Differentiate f(x) = 5 ( − 3xº – 8x³). You do not need to expand your answer. f'(x) = Factor out the greatest common factor to simplify your answer. f'(x) = =

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A: Find dydx  and d2ydx2  1+siny=2y-x3

Q: Evaluate the line integral along the given path. √(x² + y² +2²) ds C: r(t) = sin(t)i + cos(t)j + 3k…

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Q: The given point is on the curve. Find the lines that are (a) tangent and (b) normal to the curve at…

A: solutions:-x2+xy-y2=11differentiate both sides w.r.t  xddxx2+ddxxy-ddxy2=ddx112x+y+xdydx-2ydydx=0at…

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

Q: Use the Comparison Test to determine whether the infinite series is convergent. ni Σ_n² By the…

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Q: A value of sinh x or cosh x is given. Use the definitions and the identity cosh²x - sinh²x = 1 to…

A: Given that sinhx=-125Our aim is to find the value of cschx=?

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Q: 80. A cubic function is a polynomial of degree 3; that is, it has the form f(x) = ax³ + bx² + cx +…

A: f(x) = ax3+bx2+ cx + d on differentiating,   f '(x) = 3ax2 + 2bx +c which is a quadratic in x and…

Q: Find the absolute extrema and where they occur for f(x) = 5x² + 11x - 3 on [-5, 1]. Give exact…

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Q: Find the general solution of the differential equation xdy + (x^2- 2y)dx = 0. O y + (1/2)x^2= c O y…

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Q: Let f(x)= 2 sqrt(-x) +4 Find domain of f

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Q: Determine whether the vector field is conservative. F(x,y)-8+ Sad) O conservative O not conservative

A: Formula used: dxndx=nxn-1

Q: Solve for the general solution of the given DE: O 2x^2 + x cos(y) - y^2 = C x^2 + 2x sin(y) - 2y^2 =…

A: To solve the given differential equation.

Q: Evaluate te F. dr. F(x, y) = xi+yj C: r(t) = (9t+4)ī + tj, Ostsi

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Q: Evaluate the triple iterated integral. 2 [² [²xyz³ dx dy dz 1

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Q: 2. A thermometer reading 18°F is brought into a room, the temperature of which is 70°F. One minute…

A: Concept: The thermometer temperature is represented by T and room temperature by Tm Now at time  t=0…

Q: Please show your answers to at least 4 decimal places. Suppose that f(x, y) = x³y². The directional…

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Q: Find the maximum and minimum values of the function f(x, y) = x²y subject to 4x² + 2y² = 24 Please…

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Q: Which equation choice could represent the graph shown below? -10 9 8 7 -5-4-3/2 -1 Of(x)= x(x +…

A: We will find the required.

Q: Use the matrices to find BA, if possible. [2121 [11311 A = 331 B = 4311 [3201] + 2 161 129 1 12 1 0…

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Q: 77. f (x, y) = xy and D = = {(x, y)| − 1 ≤ y ≤ 1, y² − 1 ≤ x ≤ √/1 − y² }

A: Explained below

Q: Find the intercepts and asymptotes. (If an answer does not exist, enter DNE. Enter your asymptotes…

A: solution:-r(x)=x-1x+3x+1x-7x-interceptr(x)=0x-1x+3x+1x-7=0x-1x+3=0,   x+1≠0, x-7≠0x=-3, 1x-intercept…

Q: Does the graph of the function below have any horizontal tangents in the interval 0≤x≤2x? If so,…

A: To determine whether the function below have any horizontal tangents in the interval 0≤x⩽2π. If so,…

Q: PS 45 20. A large, juicy grapefruit is cut in half. The diameter of the grapefruit (not including…

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Q: Set up, but do not evaluate, an integral for the length of the curve. ST 2 x = 4 sin(y), Osys (C dy

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Q: Determine which graph is the graph of f(x) if the following are true. f(0) = -5 f'(x) is positive on…

A: Topic- Functions and application of derivatives We are given f(0)=-5 f'(x) is positive on nowhere…

Q: 0 Find the sum of the series > k=1 (a) (c) 12710 2 (b) (d) 3 (ⅱ). 3 5 11 10

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Q: Find the surface area of the part of the circular paraboloid z = x² + y² that lies inside the…

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Q: A dog food producer reduced the price of a dog food. With the price at $10 the average monthly sales…

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Q: 4. Consider f(x) = 6 + (x+3) ²/³. Find the extrema of this function using the first derivative test.

A: We have to find extrema by first derivative test.

Q: the matrix A. Select an Answer 1. A = Determine if X is an eigenvalue of A = 13 -6 -27 -3 -12 7 32…

A: Note : As per our Guidelines we can solve first question . Please Repost Remaining questions .

Q: 3x+1=32

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Q: 14 Friday 5x² + 6y² = 9 2

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

Q: PS #3 7. Can a man hit a 208 - ft ceiling of an Astrodome if he is capable of giving a baseball an…

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Q: Find the arc length of y= 2x sqrt(x), from x=0 to x=1

A: Given: y=2xx We need to find the arc length of the above function from x=0 to x=1.

Q: -6 -5 -4 -3 -2 -1 2. f''(x) > 0 8 6 4 2 3. f''(x) < 0 -4 -6 -8- -10- 1 et 2 From the function…

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Q: If f(x) = √7x, find f'(x). Find f'(2).

A: Solve

Q: 3. A tank contains 400 liters of brine holding 300 kg of salt in solution. Water containing 125 g of…

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Q: d = -1 The region R is bounded by the x-axis, y-axis, and the line in the graph and has a constant…

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Q: Convert the polar equation to a rectangular equation. 15 sec 0 5 sec 0 + 1

A: Given query is to convert the equation into rectangular form.

Q: For y = tan -1 (*² + 4) 7 dy find dx and simplify.

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Q: Find the curl of the vector field u = a) b) ▼xu =( V. (V x u) = = (7xyz², 6x² y³, 2x³ y³ z4 ).

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Q: Find the derivative of the function y = -7-5x. dx =

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Q: Find the indicated limit. Make sure that you have an indeterminate form before you apply l'Hôpital's…

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Q: Use the particular solution method to solve y - y = 2e²

A: Given that  a first order linear differential equations and we find particular solution of this…

Q: Find the indefinite below using the substitution x = tan (8). x √ √1² dx, for −1<x<1.

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Q: below

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Q: Sketch the graph of the function below, including correct signs, x-intercepts and y- intercepts.…

A: Here we have to plot a graph.

Q: state the axioms that define a group.

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Q: 3. Triple Integrals in Cylindrical and Spherical Coordinates a) Evaluate b) Evaluate R x²dV where R…

A: Concept: Integration by parts: ∫f(x)g(x)=f(x)∫g(x)dx-∫f'(x)∫g(x)dxdx The cylindrical coordinates…