Find (fog)(x) and (gof)(x), given that f(x)=8x +9 and g(x)=7x-1. (fog)(x)= (Simplify your answer.) (gof)(x) = (Simplify your answer.)

Q: 11. Find the standard form of the equation of the ellipse with: Vertices: (0, 15); Passes through…

A: 11) Given that the vertices 0,±5, which are on the y-axis and passing through the point 4,2  Since…

Q: dy For the following composite function, find an inner function u = g(x) and an outer function…

A: Given problem:- For the following composite function, find an inner function u = g(x) and an outer…

Q: 6-Determine the volume of the parallelepiped formed by the vectors U= [2,1,3], v= [1, -4,2] and w=[…

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Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

A: We have to find position vector

Q: a. b. Evaluate the following integrals 2 dx cos²x√4 tan x- tan² x I [ sin(√a)da dx

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Q: 2 Evaluate f S t(1+²in t) dt 1+ Int+C O + C O 2 (1+In t) + C O2 ln | 1 + lnt | +C 2 (1+In t)

A: Evaluate the integral

Q: interval of convergence. b. sin² x

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Q: Consider the region R bounded by y = Arctanx, x = 1, and the x -axis. Suppose that R has its…

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Q: 2 sin6 x cos⁹ x dx 0

A: See the details solution in below

Q: Solve the integral shown below. . S | xsin xdx

A: Given problem:- ∫x sin(x)dx

Q: ng the problem) an interval in which the solution of the given initial value proble (t-4)y' + (Int)y…

A: We have to find the interval of t

Q: Find the arclength of the curve y = (x² − 4)² on [2,4].

A: Given question is asking to find the length of the curve.

Q: A cylindrical can is to be made to hold 1000cm^3 of oil. How do you find the dimensions that will…

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Q: Evaluate 1¹ 1 - cos 2x sin 2x dx In | csc 2x + cot 2x | -ln | sin 2x | +C In 1|csc 2x-cot 2x |--In |…

A: The given integral is: I=∫1-cos2xsin2x   As we know the common integrals; 1). ∫cscxdx=lncscx-cotx+C…

Q: dy For the following composite function, find an inner function u = g(x) and an outer function y = f…

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Q: My - Nx If = =Q, where Q is a function of x only, then the differential N equation M + Ny' = 0 has…

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Q: What is the domain of the function f(x) = |x|? 0 (-∞,∞) ○ (0,∞) 0 (-∞,0) ○ [0, ∞)

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Q: The height of a certain amusement park ride follows the function h(t) = −³+ 11t² — 32t + 28, where…

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Q: Use any method to determine whether the series converge. ∞ 1 (2) Σ 4k k=1 The series (5) Σ k=1 The…

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Q: 0 KIN TC TC 2 KIN 0 0 02 sin o dr do de

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Q: KIN T 2 sin² x cos⁹ x dx

A: We will solve integral using Wallis formula  The wallis formula is :

Q: 8 Determine the area of the region bounded by the curves y = =, y = 2x and x = 4

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Q: A wall lamp is positioned 7ft up a wall. A 6ft tall woman walks directly towards the light at a…

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Q: For items 13, 14, and 15, consider the region R bounded by y = Arctan , r = 1, and the z-axis.…

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Q: Q1 (a) Interchange the order and evaluate the integration a+c 2x fa* ft* xy² dydx 0 a-2 c-6

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Q: Question 4. Continuity Exercise 2.5, Problem 26 a. Show that f has a removable discontinuity at x =…

A: We have to show f has removable discontinuity at x=3 and find the value of c

Q: Example 3: Find the parametric and symmetric of the line passing through the point (-3, 5, 4) and…

A: Here, the given equation of the line is: x=1+3t,y=-1-2t,z=3+t Therefore, the direction vector is:…

Q: 7. Given a = (0, 1, 3), b = (4, 5, 6), then a · b = a. 1 b. 24 8. Given a = (0, 1, 3), b = (4, 5,…

A: Let's solve. Two vector a and B are given.

Q: Which of the following is a mathematical sentence? 1.2 is a prime number. II. = 0. I and II Il only…

A: To find out the correct option.

Q: Q4- Solve the following differential equation: (1 + x²) dy + (y - tan-¹(x)) dx

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Q: 5. Two lines have equations: L₁: x = 3t + 1, y = 3, z = −t + 2, teR and L₂: x = 2s +3, y = −s + 1, z…

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Q: (x+3)(y-5) 16 = 1 25 (x+5) + (y -1)} = 1 5. - % 6.9x² +4y² +36x-24y+36=0 4. ²

A: Given problem:- FOR EACH OF THE FOLLOWING, FIND THE CENTER, VERTICES, FOCI AND ECCENTRICITY OF THE…

Q: A rectangular field is to be enclosed with a fence. The available fencing material is 150 meters…

A: This is  a problem related to maxima and minima of the function. Based on the general formula and…

Q: П 2 0 KIN 2 p² sinr de dr dø 0

A:

Q: 3. _1ffx,y) = tan—1 (), then X c) (x2 +y2)2 is ܐܐܐ )b ܐ)?x +y(

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Q: 8. Find the point on the curve y = √2x 3 from the point (1, 4)-

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Q: Q1- Find all the second-order partial derivatives of the function: s(x, y) = tan-¹(x)

A: partial differentiation

Q: Given the following vector field and oriented curve C, evaluate SF.T ds. C F= (-3y,3x) on the…

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Q: ππ 2 CAP• 0 0 0 ¢ sinr do dr dộ

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Q: dy dx If y = (sin x)¹/, then (sin x) ¹/x In(sin x) x² (sin x) ¹/x x - ln(sin x) x² x cotx - In(sin…

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Q: 6. Evaluate the following limits: 1/3 (x+8) -2 a. lim X x-0 b. lim x→-3 2 x²-9 2x² +7x+3

A: Given :limx→0x+813-2xlimx→-3x2-92x2+7x+3

Q: 1 -dx 1-x²

A:

Q: Show that the differential equation x²y³ + x(1+y²)y' = 0 is not exact, but becomes exact when…

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Q: 3. Evaluate the indicated line integrals in the complex plane by direct integration. Siz dz along…

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Q: Evaluate lim x tan a x - x cos x

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Q: Double Integrals In each problems a) sketch the domain F over which the integration is performed;…

A: Given problem:-

Q: A population of deer grow according to the model N(t) 12(5 + 3t) 1 +.04t 1 where t is in years and N…

A: Let's solve by using diffrentials.

Q: x³-y³ Determine whether the function z = g(x, y) = x² + y² (why or why not) for for (x, y) = (0,0)…

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Q: 1. The graph of y=sin z is transformed so that the transformed image has a period of 4m and a phase…

A: Given problem:- The graph of y = sin x is transformed so that the transformed image has a period of…

Q: √√3 L dx 1+x²

A: