20. The parametric chain rule states dx II dy dt. Prove this statement. dx dt 21. Explain how the parameters a, n, c, and d affect the general polar function r = acos(ne + c) + d.

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A: v(t) = 90- 30In(3t+1)     a. as the driver begins to brake , t = 0 v(t)=90- 30In(3t+1)v(0)=90-…

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Q: Convert the point (p, 0, 0) = (3, 70 6 6

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Q: 5. Use variation of parameters to solve. y" - 2y' + y = 1+x²

A: **As per our guidelines, we are supposed to answer only one question at a time. Since you have…

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Q: 2. tanh y ³ log7x) = sin(6-3x7y³)

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Q: Suppose that the supply of x units of a product at price p dollars per unit is given by the…

A: p=30+90 ln4x+8

Q: [3-R]

A: Given: An invertible function:h(x)=2x+5x-1 We are required to: Find the inverse of h(x)

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Q: Evaluate the integral. ror4(1-x²) 1/2 J-₁ Jo x dy dx

A: let  N=∫-10∫04(1-x2)12xdydx

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Q: Can the Fundamental Theorem of Calculus be used to find ſ²₂ (²) dæ? ○ Yes, f(x) = is continuous on…

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Q: Let 7 (t) = Find 7'' (t)

A: given r→(t)=<-2t2-5,-4e-4t,sin(-3t)>formula used→(i)  d dt(tn)=ntn-1(ii)  d dt(eat)=aeat(iii)…

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Q: Find the tangent plane to the equation z = 2= Calculator = 4x² + y² - 2y at the point (2,-4,40)…

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Q: For the following polynomial function f(x) = 4x + 2x²+x-6, find the lower bound within which all of…

A: Cauchy's bound theorem states that, all the real roots of a…

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Q: Exponential Growth Given that a quantity Q(t) is described by the exponential growth funct 500e0.01t…

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Q: 28. ƒ、(2,4) if ƒ(x, y) = xª ln y

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Q: Find the coordinates of the point at -270° on a circle of radius 4.5 centered at the origin. Enter…

A: given angle is (-270°) and radius is 4.5we know point on circle is→x=rcos(θ)  and  y=rsin(θ)

Q: Find the indefinite integral. Include a multiplication sign between functions. For example, z. e².…

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Q: 4. y" + 20y' + 200y = 24 3 NS. y e-10x (C₁ cos 10x + c₂ sin 10x) + = 25

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Q: Convert the point (x, y, z) = ( − 5, — 4, 1) to cylindrical coordinates. Give answers either…

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Q: Find all the zeros of the function g(x) = x3 - 3x² - 15x+125 O -5,2+31, 2-3i O -5,4+31,4-3i O…

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Q: 1. Determine the area of the region bounded by y = kx√8-x² and the first quadrant when k = y -2 0 N₂…

A: given that , y=kx8−x2 and k=1/2 the area of the curve will obtained by integrating the function in…

Q: 5. Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. a) S…

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Q: C{(1 (A) (B) (C) (D) 3/12 - s² 1 t)(3 + 2 sin 5t)}= 3 10 s(s²+25) 1 + + + 10 s²+25 10 s²+25 + 20 s²…

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Q: The graph of g consists of two straight lines and a semicircle. Use it to evaluate each integral. 4…

A: ∫abg( x )dx represents the area under the curve g( x ) with sign from a to b

Q: Find a + b, 2a + 3b, lal, and la - bl. 4 a = i + 3j - 2k, b = -3i - j + 7k a + b = 2a + 3b = |a| |a…

A: We have vector a and b. Need to perform indicated vector operations.

Q: For each of the described curves, decide if the curve would be more easily given by a polar equation…

A: a) pass through point 0,0slope =  tanπ6 = 3b) pass through point 3,3slope = infinie (vertical line)

Q: Sketch a graph that possesses the characteristics listed below. fis increasing and concave up on…

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Q: Which statement best describes creating a hyperbola? A. A place slices a double-napped cone…

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Q: Find the critical points of the following function. f(x)=x²√√x+18 Select the correct choice below…

A: d(u.v)/dx = u.d(v)/dx + v.d(u)/dx

Q: Find the absolute maximum of the function f(x) = x + (1 − x)|x - 6| on the interval [1,7]. - 06 O O…

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Q: Use substitution to find the indefinite integral. 5 dm S= (5m-4)

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Q: Let g(x) = f(1) dr, where f is the function whose graph is shown below. What is the value of g′…

A: For given question  gx=∫0x ft dt          g'x=ddx ∫0x ft dt   g'x=fx

Q: Use linear approximation to estimate the following quantity. Choose a value of a to produce a small…

A: we have to use linear approximation to to estimate 152. also we have to choose the value of a such…

Q: Consider the family of cubic polynomials of the form f(x) = ax³ + bx² + cx + d where a, b, c, and d…

A: NOTE: Refresh your page if you can't see any equations. . take derivative the critical point is…

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Q: For the following polynomial function f(x) = 3x6 + 2x³ + 6x-8, find the lower bound within which all…

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Q: Find the integral using the substitution u = =t7. [to cos (17) dt Enclose arguments of functions in…

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Q: Use the Second Derivatives Test to find the local maximum and minimum values and saddle points of…

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Q: 1. Find the Taylor Series for the function f(x) = e centered at a = In 2. Please do not use a known…

A: fx=ex Find the Taylor series for the function centered at a=ln2

Q: 73. Σ 3*

A: ∑k=1∞3-k