Answer the following using the chain rule (Complete solutions) 1. Differentiate f(x) 2. Differentiate f(x) = (cos x - sin x )-2 (3x2 - 4x + 5)8

Q: 1. Find the derivative. (a) f(x) = (6x² – 8x + 4)4 2х -5 (b). у %3D 2x2 - 10

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Q: Question Find the Taylor polynomial p3(x) for f(æ) = 5x1/3 at x = 3. Provide your answer below:…

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A: In the given question we have to find a suitable trigonometric identity to substitute in place of x…

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

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Q: Evaluate. (Be sure to check by differentiatingl) 1 dx, x# - 3 9+ 3x

A: To evaluate: I=∫19+3xdx Use the rule: ∫1xdx=ln |x|+C

Q: 1. Determine the type and stability of the critical points of the homogeneous systems: (b) 4 = x + y…

A: Solving

Q: Let f be a function defined by f(x) = In(2x2 + 1) and let g be a function defined by g(x) = 2x4 –…

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Q: 6) The laft,rght, Trapezoidal, midpoint Rule approvimations were used to esbimate aecxlar where f is…

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Q: 6. For the series E-13 * )", a. Find the first two partial sums si and s2 b. Does the series…

A: 6) ∑n=1∞314n  a.  partial sum S1=3(14)=34=0.75      partial sum S2=3(14)+3(14)2…

Q: 1. Find the derivative of f(x) = 3x³ + 2x using the limit definition.

A: We have to find derivative using definition.

Q: 2.) Suppose E is the solid which is inside the sphere x + y² + z° = 4_and above the plane z = v3 .…

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Q: Fad he averge yalue of the funchibon f fix) over the loterual [o,7] 3e- %3D

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Q: Consider the function f(x) x* + x + 1, where E 1, 2. The %3D domain of the inverse function f x) is…

A: Swap the domain and range of original function to get domain and range of inverse of that function.…

Q: Solve the given Exact Equation. Be sure to supply all the steps that lead to your answer. (cos x cos…

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Q: Three vectors are given by: J = 2î – k K = 2î – ĵ+ 2k L= 2î – 3} Determine: (i) K•L x J; and (ii)…

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Q: 1) Evaluate the integral dy dx using polar coordinate

A: Explanation of the answer is as follows

Q: A A A A A A A A A A A A A A A A A A A A A 2!, 22 23 16. The sum of the series 1+ 1! 2n 二十… is n!…

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Q: Evaluate the triple integral. Then, on your paper, sketch the solid whose volume is expressed by…

A: We can solve as follows

Q: Use the method of Lagrange multipliers to find the dimensions of the rectangle of greatest area x?…

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Q: D Find the area of Ene shaded region 2. = sincze)

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Q: Find the following limit. 2- 4t – 5 lim t - 5 t+5 answer =<

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Q: 3 dx x? + 9

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Q: A Norman window is constructed by adjoining a semicircle to the top of a rectangular window, as…

A: Perimeter of Norman window(P)=Perimeter of rectangle(P1)+Perimeter of…

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Q: Given the rate law and table below, what are the values of m and n? Rate = k[A]m[B]" [A] (M) [B] (M)…

A: Given,

Q: CCw dire 10n. Let a represent the number of meters Michaeel nas traveled since ne started running.…

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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: (3) (E) - (a) - () 2. 2. 는 (v) 1 1 1. (B) 1 1 = xP (x)fj fx+1 for x<0, 9. Given f(x)= cos nx for…

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Q: the mapping notation for this function 2. Given the function F(x) -4 *+2 al Determine the mappina…

A: we have  f(x)=4123x+3-2 the domain of the given function is (-∞,∞)and range of the given function is…

Q: For the series E=13 * a. Find the first two partial sums si and s2 b. Does the series converge, and…

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Q: Find the limit of f as (x,y)→(0,0) or show that the limit does not exist. Consider converting the…

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Q: Find the exact length of the polar curve. r = 6 sin ?,    0 ≤ ? ≤ ?/3

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Q: 5-10 Plotting Points in Polar Coordinates Plot the point that has the given polar coordinates. 5.…

A: Since you have posted multiple questions i can do first three subparts as per our company guidelines…

Q: Calculate the second and third derivatives of y(r) = ar6. (Use symbolic notation and fractions where…

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Q: Jestion rectangular garden is to be constructed using a rock wall as one side of the garden and wire…

A: Given the query is to find the dimensions of the garden.

Q: Please do 9 and 13

A: Use antiderivative formula for finding 9 and 13

Q: A metal sheet is shaped as a region R on the plane defined by the following: 0 <x < 2, 0 < y <4- x².…

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: Calculate the derivative. es g" (0), g(s) = s + 9 (Give an exact answer. Use symbolic notation and…

A: To calculate the double derivative at the point x=0.

Q: Use the divergence theorem to find the outward flux of F across the boundary of the region D. F=…

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Q: There is a line through the origin that divides the region bounded by the parabola y 7z 5x and the x…

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Q: Using the substitution u = x + 1 / Væ +1 dæ is equivalent to 1 u +1 -1/2 du /2 1/2 du (4 – 1) /…

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Q: 1 dr r²Vr² – 9 -2.

A: answer is in next step

Q: Find the inverse Laplace transform of 5s + 1 F(s) = s2 – 7s + 12

A: F(s)=5s+1s2-7s+12       =5s+1s2-3s-4s+12       =5s+1s(s-3)-4(s-3)       =21(s-3)-16(s-4)(s-3)(s-4)…

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A: In the given question we have to provide the double integration Using the formula,…

Q: y' = xy – Vx

A: Solving

Q: Question A farmer is constructing three equally-sized pens against the side of a barn for his…

A: We need to find max area.

Q: An object moves along a coordinate line with velocity v(1) = r(9 - 1) units per second. Its initial…

A: Given:    v(t) = t ( 9 - t )     x ( 0 ) = - 5    t = 13