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Q: Given the initial condition y(0) = 1, find the particular solution of the equation y' = e3x - 2y

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Q: Helicopter Task Introduction: An observer at Point A makes measurements that show that the peak of…

A: We need to solve Helicopter task.

Q: 1) The Arc Length of the curve f(x) = coshx, 0≤x≤ In3 is: d. 1/1/22 4 12 a. b. ³/1 3 2) The Volume…

A: Given

Q: Simón wants to build a rectangular pen for his animals. One side of the pen will be against the…

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Q: If y = √1 − x² sin¯¹x, prove that (1− x²) ¹ + xy = 1− x². dx

A: We can prove the given the result by differentiating the given function.

Q: The projected population of a certain ethnic group(in millions) can be approximated by p(t) =…

A: Solve the following

Q: The following is a step in the evaluation of the derivative of a function f(x) at a point x = 1…

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Q: Q2: Fill the blank: 1) lim (1+)5x x48 4x 2) lim x.e-3x = X-8 3) (csch-¹x³) = = 4) ₂° e-*dx 5) S-…

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Q: Sketch by symmetries and translations with find domain and range of the following curve: y = 2 +…

A: To sketch the curve.

Q: 4) The area of the surface generated by revolving x=y²-1, 1≤ y≤ 2 about x-axis is S=.

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Q: Q4) Find dy /dx for the following functions : a) y².cotx= [sin(x.y)]-¹

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

Q: Find the vector standard a Ā= (-3.4.5)

A: we know that if v=<a,b,c> then its standard form is v=ai^+bj^+ck^

Q: Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = 7 sin(x) + 7 cos(x),…

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Q: The value of the following limit Lim (cos(x) cot(x) is: AL

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Q: Find the formula for a cubic polynomial, ax³ + bx² + cx + d, with a critical point at x = 2, an…

A: Use double derivative concept

Q: 3x 4) 4. S-001+ 6x dx = 1+e6x a. Diverges b. converges to TL 8 c. converges to It d. converges to TL…

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Q: 5x 5 y-y-ey = e

A: Given problem:- Solve differential equation y'' -y' -2y=e5x

Q: 5

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Q: 1 1+6402 anges JP

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Q: By using the unlimited coefficients method, choose the correct answer for this equation…

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Q: The graph of a function f is shown. Use the graph to find f¹(-1). BE"F Cloudy OLO D O 99. OU Time…

A: To find out f-1(-1).

Q: 1. For the function f(x)= x³ +5x²+2x-8, explain how you determine which integral values of x you…

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Q: 4. Evaluate √x² - 2x + 1dx

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Q: ) Find (dy/dx) for: tan-¹(x² + y) - eln(x³y) = 5sinh(y)

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Q: Prove that In( +VI-X²³) = In ( ¹+ √1-x²) sech ¹(x) =

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Q: Question1: Classify the following differential equations in terms of the (Type, Order, Linearity and…

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Q: Sketch by symmetries and translations with find domain and range of the following curve: y = 2 +…

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Q: Determine whether the function defined is one-to-one. f(x)=√/32-x² -X www Is the function…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Evaluate fea cos(2x) dx

A: We have to above integration

Q: ) Prove that sech¯¹(x) = In ( ¹+ √¹-x²) X

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Q: The position function of a particle is given, in metres, as s(t)=t 4-10t 3+36t 2+10t+12 where t ≥0…

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Q: A Find (dy/dx) for: tanh ¹(x y) + e(x+y) 5 cos (y)

A: We have to determine derivative

Q: @ es the following uation sutisfied Cauchy. W w = Z² Rieman. s equation

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Q: Describe the difference between a discontinuity that is removable and a discontinuity that is…

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Q: 1. The effectiveness of studying for an exam depends on how many hours a student studies. For a…

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Q: A company determines that its weekly online sales, S(t), in dollars, t weeks after online sales…

A: Recall:., To find Average,  Ave=1b-a∫abS(t)dt We have, S(t)=600 et, a=1, b=5

Q: Using Gauss Jordon elimination, determine the intersection, if any of the following sets of planes…

A: We have to use Gauss Jordan elimination

Q: 5. Interest rate. A 2-year loan of $4650.25 accumulated $269.75 in simple interest. Calculate the…

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Q: Find dz/dt where z = 2xy - x² y² and x = 2t, y = t².

A: Given: Now,        z=2xy-x2y2  =22tt2-2t2t22  =4t3-4t6

Q: ²²1559 1≤ y ≤9 Find the length of the curve_x==y 3

A: If if x is a function of y then  the length of the curve is L=∫ab1+dxdy2dy   over the inetrval a≤y≤b…

Q: Use Newton's method to approximate a root of the equation 4 sin(x) = x as follows. Let ₁ 2 be the…

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Q: 4) Find the intervals where the following function is concave down: ππι y = 2sin² (2x) - 4x, x € -

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Q: Determine if the following operation on the two given matrices is defined, and if it is, determine…

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

Q: Explain why the integral is improper. 49 1 1²0 √/x dx X 1.6 1.4- 1.2

A: Given improper integral I=∫049    1x   dx

Q: Q6) Find the Area bounded by the curves y = √x and x = 2y-y² ,with sketch.

A: First we find the limits of integration.

Q: company determines that its weekly online sales, S(t), in dollars, t weeks after online sales began…

A: We have to find out the weekly average sales amount

Q: Consider the following. f(x) = =x+4 (a) State the domain of the function. O all real numbers x O all…

A: We have to find asymptote

Q: 3 -6 -4 -3 4 Let y = J. ,Vi= 1₁ 5 -1 Compute the distance d from y to the subspace of R4 spanned by…

A: Given y=3-6-35   , v1=-1-44-1  , v2=0220

Q: 1) The Arc Length of the curve f(x) = coshx, 0≤x≤ In3 is: d. 312 12 3 C. b. 2²/2 0.33 lorod by…

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Q: If c = 192, ZA = 79° and LB = 55°, b ; Assume ZA is opposite side a, LB is opposite side b, and ZC…

A: answer is in next step. please give a like !!