3. Differentiate the functions below. 5) y = (2x5 + 3)cos x²

Q: Find the equation of the tangent line to the function y = − x² + 7 at the point (-1,6). No decimal…

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Q: Find the absolute maximum and minimum values of the function, if they exist, over the indicated…

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Q: Sketch the region bounded by the curves, and visually estimate the location of the centroid. Then…

A: Please see the below picture for detailed solution.

Q: Consider the function f (x, y) = 5x² - 6y². Find the directional derivative of f at the point…

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Q: Find the limit of the sequence: 01 DNE e (-1)") In n

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Q: For the following trajectory, find the speed associated with the trajectory and then find the length…

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Q: An object oscillates up and down on the end of a spring, with acceleration (in m/s²) given by the…

A: Here we have to find the velocity and distance function.

Q: An employee's monthly productivity M, in number of units produced, found to be a function of the…

A: Given query is to find the year when maximum productivity achieved.

Q: Determine whether the improper integral given below converges or diverges, and clearly state your…

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Q: Derivatives inverse thank you

A: Here we have to find the tangent line.

Q: 7. S tan3 Ꮎ cosᏎ Ꮎ - dᎾ

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Q: 13. Find the unit tangent and the principal unit normal vectors at the given points. r(t) = (-4cos…

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Q: since you cant find an inverse, how do you prove the function is one to one so that you can still…

A: Given: y = 2x + x3Aim: To prove that the y = fx is a one-to-one function. Basic information:A…

Q: 37 4 S 7 9 cot8 0 csc²0 de

A: ∫π43π49cot8θcsc2θdθ

Q: EC1: Find a member of the family of solutions of ry"+y+√ = 0whose graph is tangent to the x axis at…

A: Solution: Consider  Substituting  gives,

Q: Use Green's Theorem to evaluate the line integral. Assume the curve is oriented counterclockwise.…

A: Green's Theorem: ∫CMdx+Ndy=∫∫R∂N∂x-∂M∂ydA And use the equation of the line when it passes through…

Q: dx = 8x³ 8x3 + 3x, y(2) = 0

A: Given query is to solve the differential equation.

Q: A police car is located 30 feet to the side of a straight road. A red car is driving along the road…

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Q: 20 Let f(x) = 3x + Then the equation of the tangent line to the graph of f(x) at the point (2,11) is…

A: The given function is fx=3x+20x2 and the point is 2,11.   The objective is to find the equation of…

Q: Given the equation for a “tilted” ellipse: x^2-xy+y^2=3 . Find the points (x, y) on this ellipse…

A: Here we have to find the largest and smallest values of x.

Q: An object is moving with velocity (in ft/sec) v(t) = t² – 3t+4. At t = 0, the object has a position…

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Q: 19. ſ² z² In z dz 0

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Q: Find and classify all critical points of f (x, y) = ax^n + by^n where ab cannot equal 0 and n ≥ 2

A: Given function is f(x,y)=axn+byn,  a,b≠0 and n≥2

Q: Evaluate cosh -1(3).

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Q: Find the inflection points of f (x) = x² + x³ = 30x²2 +9. Enter the exact answers in increasing…

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Q: Find the minimum cost of a rectangular box of volume 190 cm³ whose top and bottom cost 4 cents per…

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Q: Model the data using an exponential function f(x) = Abx. 0 1 2 f(x) = X f(x) Need Help? 400 Read It…

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Q: 26. Initial height = 5, limit to growth = 30, passing through (3, 15).

A: Given:- initial height =5, limit of growth=30,passing through 3,15

Q: Find u from the differential equation and initial condition. du dt _____ el.8t-2.3u, u (0) = 3.7.

A: dudt=e1.8t-2.3u   given  u(0)=3.7

Q: $ Let F= (y.x) and C be the circle of radius 5 centered at the origin oriented counterclockwise.…

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Q: 6. f(x) = (x+3)(x - 5)√x-3

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Q: Evaluate the integral using partial fraction method (x² + 5) (x² + 1) (x − 9) (x − 8) - J dx

A: Given integral:- ∫x2+5x2+1x-9x-8dx

Q: Find dy and evaluate when x = −2 and dx = 0.2 for the function y = 3x2− 4x + 2

A: Given function:- y=3x2-4x+2

Q: find the derivatives of the functions using the product rule. 1. √√625x² ⇒ √625 - x² x20 2.

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Q: Find the centroid of the region bounded by the given curves. x + y = 2, x = y2

A: According to question,Given curves,x+y =2,x = y2

Q: Calculate the integral, if it converges. If it diverges, enter diverges for your answer. 1,100- dv V…

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Q: 2. Find the gradient of the tangent line of the function below at x = 0. y = 1 + 2x √√₁-x²

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Q: IP 4-91/2 I |

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Q: Find a fourth-degree polynomial with integer coefficients that has zeros 3i and -1, with -1 a zero…

A: To find a fourth-degree polynomial with integer coefficients that has zeros 3i and -1, with -1 a…

Q: , Let ƒ'(x) = ƒ'(5) = f(x) = √4x² + 3x +5 Give the (x,y)-coordinates of the point on the graph of f…

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Q: AB3: Evaluate [² xf² (4-x²) dx =-5 AB4: Using a trapezoidal approximation with the three…

A: Note:- Kindly check the answer again i am giving best from my side.

Q: Evaluate the integral using partial fraction method S Evaluate the integral using integration by…

A: To find integral. As per our guidelines we are supposed to answer?️ only one question. Kindly repost…

Q: )(a) Let g(x) g'(x) = = (c) Let H(x) = H'(x) = 6 √7x² + 3 (b) Let G(x) = √√√8 + √5x. Find G′ (x).…

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Q: Evaluate sinh -1(4/3)

A: Given: sinh-1(4/3)

Q: 2 An object is moving with a uniform acceleration a = 2ms-², determine the functions for: a)…

A: We will find the required.

Q: etermine the absolute extrema of the function f(x) = (x - 3)e terval -2≤x≤1. on the

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Q: Consider the (x, y) table below: X y 1 48 2 72 3 108 4 162 Find a function of the form f (x) = a b…

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Q: dr Let A be the area of a circle with radius r. If dt = 3, find = dA dt when r = 4.

A: Area of circle having radius 'r'  = πr2  Chain rule of differentiation :  dydx= dydu× dudx Power…

Q: Suppose an oil spill covers a circular area and the radius, R, increases according to the graph…

A: By the use of graph, we need to find out the value of R(40), value of t when R(t)=50 and also R(0).

Q: Consider the graph of Cx + Ay = B where A, B, and C are all positive consta (a) Find the coordinates…

A: Given: Cx+Ay=B