Find the average value of f(x) = -x+1 x3 Submit an exact answer using fractions and/or roots if needed. Provide your answer below: over the interval [-3, -1]. The average value of f(x) is

Q: Describe the domain and range of the function. f(x, y) = In(xy-1) Dor

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Q: Set-up and evaluate the triple integral for the mass of the box 1≤x≤2, 1≤y≤16, 0≤z≤ with √√y density…

A: To setup and evaluate the triple integral for mass of the box.

Q: (Simplify your answer. Type an exact answer, using radicals as needed.) b. y = (Type an exact…

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Q: FIND: hf(x)dx 2 g(x) dx = = f₁₁ f(x) dx = = if g(x) is an odd function. if f(x) is an odd function.

A: We need to find integral.

Q: Find the general solution of the differential equation y" 10y' +61y = 0. NOTE: Use c₁ and ce as…

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Q: Find the general isolation of the following: 1. (x³y³+1)dx +x4y²dy=0

A: Please see the below picture for detailed solution.

Q: Find the curvature K of the curve, where s is the arc length parameter. r(s) = (1 + s)i + j K = (No…

A: The given problem is solved below in detail.

Q: Question 1 a) Find the value(s) of y such that the vectors U₁ = and u₂ = are parallel. b) Find the…

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Q: f(t) = 4e-3t - sin 4t + cos 2t

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Q: 3 2.)f x³ (4 + x²)² dx ; Use rationalizing substitution

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Q: QUESTION 1 Let I = fxe³x. To solve I, we need to apply O Integration by substitution O Integration…

A: The answer is given below.

Q: 4. y = Ae bx are cosax + Bebx sinax, where a and b(lowercase) parameters. (not to be eliminated)

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Q: Q1: Answer two only (A): Solve the following linear equations by Cramer's rule: x + y + 2z = 1…

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Q: Which of the following describes the graph of h(x) = −3(x − 1)²(x + 1)²(x + 2)? O-12 O -10 -0 -4 -12…

A: see below the answer and explanation

Q: dy 5: Find for the following functions: dx (1) In (x - y) = xy + y³; (2) y = tan³ √/cot(7x); (4) y =…

A: Since we are given with multiple number of question and answered according to the guideline

Q: f(x) = x+2-e² Use the initial estimate x1 = 0.5: *1 = 0.5 x2 = I3 = C4 = I5 = I6 = 27 = Submit…

A: To find he root of the equation using newton method

Q: Q3: Evaluate the following integrate: (chose three only) 1. dx 1+x4 2. ex-edx ex+e-x 3. fxsec² x dx…

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Q: (B): Find the unit vector perpendicular to the vectors: 3i - 4j + 5k 4i + 5j - 6k du

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Q: Q2: Solve the following integrals: (3) dx

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Q: Evaluate the following limit. sin xy + cos xy 2y lim (x,y) →(0,)

A: The objective is to evaluate the limit.

Q: cos¹3 xdx 2. Dễ sin12xcos®xdx 1.

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Q: Given: f(x) = 0.2 + 25x-200x^2 +675 x^3-900 x^4 + 400 x^5 from a = 0 to b = 0.8 and segment equal to…

A: Given that      f(x) = 0.2+25x-200x2+675x3-900x4+400x5   from a=0 to b=0.8 and segment equal to 8.…

Q: Evaluate the following limit. t sinj+ sin = 1+ k t -k π lim costi-5 1-x

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Q: The half-life of Strontium-90 is 28.79 years. If a sample contains 490 mg, how many mg will remain…

A: Given half life is 28.79 years Initial mass =490mg To calculate mass after 180 years.

Q: Q1: Fill in the blanks for the following statements (chose five only) 4n 1. lim→∞ 2n+1 log10 (3x -…

A: The objective of the question is fill the blanks.

Q: (B): If A = 2i +3j - 4k; B = 3i - 4j+5k and C = i + j-k, find: (iv) (3A + 4B).C (i)A.B (ii) B.C…

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Q: 1) Consider the DE: xy' +(5x-1)y = 0. A) Determine whether the DE is linear or nonlinear and find…

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Q: Find the derivative. G(t) = sinh(ln(t))

A: Topic = Derivative

Q: (C): Solve the following equations:- (1) sin 2x + 2 sin² = 1

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: Describe the domain and range of the function. g(x, y) = x√y

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Q: The curves y = 2x - x 2 and y = 3x2 - 6x are used to form the boundary of a thin plate of uniform…

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Q: Find the volume of a solid of revolution formed by revolving the region bounded by the graphs of…

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Q: Q / if w = tan x and x=4²++ Find dw dt

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Q: Q2: Solve the following integral (1) 7x²+14x+15 (x²+3)(x+7) dx dx ; (2)

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Q: What is the distance between two points (3,-1) and (-2,-5). 3

A: Given that the two points (3,-1) and (-2,-5)  To find the distance between the two points.

Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by y =…

A: y = x5 y =1  find V = ?   V = π∫(f(x))2dx here we have to find limit of x  here first quadrant given…

Q: Q5: Find for the following functions: dy dx (1) In(x - y) = xy + y³ ; (2) y = tan³√/cot(7x);

A: To find derivative.

Q: Which radical function has a domain of (xe Rx≤3) and range of (y e RIy2-4)? Oy--√x+3-4 Oy--√x+3+4…

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Q: y = sin(x), y = 0, x=0, x= π Exercise (a) the volume of the solid formed by revolving the region…

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Q: For what values of a and b is the line 2x + y = b tangent to the curve y = ax² when x = 4?

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Q: 3): Find the tangent equation to the curve y = sin² x at point x =

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Q: nd the limit (if it exists). (If an answer does not exist, enter DNE.) 15 lim (x,y) → (0,0) x6y²

A: To  find the  limit.

Q: 2x+3 (2x² + 6x − 1) b. f 1)s dx

A: B only Integrals by Substitutions

Q: Q5: Find for the following functions: dy dx (4) y = x sinh 2x - cosh 2x

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Q: -1 t² Vta 6 dt

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Q: Describe the domain and range of the function. xy x-y z Domain: 0 {(x, y); y # 0} 0 {(x, y): x*y} O…

A: To find domain and range of the given function.

Q: 8 If f(x) = 3 + = + x 6 x2 find f'(x). Find f'(4). Round to 3 decimal places if necessary.

A: Given that f(x)=3+8x+6x2-(i)Our Aim is to find f'(x) and f'(4).

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) x + y lim (x,y) → (0, 0) x²…

A: To evaluate: lim(x,y)→(0,0)x+yx5+y

Q: S 4sin x cos xdx I

A: topic- indefinite integral 2sinθcos(θ)=sin(2θ)sin2(θ)=1-cos(2θ)2

Q: Consider the position function below. r(t) = (1-1²,3-5t4) for t≥ 0 a. Find the velocity and the…

A: Given;  r(t)=<1-t2,3-5t4).