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Q: he given values of the ndicated derivative.

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Q: when r = 5 and dt An expanding sphere has radius r = 0.6t cm at time t (in seconds). Let V be the sp...

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Q: 14. If we let u = 4x – 1 for the s²tan(4x-1)-3 cos"(4x-1) dx. what will be the cos(4x-1) resulting f...

A: This is a integration problem

Q: Instructions: Use Rules of Differentiation to differentiate the following functions. Show your solut...

A: derivative

Q: Problem 2: A piece of string whose length is given below is cut into two pieces. One piece is used t...

A: The length of string is 48 cm.Let the length of the one piece is x,Suppose, equilateral triangle wit...

Q: dy = ky fits this population growth, express the dt A recent report by a country's census predicts t...

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Q: Solve the differential equation with appropriate method. Finalize answer free of logarithms and radi...

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Q: 7. Consider the integral 2m* g(x) dx. There is a function g(x) such that when u = Inx the resulting ...

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Q: D Express the interval in (a-k, a+R) aad 1 x.-alc.R I(3x+1)?(<!

A: |(3x+1)2| &lt;1 both side we take square roots |3x+1|&lt; +1 3x+1 &lt;+1 3x+1&lt;1    or    3x+1&lt;...

Q: Evaluate the integral dx 2x리x-3월 x2 1 3 + V2x In A + C 2/3"3 - V2 | ® In(2x x - 3{x²) +c 1 In + C 2/...

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Q: At 9 AM, ship B is 65 miles due east of another ship A. Ship B is then sailing due west at | 10 mi/h...

A: Given

Q: Find the solution of the following equations: 1. у' —х-4ху 2. (2xy + x² + x+) dx – (1 + x²) dy = 0 3...

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Q: dx The integral can be rewritten as 1- x (a) lim (-2+ 2v1-s) (b) lim (-1+2vī-s) S--0 (c) lim (-2+v1–...

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Q: p dq , for demand q and price p. Find the general equation q = f(p) where E = 3. (Hint: Set the elas...

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Q: Find the radius of convergence of the power series. 00 E(-1)"n+ 9 n = 0

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Q: Find the Taylor polynomials of orders n = 0, 1, 2,3, and 4 about x = x0 and then find the nth Taylor...

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Q: 18. dx The integral - can be rewritten as V1 - x (a) lim (-2+ 2v1-s) (b) lim (-1+2vī -s) s--00 s--00...

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Q: IV. Constructing. Construct the table of values, graph the function and find the indicated limits ea...

A: 1. limx→+∞3x2. limx→-∞4x

Q: Evaluate the integral: I = 2x S where the solid S is defined as: S = {(x, y, z) E R³ : x > 0; 0 < y ...

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Q: Given F(s) = L(f), f(t), a, b, L, n are constants. Show the solution. 1 1) (s+v2)(s-V3)

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Q: 1+ Inx 6. Find f(x) so that when u = f(x) the integral an( f(x)) dx can be rewritten as cot u du. (a...

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Q: ces 3. Find dæ/dy (watch out!) of the relationship 3-5% + sin y = In x + Vy3

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Q: dx The integral | can be rewritten as V1. - X (a) lim (-2+2v1 – s) (b) lim (-1+2v1 – s) S--00 S--00 ...

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Q: 0o COS 17. Determine whether 2 converges or diverges. Evaluate it if is convergent. dx 18. Determine...

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Q: 16. Sketch the region enclosed by y = |x| and y = x2 - 2, and find its area.

A: To evaluate the area between the following curves

Q: dx The integral can be rewritten as -∞ V1 – x (a) lim (-2+2vī1-s) (b) lim (-1+ 2v1 – s S--00 S--00 (...

A: Given ∫-∞0dx1-x Let t=1-x differentiating with respect to x, dt=-dx ∫-∞0dx1-x=-∫-∞0dtt=-∫-∞0(t)-1/2 ...

Q: Find the second derivative of the function. 1+20 (2-0) 20

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Q: The growth in the number (in millions) of Internet users in a certain country between 1990 and 2019 ...

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Q: Suppose that the sum of the three vectors u, v, and w shown in the figure is the zero vector. If w-2...

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Q: Use the binomial series to find the Maclaurin series for the function. 1 f(x) %3D (1 + x)5 f(x) =

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Q: Use the binomial series to find the Maclaurin series for the function. f(x) = V1+ x CO f(x) = 1 + -x...

A: From binomial theorem we know, 1+xn=1+nx+n(n-1)2!x2+n(n-1)(n-2)3!x3+....

Q: How many ways are there to represent a function? Find the domain of the following function x²+3x+1 V...

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Q: Evaluate the integral cot 2x S- Vcot? 2x - 15

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Q: Find the solution of the following initial value problem: an = 14a,-1 – 49a, 2; ao = 0, a1 = 6 %3D a...

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Q: Use the binomial series to find the Maclaurin series for the function. 1 f(x) = (1 + x)3 f(x) =

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Q: Find an equation for the graph sketched below 8- 7- 5-

A: Given: - The graph is, To find: - The equation for the graph.

Q: 2 f(x)dx Given: There is a function F(x) such that when u= -x³, the 2 du resulting integral is Evalu...

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Q: Find the solution of the following initial value problem: An 14a,-1- 49an- 2; ao = 0, a1 = 6 %3D an ...

A: Let us take an=rn. So, the characteristics equation will be       r2-14r+49=0⇒r=7, 7 Further, we hav...

Q: If f(x) + x²[f(x)]³ = 10 and f(1) = 2, find f '(1). f'(1) = %3D %3D

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Q: To determine how fast a change in weight will occur, the most plausible assumption is that is propor...

A: Given that dwdt is proportional to the net excess C-19.25w

Q: A certain index I is a measure of soil moisture. An article described the rate of change of I with r...

A: dIdW=0.0634.6-I  

Q: The differentiable function  f  is such that for all  x  with  3 ≤ x≤ 7 , we have  4 ≤ f'(x) ≤ 6...

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Q: Evaluate the integral tan 4x dx Vtan? 4x - 24 tan 4x 1 Arcsec 4/24 V24 +C O 1 sec 4x Arcsec 20 + C O...

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Q: Use the binomial series to find the Maclaurin series for the function. f(x) = V1 + x %3D f(x) = 1 + ...

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Q: Find the radius of convergence and the interval of convergence. El-1)«(# + 2)2*+1 k2 + 4 A=1 Radius ...

A: Given series ∑k=1∞(-1)k(x+2)2k+1k2+4 want to find radius of convergence and interval of convergence 

Q: Find the nth Maclaurin polynomial for the function. 4x – 4 f(x) n = 4 %3D X + 1

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Q: Use sigma notation to write the Taylor series about x = 4 for the function. 1 x + 3 1 -1* 7*+1 (x – ...

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Q: Solve the differential equation with appropriate method. Simplify final answer the simplest possible...

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Q: Σ n = 0

A: Follow the procedure given below.

Q: Find the radius of convergence of the power series. (If you need to use co or -co, enter INFINITY or...

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