Calculate S3, S4, and S5 and then find the sum for the telescoping series Σ(112) S3 = where Sk is the partial sum using the first k values of n. S4 S5 S S = = n=5

Q: 4 decreasing N 2 (i) Identify the critical numbers of f. (Enter your answers as a comma-separated…

A: Topic:- application of calculus

Q: nd the a. 17, 30, 43, 56, 69, 82, ... 1 3 7 11 15 formula for the nth ter

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Given ƒ''(x) = 9x − 3 and f'(0) = 5 and f(0) = -6. Find f'(x) = and find f(1) = 3x + 5

A: We have to find value of f(1).

Q: A resistor shaped in the form of an annulus has an outer radius ba inner radius a and its resistance…

A: solution:-a<r<bR=∫abρdr2πr=ρ2π∫abdrr=ρ2πlnrab=ρ2πlnb-lna=ρ2πlnba

Q: Find the derivative of f(x)=x12

A: I am attaching image so that you understand each and every step.

Q: Question ( ,. For the limit, Select one: O True O False 2x² sin x + 3y³ lim (x,y) →(0,0) 3x³ + 2y²…

A: lim(x,y)→(0,0) 2x2sinx +3y33x3+2y2 apply the limit for this  this is the question of limit and…

Q: Consider the function y = e. Find y'.

A: Given query is to find the derivative.

Q: Evaluate the improper integral or state that it diverges. -2 88 9dx 2 Select the correct choice…

A: Solution : Given improper integral is

Q: INSTRUCTIONS: Differentiate with respect to x: y=x²

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Q: 19. a'(t) for a(t) = In 1-cost 1+cost

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Q: The economy of a small island nation is based on two sectors, coal and steel. Production of a…

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Q: If √√√x + √√y: = 6 and y(25) = 1, find y' (25) by implicit differentiation.

A: If x+y=6 and y25=1, then to find y'25 by implicit differentiation.

Q: d the distance between each pair of parallel line 1210. 2 m b=\ LM = 1 line: +1 y = 2x + 1 y = 2x -…

A: Given query is to find the distance between the lines.

Q: Find the limit. Use l'Hospital's Rule if appropriate.  lim x→0 3x − sin(3x) 3x − tan(3x)

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Q: Evaluate V = the double integral of (xy)dxdy D is bounded by y=x-1 and y2==2x+6

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Q: Find a degree 3 Taylor polynomial approximation of f(x) = (1+x)¹/2 centered at 0.

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Q: A vehicle purchased for $25,000 depreciates at a constant rate of 8%. Determine the approximate…

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Q: y=tx y=kx base view cross-section The base of a certain solid is the area bounded above by the graph…

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Q: dr Let A be the area of a circle with radius r. If dt Question Help: Video Message instructor Submit…

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Q: 15. pot INSTRUCTIONS: A bacteria culture grows with a con- stant relative growth rate. The bacteria…

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Q: Find the equation of the tangent line to the graph of the function f(x) = 2+1 2 the point (0₁-1).

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Q: Look at the effects of different bases on f(x) = log(x): -5 140 x

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Q: A cylinder shaped can needs to be constructed to hold 450 cubic centimeters of soup. The material…

A: Given A cylinder shaped can needs to be constructed to hold 450 cubic centimeters of soup. The…

Q: 8 .3 X (1+x)5 - dx

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Q: Evaluate the double integral. 16 (2x + y (2x + y) dA, D = {(x, y) | 1 ≤ y ≤ 4, y = 3 ≤ x ≤ 3}

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Q: Find all the first and second order partial derivatives of f(x, y) = -7 sin(2x+y)+5 cos(x - y). af…

A: See the details solution in below

Q: 2 (²) 13. f'(t) for f(t) = arctan 14. g'(0) for g(0)=√√30+tan² (40)

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Q: Determine whether the following series converges. Justify your answer. 8 + 10 Σ 8 k=1 k

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Q: The population growth model of a city is given by: dP P(0) = 235. P = 0.34 P, The population size…

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Q: Find an equation for the tangent line to the graph of y=(x3 −9x)12 at the point (−3,0).

A: Given query is to find the equation of the tangent.

Q: Consider the function y= x Find y'.

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: The following table shows the average life expectancies in several countries. Assume that all…

A: The following table shows the average life expectancy in several countries. Assume that all premiums…

Q: A cell culture contains 7 thousand cells, and is growing at a rate of r(t) thousand cells per hour.…

A: Use the formula given and the initial amount cell to find the final amount.

Q: Solution: Form the Lagrangian: Next, solve the system , or maxf(x, y) = -ry+3 Subject to: x² + xy +…

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Q: Find the limit. Use l'Hospital's Rule if appropriate.  lim x→0+ (tan(6x))x

A: eln(x) = x ln (x)a = a ln(x)

Q: 2. Find the time required for an investment to double in value if invested in an account paying 2%…

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Q: solve 15=60(e)^-.15t using logarithms

A: Given 15 = 60e-0.15t

Q: A street light is at the top of a 11 ft tall pole. A woman 6 ft tall walks away from the pole with a…

A: A street light is at the top of a 11 ft tall pole.  A woman 6 ft tall walks away from the polewith a…

Q: Differentiate. y=12 sqaure root of x

A: d dx(xn)=nxn-1ddx(constant)=0

Q: a) Find the linear approximating polynomial for the following function centered at the given point…

A: Solution: a) f(x)=e-x Now it's the first derivative f'(x)=-e-x Now it's the second derivative…

Q: A company determines that its weekly online sales, S(t), in hundreds of dollars, t weeks after…

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Q: 3) a) Given; A = 7 11 [4 2. (ii) (iii) B Use the above matrices to find the following: (i) BC ACT…

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Q: Consider the Cobb-Douglas Production function: P(L, K) = 28L0.5 -0.5 Find the marginal productivity…

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Q: Identify the open intervals on which the function is increasing or decreasing. (Enter your answers…

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Q: -1 Find the domain and the range of g(x) = sin-¹(3x + 1). Domain: Range: << ≤ y ≤ <

A: NOTE: Refresh your page if you can't see any equations. . as we know, the range of the sine inverse…

Q: t²y' + 2ty - y³ = 0

A: To solve the following differential equation.t2y'+2ty-y3=0

Q: 5. Calculate the arc length of the graph of on the interval [1, 2]. |2 x3 f(x) ) = 1/2/2 + 1/2 X

A: NOTE: Refresh your page if you can't see any equations. . and the given interval is  so the lower…

Q: The concentration C of a chemical in the bloodstream t hours after injection into muscle tissues is…

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Q: Find the absolute maximum and absolute minimum values of f on the given interval f(x) = x / (x2 - x…

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Q: d the equation of the surface in Cartesian coordinates, given the equation in cylindrical…

A: Given query is to find the equation in Cartesian coordinates.