(5* )csch x²+1 dy if Find dx 1. (a) y = x >0. (ecosh 5x) In Vx +1 )

Q: Logistic population model is given by d P/dt = 10 P (0.2 – P/5000). Analyze and show how this model…

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Q: 72 (29.4) Determine whether the series (-1)" is absolutely convergent, condi- n2 + 1 n=1 tionally…

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Q: xp sin 5x cos 3xt cos 5xsin 3x xp x²+ 2x + 5 EX Find:

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Q: Direction: Determine the Inverse Laplace Transform of the functions using the Laplace of Integrals…

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Q: Find the directional derivative of f(x, y) at P(5,0) in the %3D x + y direction of Q(3, –3). NOTE:…

A: f(x,y)=20x+y

Q: Find all the complex roots. Write the answer in exponential form.   The complex fourth roots of…

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Q: 10 40 What does that mean 11 Suppose f(x)dx : f(x)dx is equal to? 10

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Q: Find the directional derivative of the function at P in the direction of v. h(x, y, z) = xyz, P(8,…

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Q: ance between the skew y = 5+ 2t, z = 5 – 4 y = 6, z = 1+3 e exact answer.

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Q: Use vectors to find the lengths of the diagonals of the parallelogram that has i +j and i – 14j as…

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Q: dx 25. Integrate: S Ve-2x –1 А. Sec-1e* + С В. Sec-1е-* + С С. — Sec-1e* + С | D. —Sec-1e-* + с

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Q: Find an equation of the plane that passes through the point P(5, 6, 2) and has the vector n = (1,7,…

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Q: 4. The function g(t) = (8t)* – cosh² t + sinh? t satisfies g'(c) = 0 for which value of c? %3D (a) c…

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Q: (0³+ 38+ 3D+ 1)y-8sinx ylo): -/ y'l0)= 3 y"16)=5 5-

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Q: The line through (8, 5) that is parallel to 3i+2j. Ox = 8+51, y = 3+2t Ox = 8+81, y = 5+5t Ox =…

A: Given query is to find the equation of the line.

Q: х3+9х2+20х 4. lim х-3+ х2+x-12

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Q: (a) f(x) dx 10 15 (b) f(x) dx

A: Here we have to find the given integral using the area under the graph

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Q: Use synthetic division to find the quotient and the remainder. (x* - 4x° + 4x + 4) = (x – 2) ... (x*…

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Q: Find the area of the parallelogram that has u = 2i – j + 2k and v = 2j + 3k as adjacent sides. NOTE:…

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Q: Use the binomial theorem to expand the binomial expression below and state the range of values of x…

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

Q: k-1 Consider the geometric series ) 3 k=1 (a) Find the formula for the nth partial sum of the…

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Q: Find the arc length in the second quadrant of the curve x23 +y2/3 = 25 from x = - 125 to x = – 8.…

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Q: Evaluate the definite integral. Use a graphing utility to verify your results. 25 dx

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Q: 3. Find all possible functions with the given derivative y' =- 2

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Q: Find the directional derivative of f at P in the direction of a. f (x, y) = 11 tan ; Р(-12, 12); а—…

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Q: 8. Ssin(1 – Int)dt

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Q: Find an equation of the plane that is parallel to the plane x + 4y – 3z + 16 = 0 and contains the…

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Q: Express the limit as a definite integral on the given interval. lim > x; In(2 + x;2) Ax, [2, 5] n-…

A: The solution is given below

Q: С. lim х-2 х+1

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Q: Find two unit vectors in 2-space that make an angle of 45° with 9i + 4j. NOTE: Enter the exact…

A: Solution: Let u = ai+bj makes an angle of 45 degree with v = 9i +4j

Q: +t, 2t +t, 6t} O sis a basis of P O sis not a basis of P3.

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Q: s (e² + 4 cos 8z dz 1+sin 8z,

A: A detailed solution is given below

Q: Find the third order derivative of y = In(cos(2x))". A. y' = -40sec²(2x)tan(2x) B. y' = -80sec…

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Q: 4) The domain of f(x) = 4 cos-(3x- 1) + 5 is 3) If f(x) = 1+ x+x? then f-1(1) = a) 1 d) 2 e) non b)…

A: Since you have posted multiple questions i can do first three questions as per our company…

Q: A. Integration By Parts 1. ſx5Vx3 + 1 dx 2. S/* x sin 2x dx 3. S- x³ex? -dx (x2+1)2

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Q: S sin x In(cos x) dx

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Q: Solve the differential equation with the appropriate method. Finalize the answer free of fractions…

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Q: MY NOTES ASK YOUR TEACHER Consider the following functions. f,(x) = 4, f,(x) = cos2(x), f,(x) =…

A: Let's find.

Q: |P(Vi + VE – t) dt

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Q: Determine £(F}. F). 21 4s-18s +6 F(s) = %3D s(s-5)(s-6)

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Q: Find the vector component of v = 2i – j + 3k along b = i + 4j + 8k and the vector component of v…

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Q: Billy savings account is currently $200 overdrawn. Billy plans on depositing $75 each week for the…

A: It is given that Billy savings account is currently $200 overdrawn and he plans on depositing $75…

Q: Use the Lagrange multipliers to find the maximum and minimum values of f(x, y) = 2x + y – 2z subject…

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Q: f(x+Ax)-f(x), Ff(x) = v2x + 1, what is the lim Дх--0 Ax

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Q: 2. The graph of y = cosh a is (a) concave up on its entire domain because y" = coshr > 0 for all r €…

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Q: u = 5i + 4j, v= 3i + 2j (a) Find the projection of u onto v. (b) Find the vector component of u…

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Q: Suppose f( – 1) =7, f'(– 1) = 4 , and g(x) = r°f(x). The tangent line to g(r) at z = 1 is given by Y…

A: Given: gx=x3fx, f-1=7, f'-1=4   The expression for the equation of the tangent line is: y-y0=mx-x0…

Q: GIVEN : 2x 2х - 2x ) + 6 1 1 f (x) = 1 --x 8 g(x) = 3(x + + 4 h(x) = 6 - || 3 a.lim -4 · f (x) d.lim…

A: For (a),     limx→2-4 f(x)=limx→ 2-41-18xPlug in the value x=2=-41-18· 2=-3