Find a general solution to the given differential equation. z"' + 3z'-3z=0 A general solution is z(t) = .

Q: Suppose that the marginal propensity to consume is dc (in billions of dollars) dy and that…

A: given,  dCdy=0.2-e-0.5y

Q: You are given the following information about the function f(x): a) Domain: {x ER} b) Vertical…

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Q: 3 ** - 9 = 3.3*

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Q: 12. Consider the fun. four important ir A, and C are the defined at BP of garabre will not Find A…

A: Given function  f( x ) = 6x + 8x-1We can find the critical points by f'( x ) = 0

Q: lim h-m √5x+5h - √5x h where 0 is consta

A: Find the limit  limh→05x+5h-5xh, where x>0 is a constant.

Q: 2 2. Consider the series Σx-₁(-). Find a formula for the nth partial sum S, and k k+2 determine if…

A: we have given series ∑k=1∞ 2k-2k+2

Q: Find a vector equation for the line segment from (4, -1, 4) to (6, 5, 3). (Use the parameter t.)…

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Q: Find the angle between the vectors. (First find an exact expression and then approximate to the…

A: Given that a=2,3 , b=3,-1

Q: 5. Determine whether each of the series converges conditionally, converges absolutely, or diverges.…

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Q: y lim f(x) = -∞ X-a- (B) a -X lim f(x) = +00 X-a+

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Q: Use integration by parts to evaluate the integral: S² In(x) x² -dx = Report your answer accurate to…

A: ∫13lnxx2dx

Q: L10 (a) Estimate f(x)dx.

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Q: ppose f(x) is a continuous differentiable function. Some of the values of the function and its…

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Q: Evaluate: 1. lim (1-tanx) sec (2x) X-T4

A: We need to calculate: limx→π41-tan x sec2x This can be evaluated as follows:

Q: The graph off shown below has vertical asymptotes at x = -5 and x = 6. Find the following limits.…

A: The graph of f shown below has vertical asymptotes at x=-5 and  x=6. To find the following limits.…

Q: Find |(7.201³ (7x³ + 2x7) dx + C

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Q: Write the given system in the form x' = P(t)x+ f(t) x' = 4x + 4y + 4e' y' = 7x-y-t

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Q: Please solve this answer ASAP and correctly thanks. Given the function f(x) = x3 - 6x2 + 9x + 10…

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Q: Construct the exponential model that satisfies the given initial value problem. dy dx an 0.4y, y(0)…

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Q: Calculate the derivative of the function. r(s) = (7s + $0.4)-1 r'(s) =

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Q: Use row reduction to find the inverse of the given matrix if it exists, and check your answer by…

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Q: Find the area of the region under the curve y = f(x) over the indicated interval. f(x) = 1/2; x22

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Q: Find the vector that has the same direction as (3, 6, -2) but has length 2. 6 12 7

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Q: Consider the function f(x) = M x² + 7x + 12 x - 3 a. Find the first derivative. f'(x) b. List any…

A: According to our guidelines we can solve only 3 subparts so please post other parts separately.

Q: Find the equation of the tangent line to the graph of the given function at the point with the…

A: fx=x+3x

Q: 2.1 Consider the region between the curve y = 2² and the x-axis on the interval [0, 2], shaded…

A: Curve y=x2, x=0, [0,2]

Q: Baby Boomers and Social Security Benefits Aging baby boomers will put a strain on Social Security…

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Q: Use the graph of f(x) to answer the questions below. f (x)] 2 B (a) Questions about f'(x). C Use the…

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Q: 8. Find the indefinite integral. 2 √√₁+4x² (8x)dx

A: let  H=∫1+4x2(8x)dx

Q: Find the centroid of the region bounded by the graphs of the functions 1 7 7, and x = y = 6 sin(x),…

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Q: What is the value of L if the function is continuous at z=0?. f(x) = { 1 sin (10) if a #0 if x = 0

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Q: 1+ sin x 58. sin x cos (y − 1) = 2

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Q: A population of bacteria is growing according to the equation P(t) = 1300e0.07t, where t is the…

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Q: A stone is thrown straight up from the edge of a roof, 875 feet above the ground, second. that the…

A: Acceleration  a(t)=-32dvdt=-32v=∫-32 dtv=-32t+C Initial speed: 18 feet per second…

Q: 00 Σ n=2 In n 2 n

A: Note:- As per the guidelines we are supposed to attempt only one question so please upload the next…

Q: Find an equation of the sphere that passes through the origin and whose center is (4, 3, 3).

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Q: (a) Find symmetric equations for the line that passes through the point (2, -2, 7) and is parallel…

A: We need to find the symmetry equations for the line that passes through 2, -2, 7 and parallel to…

Q: 1(4)= 2. Find the intervals on which f(x) is increasing, the intervals on which f(x) is decreasing,…

A: f(x) = -4x2 - 24x -24

Q: 1. Does the following sequences converge or diverge. If it converges, give the limit of the…

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Q: 5. Use imp 2x 3

A: Derivative ddx 2x3-y3-3=0   2·3x2-3y2y'-0=0       3y2y'=2·3x2   y'=2x2y2

Q: A box with a square base and open top must have a volume of 256000 cm³. We wish to find the…

A: We know that volume of the box is the product of area of the base and the height of the box.  Let x…

Q: Find the distance from (3, -5, 7) to each of the following. (a) the xy-plane 7 (b) the yz-plane 3…

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Q: If ƒ(x) = (8x − 3)³ · (2x² + 5)¹, find ƒ'(x) using logarithmic differentiation.

A: fx=8x-332x2+54

Q: Solve (D2+20D+200)y = 10 O y = e-10x (c₁sin10x + c₂cos10x) + 20 Oy=e-10x (c1sin10x + c₂cos10x) +…

A: Given

Q: 5. Evaluate the following limits: x²+2x-8 x+2x²-x-2 (a). lim (b). lim (c). lim √2x+9-3 X 7t-√491²-8t…

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Q: Find the derivative of y = xsin ¹2x

A: y= x sin-12x

Q: 3. a. Convert 225° to radians b. Convert 13/12 to degrees: approximate to 3 decimals

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Q: J & W 6n-S nzl

A: Let 0≤an≤bn for all nif∑n=1∞ bn  converges then ∑n=1∞ an convergesif∑n=1∞ bn  diverges then ∑n=1∞ an…

Q: Find the angle between the vectors. (First find an exact expression of the cosine angle and then the…

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Q: 6. Find the arclength of the curve y Note: L = 1+ (f'(x))² dx √ 1 x²+1 for -2 ≤ x ≤ 2.

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