1.) Find the area bounded by the lines and curves y = 4x – x°, x =1 and x = 3

Q: Match the vector field with its graph. F(x, y) = yi -5+ 1信 5 5

A: We have to graph the vector field of the given function

Q: Determine the intersection point of the two lines or show that they do not intersect. a. Does the…

A: Please see the answer below.

Q: Solve for the indicated higher-order partial derivatives, fæx, fæy, fyy- · f(x, y) = Vx² + y?

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Q: Calculate the first, second, and third derivatives of y(t) = 2016/5 – 6127. (Use symbolic notation…

A: We will use simple differentiation rules to solve this question.

Q: 4. Find the point on the graph of f(x) 5x + 20x – 3 where the tan gent line is horizontal. 5

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Q: When a factory operates from 6 AM to 6 PM, Its total fuel consumptlon varies according to the…

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Q: 2. a) Determine the coordinates of all point(s) on the graph of y = 2x In x where the tangent line…

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Q: Suppose the motion of an avalanche is described by the function s)- 4, where s is the distance in…

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Q: Find: 1. Sjs(x)dx

A: Given:

Q: az 9- z2 – 2xz 16 find | ax ду at the point (1,1) 10- x+ 2xy – y² = 2 find ax 11- Find The slope of…

A: 9)z2-2xz=16differentiating w.r.t. x;2z ∂z∂x-2z(1)-2x ∂z∂x=0(z-x)∂z∂x=z∂z∂x=zz-x

Q: Find the area of the region outside r = 5 + 5 sin 0 , but inside r = 15 sin 0.

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Q: Consider the definite integral V11 dæ. - 2x -3 The most appropriate substitution to simplify this…

A: Solving

Q: • F(x)=x2 -7x+20, g(x)= 2x+6.

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Set up the definite integral required to find the area of the region between the graph of y 15- and…

A: Area between the two curves f(x) and g(x) over the integral [a,b] is given by A=∫abfx-gxdx

Q: Find all the values of t where the tangent line to the parametric curve is horizontal or vertical.…

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Q: x²y' + 2xy – 2y = 0

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Q: Derivative of f(x) = sin(x) 2 For each x-value indicated, drag the purple dots up or down to…

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Q: Use logarithmic differentiation to find dy/dx. 4 y = x> 2 x* + 4 dy dx

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Q: 3 sin-xe 5%

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Q: Determine an equation of the line tangent to the curve Y = 10 at the point with x- coordinate 1.…

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Q: sequence. Always justify your answers In(1+ 2e") 1+ncos(2m) sinn+cosn а) а, 3D b) a, = \n+1-Jn с) а,…

A: Solving

Q: Given, f (x) = for æ + 3; f-1 (æ) x +2 x – 3 | Of-1 (x) x-1 3x+2 Of1 (x) = * Зх +2 x-1 x- 2 f-l (x)…

A: We have to find f^-1(x)

Q: Find c 0 such that the area of the region enclosed by the parabolas y- x- c and y = c-a2 is 100.

A: To find the value of c such that area of the region enclosed is 100.

Q: Question 4 Solve the initial value problem: y' = – 0.03y + 6 y(0) = 50 - y(t) =

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Q: power line is to be run to an offshore facility as shown in the figure above. The offshore facility…

A: Solution: Cost function C(x) = 50000(8-x) +x2+1(80000)

Q: Find the area of the shaded region. The image is not to scale. y = F y=- Consider c=64. Enter the…

A: If f(x) and g(x) are continuous on [a, b] and g(x) < f(x) for all x in [a, b] then the area…

Q: S=sin(In x) dx

A: To evaluate the given integral.

Q: Find the length of the spiraling polar curve 2e 40 From 0 to 27. The length is

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Q: Suppose that csc(t) = and that tis in quadrant IV. Find the exact value of cos(t). -3/2 V5 V5 3 -2/3…

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Q: Suppose that z = x/y, where x and y are differentiable functions of u and v such that x = dx/dv 3, у…

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Q: Find the maximum and minimum values of the function f (x) -3x on the interval 1+x2 0<x<6.

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Q: 14) Test the secies for convergane divergence or 2. (-1)"

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Q: Here is a related rates problem: All edges of a cube are expanding at a rate of 5 cm/sec. Let the…

A: We have to choose correct options

Q: Please do 9 and 13

A: Use antiderivative formula for finding 9 and 13

Q: A rectangular picnic area of 8000 m² is being constructed along the edge of a river. It will be…

A: Explanation of the answer is as follows

Q: Select the conic section represented by the equation. 7x 2 + 7y 2 + 3x - 5y - 1 = 0 hyperbola…

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Q: dx 4

A: Answer is in step 2.

Q: If f(x) : = 4 In(x² + x + 1), at what value of X is f' (x) = 4? O a) -1 O b) 2 O c) o d) None of…

A: This question can be solved using the concept of differentiation of function of function.

Q: Write out the first four terms of the series to show how the series starts. Then find the sum of the…

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Q: Calculate y" and y". 4х — 7 y(x) %3D (Use symbolic notation and fractions where needed.) y" (x) =…

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Q: 6 Determine the interval of convergence for the power series that can be used to represent the…

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Q: Find the arc length of the polar curve described by: r = 5+ 5 cos 0

A: Use the formula for the arc length in polar coordinate.

Q: Find all the values of t where the tangent line to the parametric curve is horizontal or vertical.…

A: x=32t-cos tdxdt=32+sin tvertical tangent line:dxdt=032+sin t=0sin t =-32t=2nπ+4π3  and t=2nπ+5π3,…

Q: The line given by r (t)=(14+5t, -3t, 1+7t) and the line given by r(t) =(3-3t, 5+2t, -2+4t).

A: Follow the procedure given below.

Q: The winner of a "million dollar" lottery is to receive $40,000 plus $40,000 at the end of each year…

A: In our question we are given that winner receives $40,000 plus $ 40000 at end of each year for 39…

Q: d²y 2. Find the second derivative, dx² a. x = t² + 1 and y = t³ b. x = - t2 + 2 and y = sin(t+ 1)

A: Let's find.

Q: 12 f(x) dx = | f(x) dx = f(x) dx where a = Σ and b = Σ

A: Use additive property of integral to simplified the integral.

Q: Q4) Find for the following functions (choose five only): dx 1. у %3D 2** + е2х-1 2. y = sec x tan x…

A: 1) y=2x2+e2x-1Differentiatey'=2x2ln(2).2x+2e2x-1dydx=2x2+1.xln(2)+2e2x-12)…

Q: e slope of the surface z = int (2. 3) is xy² in the x-direction at the and the slope of this surface…

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Q: Write the 4 x 4 elementary matrix which accomplishes the row operation R3 - 5 R2 ---> R3 when you…

A: let  I be the 4×4  identity matrix I=1000010000100001