Evaluate lim x -3 3 cos (-6-2x) + x 3x + x² and write your answer in simplest form.

Q: Find the equation of the tangent line to y = 7e* at x = 8. (Use symbolic notation and fractions…

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Q: graphs y = 0.8x figure. If the line x = k divides R into two regions of equal area, what is the…

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Q: Let W (s, t) = F(u(s, t), v(s, t)) where W,(1,0) = = Wt(1,0) = u(1,0) = 5, u, (1, 0) = 5, ut(1, 0) =…

A: Let where To find .

Q: Consider the sequence.     20 ,    20 +    20 ,    20 +    20 +    20…

A: The objective of the question is to understand the given sequence, compute the first five terms,…

Q: dx dy √5+2x²+2y² Where R is circular area has radius a. Centre of region R is point (0, 0). 2.…

A: The objective of the question is to evaluate the double integral of the function √(5+2x²+2y²) over a…

Q: The temperature at a point (x, y, z) is given by T(x, y, z) = 400e-x² - 3y² - 9z² where T is…

A: Given: To Find: (a) To find the rate of change of temperature at the point  in the direction towards…

Q: Determine the interval of convergence of the following power series (−1)n-12n+1 Σn=0 (2n+1)! ²

A: The objective of this question is to find the interval of convergence for the given power series.…

Q: -6 Let f(x) = Find f'(x). √√7x2+2 f'(x) =

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Q: Find the domain of the function. f(x) = 2 x³ 3 x - 7x+6 The domain off is (Simplify your answer.…

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Q: Calculus 2 Let A E RNXN be a symmetric, positive definite matrix and b E RN a vector. If x ERN,…

A: The integral Z(A, b) as a function of A and b is given by: Z(A,b)=e21​bTA−1b(2Π)Ndet(A−1)​ This…

Q: The sixth degree term of the Taylor series expansion for f(x) = e Select one: a. O b. O c. O d. - 1…

A: To determine the coefficient of the sixth degree term of the Taylor series expansion for  about .

Q: Let / be the length of a diagonal of a rectangle whose sides have lengths x and y, and assume that x…

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Q: The cost to manufacture x computers per day is modeled by the following equation: C(x) = 20,000 +25x…

A: The cost to manufacture x computers per day is modeled by the following equation: To find the rate…

Q: MR₁ = To Let R₁ and R₂ be relation on a set A represented by the matrices 50 1 07 1 1 0 1] 0 1 0 1 1…

A: The objective of the question is to find the matrices that represent the union, intersection, and…

Q: Can you please show how to solve for x and y in step 4.

A: We have to solve for x and y value given in step 4.

Q: 6. Find the derivative of the following. *SIMPLIFY your answer: 2x a) f(x) = (√2/² 4x-x 2 b) f(x) =…

A: The given functions (a) (b)

Q: Which of the following series diverge? = N/W 2 K² +1 1. Z K=05K² +7 I. II. Ex-2(-1)*(x²+4) m. ΣΧ.…

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Q: 18. Use limits to find the area between the graph of the function and the x axis given by the…

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Q: Let Compute dw Əs dw Ət -(-3,-4)= -(-3,-4) = w = -5xy + 4yz - xz, x = st, y = est, z = t²

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Q: Use the accompanying sections of a table of integrals to evaluate the following indefinite integral.…

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Q: Find the critical points of f(x) = -6x4 + 2x² - 8 and apply the Second Derivative Test (if possible)…

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Q: 2. The domain of the function is y 4 2 -4-2 0 2 4 x

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Q: (5.) Let u(x, y) = ln(x² + y²) (a (b. (c. State the domain of u: Determine lim f(x,y) (x,y) →(0,e)…

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Q: ƒ(x) = = ax² + 3x + b 9x² - 6x + 2a if x ≤ 0, if x > 0.

A: f(x)={ax2+3x+b if x≤09x2−bx+2a if x>0

Q: Evaluate the following integral or state that it diverges. Ĵ dx 2 -∞ x + 225 Select the correct…

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Q: Fill in the equation for this function. 2 UN -π/2 TT/2 4 TT 3m/2 f(x) = [ ? ]cos(x − −˜_ ) + π

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Q: Use the graph of H shown to the right to find the limit. If necessary, state that the limit does not…

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Q: Geometric series can be found by transforming f(x)= to series form using = [% Σn=0x" =1+x+x² + x³ +…

A: The objective of the question is to understand why the geometric series representation of the…

Q: Let f(x) = 9x² x-9 (a) Find the interval(s) where f(x) is increasing. (Enter your answer using…

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Q: x²-x-20 18. Find the coordinates of the hole in the graph of f(x) = x² +7x+12 Hole:

A: Hole is at x=-4.Explanation:

Q: Find the area under one arch of y = sin(x/2).

A: The objective of this question is to find the area under one arch of the curve y = sin(x/2). In…

Q: (a) Find the approximations T10 and M10 for + T10 = M10 = 27 e¹/x, |ET| ≤ IEMI ≤ dx. (Round your…

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Q: Solve the differential equation by undetermined coefficients. y'' + 2y' = 2x + 9 - e-2x

A: The objective of the question is to solve the given second order linear differential equation using…

Q: (BC Topic) For what value of K will all three series below converge? x 3 Series II. Σ II. Ž¹ n=1 n =…

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Q: A rancher has 100 feet of fencing to enclose two adjacent rectangular corrals, as shown in the…

A: The area of the rectangular corral is .The objective is to find the value of  that has the maximum…

Q: Solve. log6(q) = -7 q

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Q: Suppose that the Wronskian of y₁ and y2 equals e¹2x, and y₁ = ex. Find y2 if we also know that y2(0)…

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Q: Consider the following series and level of accuracy. 00 Σ n = (-1)^50¹2 (104) + Determine the least…

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Q: Evaluate the following integral. 48x² S (x - 15)(x + 5)² 48x² (x − 15)(x + 5)² √ S. dx dx = 48 7…

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Q: If f(x, y) = xy² + arctan(cosx), then fyy is

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Q: If f(x) dx = 5x³ – 7x6 + C, find f(x). f(x) =

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Q: Which of the following series is absolutely convergent? Select one: O a. Σ(-1)*+1 IVE k+8 O b.…

A: Given that,which of the following series is absolutely convergent.

Q: Problem #6: Calculate the Wronskian for each set of functions. Problem #6(a): Problem #6(b): Problem…

A: To find wronskian for given sets

Q: r(t) = (e¹,8, 5t-¹),t = 5 v(5) =

A: The Position vector is given as follows

Q: УТ 41 2 -4-2 0 -2 4 4 x

A: (7)

Q: Integrate by means of substitution a) S√√4x - 7 dx =

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Q: Consider approximations to the gradient of the curve y = e* at the point where x = (a) What is the…

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Q: an = 1-n3 70-4n²

A: For the sequence given below, to determine whether it converges or diverges. If it converges,then to…

Q: 10 -6 -5 -4 -3 -2 -1 8 4 2 2 -4- -6- -8 -10+ The function graphed above is: Concave up on the…

A: The graph of a function is given below.To find the intervals of concave up and down and the point of…

Q: f(x) = 1-x², ax + b, ((x-1)³ + 2, x ≤ 0 0 1

A: f(x)={1−x2,x≤0ax+b,0<x≤1(x−1)3+2,x>1