Given that ſ♫ sin xdx = 2, find the average value of the sine function on the interval [0, π]. Also, find the smallest value of x at which the average value occurs.

Q: Problem 8. [10 pts] For each of the following answer True or False. If it is false, explain it. (a)…

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Q: Find the tangential and normal components of the acceleration vector. r(t) = cos(t)i + sin(t)j + tk…

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Q: Suppose that a particle moves along a straight line with velocity v(t) = 10 - 1t, where 0 ≤ t ≤ 5.5…

A: Given: v(t)=10 -t, 0≤t≤5.5

Q: Find the Taylor or McLaurin series for the following functions X f(x) = 1 + x², a=0

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Q: Find the Taylor or McLaurin series for the following functions f(x) = ln(1+x), a = 0

A: According to the question we need to find out the McLaurin series.

Q: Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. b…

A: We need to solve for the remaining angles and sides of the triangle.

Q: Find the tangent equation to the curve y = sin² x at point x = 3.

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Q: 3+13 -t 5. Consider the vector valued functions x₁(t)= and x₂(t)= t2 -(3) (a)Compute the Wronskian…

A: Disclaimer: “Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: Find the limit. lim X→x ←+ -54 -3 -2 -1 00 O-2 f(x) 00 SIEX) 4 m 2 14 -3 2 3

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Q: Use integration by parts to find the indefinite integral. (Use C for the constant of integration.…

A: Note: ln(a×b)=ln(a)×ln(b)....(i) ln(an)=n×ln(an) ..........(ii)

Q: Q5: Find dx for the following functions: (1) xcinh 2x coch 2x (3) y = e* sin² x In√x

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Q: (a) lim x² - x + 6 X2 x 2 x² + 2x - 3 x² (b) lim x - 6 x 3 x² - 2x - 3 x - 4 (c) lim x+4√√√x-2

A: a.limx→2x2-x+6x2+2x-3=4-2+64+4-3=85b.limx→3x2-x-6x2-2x-3limx→3x-3x+2x-3x+1limx→3x+2x+1=54

Q: 7√2 2 0 x² 49-x² dxl

A: The given integral,        ∫0722x249-x2dx

Q: Q3 :(A): By using "L' Hopital rules "; Find the limits of : (2) limx-o x-³ (tan-¹x - x)

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Q: At what rate is the angle between a clock's minute and hour hands changing at 7 o'clock in the…

A: To find: Rate of change of angle between a clock's minute and hour hand at 7 AM. In other words, the…

Q: Find the radius of convergence, R, of the series. R = Î n = 1 I = n2n Find the interval, I, of…

A: We have to find out interval of convergence

Q: Q1: Answer two only (A): Solve the following linear equations by Cramer's rule: x+y+2z=1 2x-y-z=0 x…

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Q: 3. Evaluate the definite integral below: S¯¼ √x² + 2x − 5dx + Sq − √x² + 2x − 5dx

A: To solve the following integral problem

Q: • The orthogonal trajectory of the equation given below is already given. What is the value of "n"?…

A: The given equation x2+3y2=r2

Q: Answer the following questions for the function defined on the interval [-5,7). a.) f(x) is concave…

A: Use derivative concept

Q: Complete the following steps for the given function, interval, and value of n. a. Sketch the graph…

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Q: Calculate approximations of tan(π/4-0.1) by using Taylor polynomials P₁(x), P2(x), P3(x). Use c=π/4.…

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Q: (C): It w = tan x and x = 4t³¹ +t: Find d?

A: Given that w=tanx  and x=4t3+t. We have to find dwdt. We can write,  dwdt= dwdxdxdt  [ using chain…

Q: =) S sin6 x+cos6 x sin³ x cos³ x dx

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Q: Q1: Fill in the blanks for the following statements (chose five only) 4n 1. lim→∞ 2n+1 log10 (3x -…

A: The objective of the question is fill the blanks.

Q: (xx) 2. 6. 3. 7. 8. 9. 10. 11. 16. 17. 12. 18. 19. 13. 14. 15. To divide a decimal number by 1000,…

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Q: Q2: Solve the following integrals: (3) dx

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Q: 3 2.)f x³ (4 + x²)² dx ; Use rationalizing substitution

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Q: Find the general solution of the following differential equation. y" − 14y' + 40y = 0 NOTE: Use c₁…

A: Find the general solution of the following differential equation. y" — 14y' + 40y = 0

Q: (A): Solve the following linear equations by Cramer's rule: x + y + 2z = 1 2x-y-z = 0 x +2y-z = 4

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Q: 2. Integrate the rational function below without using partial fraction decomposition. S -dv

A: Integrate the rational function below without using partial fraction decomposition v2/(v6-1)

Q: Let h(x)=f(x)g(x) where f(x)=−3x2+4x−1 and g(x)=−x2+4x+3. What is h′(4)? Do not include "h′(4)=" in…

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Q: A manufacturer estimates that it's product can be produced at a cost of C(X)=40000-100x+x^3. If the…

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Q: Guy wire to a 100-ft tower has a tension of 500 pounds. Writew the component form of the vector f…

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Q: Q3 :(A): By using "L' Hopital rules "; Find the limits of : (1) limx-ol: 1-cos x sin²x (2) lim, o…

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Q: Q4: Answer two only: 4 2 (A): If A = 2 l-2 Find AB and AC. 1 -1 01 0; 1 2 B = 2 l-1 3 1 -2 -2 and 2…

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Q: (B): If A = 2i + 3j - 4k; B = 3i - 4j + 5k and C = i + j - k, find: (ii)B.C (iii)A. (B+C)and (A+B).C…

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Q: Q5: Find for the following functions: (4) y = x sinh 2x cosh 2x (3) y = e* sin² x In√x

A: The given functions,3) y=exsin2xlnx4) y=xsinh2x-12cosh2x

Q: 10.¹ (3x² - y²) dx + (xy − x³y¯¹) dy = 0 2 du

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Q: 8 If f(x) = 3 + = + x 6 x2 find f'(x). Find f'(4). Round to 3 decimal places if necessary.

A: Given that f(x)=3+8x+6x2-(i)Our Aim is to find f'(x) and f'(4).

Q: 7. Use the Method of Lagrange Multipliers to find the extrema value of a function f(x, y, z) = 2x² +…

A: Concept: Lagrange multipliers: A straightforward and elegant technique for determining the local…

Q: Q / if w = tan x and x=4²++ Find dw dt

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Q: , 4x²+x+17 (x+1)(x²+4) dx I

A: Hee, to evaluate the given integral we have to rewrite the rational function.

Q: Find three mutually orthogonal unit vectors in R³ besides ti, tj, and tk There are multiple ways to…

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Q: B. Solve one of the following inequalities. Write your answer as an interval or union of intervals.…

A: Please see the answer below.

Q: g(x) dx = (Simplify your answer.) 7 4g(x)dx= 2 (Simplify your answer.) 7 [g(x)-f(x)]dx = (Simplify…

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Q: a. b. C. Evaluate the following double integrals: (2xy + 3y²)dydx (r)drde (e-²) dydx (Changing the…

A: We need to evaluate the given double integrals. Please see below fora detailed answer.

Q: The radius of a right circular cone is increasing at the rate of 6cm/sec while  its altitude is…

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Q: (C): Solve the following equations:- (1) sin 2x + 2 sin² = 1

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Q: LI) Prove that (3

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