Find the scalar component of u in the direction of v, scal, u and the orthogonal projection of u onto v, proj, u: u= (5,0, 15) and >= (0,4,-2)

Q: Express the limit as a definite integral on the given interval. 4 lim [3 - 4(x,*)² + 6(x;*)³] Ax,…

A: Given:- limn→∞∑i=1n3-4xi*2+6xi*3∆x Interval 0,4

Q: Use a power series to represent the function f(x) Provide your answer below: M8 n = 0 6x + 4…

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Q: Ms. Yang is planning South Glen's annual community talent show. After tryouts, she selected 20 acts…

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Q: ΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑ 11. Let f be the function defined by f(x) = [x – 2] for all x. Which…

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Q: The velocity (in feet/second) of a projectile t seconds after it is launched from a height of 10…

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Q: The area of the region that lies to the right of the y-axis and to the left of the parabola x = 4y -…

A: Answer is in step 2.

Q: 7. The distance in feet a ball has rolled after t seconds is given by the function f(t) = √t (a)…

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Q: 4. Use a linear approximation to estimate tan (47°).

A: Let's find value of tan(47°) by using linear approximation.

Q: Evaluate > f zy³dz + z³dy, where C' is the rectangle with vertices (0,0), (6.0), (6,2), and (0,2).

A: To find:- ∮cxy5dx+x3dy Where C is the rectangle with vertices 0,0,6,0,6,2,0,2

Q: Given a = log7 5 and b = log, 4, use logarithmic properties to represent each of the following…

A: Given that a=log75 and b=log74, using logarithm properties to represent each of the given function…

Q: Find the c value that satisfies the Mean Value Theorem. f(x) = 3 + √√x on the interval [0,4]

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) sec³(x) tan(x) dx

A: Evaulate the indefinite integral

Q: Find the volume of a solid obtained by revolving the region between the graph of f(x) = x(1 − x) and…

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Q: Find the nth Maclaurin polynomial for the function. f(x) = e-6x, n = 3

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Q: Find the Taylor series for each function centered at the given value of a (assume that each function…

A: Given,           fx=sinx , a=π2To find : Find the Taylor series for each function centered at the…

Q: Let a1 = 2. Let an+1 = 2 − 1/an. Prove that an is decreasing and bounded below by 1. b. Determine…

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Q: 3) Graph 1 period of y = 4cos(2x - π)

A: We have to graph one period of given function.

Q: Find the center, foci, vertices, and eccentricity of the ellipse and sketch the graph. 16x² + y² =…

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Q: Find the total area of the shaded region. 10- 8 6 4 Ay 15 2 p y=9 π/2 2 y=9 cos x it 3m/2 N X 2x J

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Q: (D2 + 5D + 4)y = 3-2x, Find Yp a. 11 8 O b. O C - Od 11 8 11 8 11 8 00 + O e. none X 3 + X 3 X 3 X 3

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Q: 1 2 A= -2 4 -2 4 3 5 -1 5 4 3 3 7 6 6

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Q: 120 2 A sides of lengths 6,10 and 7. Find the mesure of it's largest angle to the nearest degree…

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

Q: In the year 2000, the population of a small city was 50,000. The population grows at a rate of r(t)…

A: given rate is  r(t)=1200e0.04let t=0 denotes the year  2000for 2020, t=2020-2000=20

Q: Consider the following integral. Br -2 f(x) dx 0 = where f(x) = Rewrite the given integral. 2 [²1(x)…

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Q: In an arithmetic sequence, the 8th term is 17 and the 17th term is -10. Show all work for each of…

A: We know that  an=a+n-1d where a= first term, d= common difference Given that 8th term is 17 and 17th…

Q: Find the following indefinite integral using integration by parts. [(3x + =0+c (3x + 9)e* dx =

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Q: 2. Evaluate the indefinite integral using the substitution method. [((x+5)(z-5)) d

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Q: Evaluate the integral. 6. (2e + 8 sin(x))dx

A: We have to evaluate the integral ∫0π 2ex + 8 sinx dx.

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) √² dx 2 + 8x 1 + x²

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Q: Find the surface area of the helicoid (spiral ramp) with vector equation F(u, v) = (u cos v, u sin…

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Q: In this question, you will investigate whether the improper integral [ 21/12 converges or diverges.…

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Q: Evaluate the integral. 1 [²(6x (6x² + 5ex) dx

A: Solve by integration

Q: A river is flowing downstream at a constant rate of 5 ft/s. We take a rectangular net that is 6 ft…

A: Given river velocity ( v ) = 5 ftsrectangular net whose area is A A = length × breadth

Q: Question 9 (D2 + 5D + 4)y = 3 - 2x, Find Yp a. 11 8 O b. O C. 11 d. 11 11 8 8 ४ | 3 O e. none + 8/3…

A: The given differential equation is: D2+5D+4y=3-2x So, we can also write as: y''+5y'+4y=3-2x

Q: The Pythagorean Theorem Find the perimeter and area of the right triangle shown below. X Perimeter =…

A: To find the perimeter and area of the right triangle shown below.

Q: 2 0 √√2x-x² X √3 dydx 2 [x² + y²

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) Je sin(6t) dt ecos(6t)…

A: Given integral ∫ecos(6t)sin( 6t ) dt

Q: (D4-1)y= sinx, Find Yp O a. O b. 1 1 10 - sin2x 15 O c. 1 10 -sin2x -cos2x O d. 1 15 O e. none…

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Q: Use l'Hopital's Rule to evaluate commonly known limits. lim 0 x O lim Use l'Hopital's rule to…

A: Use  l hospital rule to find  the limit.

Q: For a segment of a radio show, a disc jockey can play 7 records. If there are 10 records to select…

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Q: 5. 6. 7. dx x² + t√t2² + x² dt tx dy de dx dy 0sec(y/0) + y Ꮎ 4y - 3x 2x - y

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Q: (15) Determine whether each integral is convergent or divergent. Evaluate those that are convergent.…

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Q: A pair of dice is rolled. What is the probability of getting a sum of 12? What is the probability of…

A: Solution: When two dice are rolled

Q: Consider the function f(x) = z ln(z). Let T be the nth degree Taylor approximation of f(2) about z =…

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Q: 14 Approximate (²-6) dx using 4 rectangles. [6²

A: Given, ∫214x2-6dx, n=4

Q: 1 sec. and Find the average rate of change of d(t) between the values (a) t = t = 3 sec., between…

A: According to bartleby guidelines we supposed to do the first three subparts of multiple subparts…

Q: 2. Evaluate the indefinite integral using the substitution method. / ((r + 5)(x − 5)³) dr. P

A: Here we have to evaluate the given indefinite integral by substitution method.

Q: Find the roots of (D4 + 4)y = 0 O a. +2i, 2i + 2 O b. 2+2i, ti OC. 1 ti, 1 ti c. - O d. - 1 ti, 2+2i

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Q: Our goal is to estimate the rate of change of d(t) at precisely the time t = 3 se This will be…

A: Given: dt=61.490-t

Q: Find the indefinite integral x² S ²-16 =dx = +c

A: INTRODUCTION:   An integral is considered to be indefinite if it has no upper or lower bounds.  In…