3. Find the length of the curve r = e® for 0ses 2n.

Q: For each problem, find the particular solution of the differential equation that satisfies the…

A: The given differential equation is: dydx=exy2 ; y-2=2e3+3e3e   As we know that; The Power rule:…

Q: If f(x) = 2/x and g(x) = 4/x, find f(g(x)) and g(f(x)). f(g(x)) = g(f(x)) =

A:

Q: lim, 1 f(x) = %3D

A: limx→a f(x) =L if and only if limx→a- f(x) = L =limx→a+ f(x) .

Q: Given the following differential equation y' - 3y = 0 Plug in the appropriate power series for "y"…

A: Use power series  for finding the correct option

Q: The circumference of a sphere was measured to be 87 cm with a possible error of 0.5 cm. Use linear…

A: Given that the circumference of a sphere was measured to be 87 cm with a possible error of 0.5 cm .

Q: evergreen nursery usually sells a type of shrub after 5 years of growth and shaping. The growth rate…

A: Given query is to find the height function and the height of the shrubs when the sold.

Q: Business Decisions Sharon, the owner of the Brentwood Motel, is planning to renovate all the rooms…

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Q: e-2 h(x) 1 + e(3x² + 8) %D is e-2(-2)(1 + e(3x2 + 8)-e(3x² + 8)(6x)(e=2) O h'(x) = (1 + e' e(3x2 +…

A: Given query is to find the derivative of the expression.

Q: Find the exact length of the polar curve. r = 3 cos(theta),    0 ≤ theta ≤ pi

A:

Q: 3. Using the definition of the limit, and given that -7 lim x-2+ x – 2 - 0o, for any N > 0, there is…

A: Given that         limx-->2+{-7/(x-2)} = -∞

Q: Solve the initial value problem. x2у" - 4хy' - бу%3D 0, у(1) %3D з, у'(1) %3D 4

A:

Q: The r.m.s. value of f(t) = v2x – 1 across [-2,1] is Answer:

A:

Q: True or False: If lim f(x) = 4 and lim g(x) 3, then %3D %3D lim[-3f(x)² – 49(x)] = -60 O False O…

A:

Q: Sketch the region R of integration and switch the order of integration. IT rx, v) dx dy 3 У 2 3 3- 3…

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Q: Trapezoidal Rule. Use the Trapezoidal rule to approximate the integral 3e* dx with n = 4…

A:

Q: 15. Apply the Mean Value Theorem to f(x) = Vx – 2x using the interval [0.4]

A:

Q: Consider a triangle AB C like the one below. Suppose that B=42°, C=65°, and c=47. (The figure is not…

A: Given B=42°,C=65° and c=47We know sine rule is sin Aa=sin Bb=sin…

Q: Find the area under the curve y = 0.5x 15 from æ = 7 to a = t and evaluate it for t = 10, t = 100.…

A:

Q: Ise implicit differentiation to find the specified derivative at the given point. ind dy at the…

A: Given query is to find the derivative of the expression.

Q: fx,у) %3D -2у + зху + 8у - 4х2- бх — 7 then f equals ху О Зу - 8х — 6 O -12y O Does Not Exist Оз…

A:

Q: Given f(r) = 7T, find f'(1) using the limit definition of the derivative, f(r + h) - f(x) f'(x) =…

A:

Q: 37 Comvert the point (r, 6, 2) = (2, ,1) to Cartesian coordinates. Give answers either as…

A: Given, (r,theta,z)= (2, 3pi/4,1)

Q: Use APQR, as needed, to complete the given parts. Part 1: Let h be the height of APQR. Find the…

A:

Q: Flight of a Model Rocket The height (in feet) attained by a rocket t sec into flight is given by the…

A:

Q: A particle is moving with acceleration a(t) = 36t + 8. its position at time t = 0 is s(0) = 17 and…

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Q: (2) Prove by contradiction that if 3z2- is irrational then r is irrational. 215

A:

Q: 8. (Section 4.3) A motorboat is traveling at a constant velocity of 5 meters per second when it…

A: Given,            A motorboat is traveling at a constant velocity of 5 meters per second when it…

Q: Evaluate the iterated integral. T/2 r10 cos(0) r dr de

A:

Q: Cost Function. Suppose the cost to manufacture a product is given by f(x,y) = x²+Vỹ The domain of…

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Q: * TO 7. Determine a function whose graph has vertical asymptotes at x = ±2 and a horizontal…

A: The objective is to determine the required function.

Q: uestion 2 rite a chain rule formula for the following derivative. for z = f(r, s); r= g(t), s = h(t)…

A:

Q: Second Derivative Test. Consider the function f(x,y) = 2xy + 3ln(x) + 10y (a) The critical point of…

A: The given function,   f(x,y)=2xy+3ln(x)+10y

Q: NOTE: Each question must be submitted individually. Press 'Submit Answer' for each question before…

A:

Q: Integration by Substitution. The rate of growth of Grass carp, one of the most common type of fish,…

A: The given data is: ∫025x+10x2+4x+4dx

Q: S x²(csc2x³)(cot2x³)dx

A: Given problem:- ∫ x2 (csc(2x3) (cot(2x3) dx

Q: An airplane flies at an altitude of y = 2 miles toward a point directly over an observer (see…

A:

Q: Find the equation of the tangent line to the curve y = (2? - 8)' at point (5, 2). y =

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Q: Fundamental Theorem of Calculus. The Fundamental Theorem of Calculus says: All of the statements are…

A: The given data is: The fundamental theorem of calculus says:

Q: Flight of a Rocket. Suppose the altitude (in metres) of a rocket t seconds into flight is given f(t)…

A: Use derivative for finding the interval

Q: The plane with normal vector - 7) containing the point (4,-1,1) has equation Ar + By + Cz = D. If A…

A:

Q: A differentiable function /has one critical number at x 6. Identify the relative extrema of f at the…

A: We need to choose correct opiton.

Q: choice - Fundamental Theorem of Calculus. The Fundamental Theorem of Calculus says:  a) The…

A: The Fundamental Theorem of Calculus says.

Q: Find the tangent line approximation for V5 + x near a 4.

A: Find your answer below

Q: Integration by Substitution. The rate of growth of Grass carp, one of the most common type of fish,…

A: Given integral ∫13 2x+6x2+6x+2 dx

Q: Find the vector projv u if v= 5i +jand u = 2i+V17/

A: Use vector projection formula and dot product.

Q: 6. (Section 4.3) Find the area under each curve over the indicated interval. (a)y = 6- x2, (-2, 1]…

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Q: 12. Find dy for y = sec (3x). %3D

A:

Q: The line y=-Lx+8 has perpendicular whrich is fangent to the graph of Find the value of ke y = (x²2)…

A: Explanation of the answer is as follows

Q: Find the gradient field of the function, g(x,y,z) = e 3z - In (x +2y).

A:

Q: Determine whether the statement is true or false. If it is true, explain why it is true. If it is…

A: The given expression,         ln(a)-ln(b)=ln(a-b) for all positive real numbers a and b