = Number [.35 14 0 -28 Also given that B = a A

A: To find the value of alpha

Q: 3. Sketch the graph of a continuous function f(x) with domain [0, 2] which is differentiable up to…

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A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: Find the directional derivative Du f(x, y) of the function f(x, y) = 6xy² + 3x²2 at the point (-1,2)…

A: Let's find directional derivative at given point and direction.

Q: Use the Laplace transform to solve the given initial-value problem. y' + y = f(t), y(0) = 0, where…

A: As we know that  L(au(t-c))=ase-cs, L(y')=sY(s)-y(0), L-1(1s)=1 and L-1(1s-a)=e-at,…

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Q: Hi! Can I have some fraction examples solved? I need an example on "paper" if you can. 5 1/7 - 1…

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Q: why is e and the natural logarithm, rather than other bases, are used in so many situations

A: We have to explain why is natural logarithm is used more.

Q: calculate [_²["²|3x³y²|dydx.

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Q: entiable at x = -1. f(x) = 3ax 3 bx² + 3x b= + 3x - 8 for for Submit Answer x -1

A: See the details solution in below

Q: For the function f(x) given below, evaluate lim f(x) and lim f(x). x-x X118 Provide your answer…

A: Given query is to find indicated limits.

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Q: Suppose you have a triangle whose height is 10 times its width. If the base of this triangle has a…

A: We need to find area.

Q: ) Let r(t) =(√5-t, ¹+2,t sin t). (1¹) C A) Find the domain of r(t). B) lim r(t)=? 1-0 c) fr(t)dt =?

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Q: lim t→∞0 (1- 314 t t

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Q: Use your derivative rules to find the derivative of the following functions: 1. f(x) = x¹ cos(x)…

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Q: Consider the function f(x) = 3-6x², -3 ≤ x ≤ 2. The absolute maximum value is and this occurs at x =…

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Q: Write the first three terms of the sequence whose nth term is given by the formula. 1. an-n-1 1 4n…

A: To find the first term , we need to substitute n =1 in an . For second and third term substitute n=2…

Q: Suppose that for a particular product, the number of units x produced per month depends on the…

A: We can solve the given problem by using the concept of derivatives.

Q: QUESTION 9 Given f(x) = x². Determine the minimum distance between the point (10; 2) and a point on…

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Q: 15. A person in a rowboat two miles from the nearest point on a straight shoreline wishes to reach a…

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Q: dx z/L1(zx — 6) вх І

A: The given integration is: ∫x149-x2172dx

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A: d dX(lnx=1xd dx(constant)=0 given   ∫1010x-11dx=ln10x-11+c

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Q: All 80 rooms in a motel will be rented each night if the manager charges $40 or less per room. If he…

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Q: The gas equation for one mole of oxygen related its pressure P (in atmospheres), its temperature, T…

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Q: Work Problem solutions and justify your answers. 1) dy dx Write step-by-step Consider Bernoulli's…

A: Answer is in step 2

Q: Evaluate the following sum of iterated double integrals: 2y 1.² 1th ²² e4x-x² 4-2y dx dy + + ₁² ²²…

A: To find:- ∫01∫02ye4x-x2dxdy+∫12∫04-2ye4x-x2dxdy

Q: Find the linearization L(x) of y = 5x ln(x) at a = 1. L(x) =

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Q: Consider the following function. h(x) = x-1¹/3(x-8) Find the derivative of the function. h'(x) = X =…

A: we need to find out the derivative h'(x).

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A: To find the formula for distance.

Q: A function is said to have a horizontal asymptote if either the limit at infinity exists or the…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Suppose F(4) = 6, F(5) = - 10, and F'(x) = f(x). 5 f(x) dx [5

A: Topic - definite integral We are given, F(4) = 6 ,F(5)=-10 and F'(x)=f(x) We need to find ∫45f(x)dx

Q: Let f(x) f'(x) = = f'(5) = 4x² + 2x + 2 (round to 3 decimal places)

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Q: If f(x)= f'(x) = f'(1) = places) tan x - 3 sec x > Next Question (round to 3 decimal

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Q: Consider the function Evaluate the following (a) f(5) (b) f(x) + f(5) (c) f(x-2) 3 f(x)=2x² +9x+3.

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Q: Use a table of integrals to find the area of the region bounded by the graph of y= 5 0 Click here to…

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Q: Find the equation of the tangent line on the curve x² + y² + 2y = 0 at (0, -2). A B с D x=0 y=-x…

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Q: B. Using the definitions of limit and/or infinite limit, show that if limn→∞ sn = ∞, then also…

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Q: B. Given the matrix 1 20 A 0-1 4 52 a Find the value of a for which the matrix is singular.

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the…

Q: If f(x) = 3x³ - 6e*, find: f'(x) = ƒ' (3) = ƒ''(x) = = f''(3) =

A: Given, f(x)=3x3-6ex