Find the third derivative of the given function. o1) = ()2 - 3)* g"(t) =

Q: x3 + 3x2 + 4r +1 dx (r2 + 2x + 2)2

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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: dx For the integral , which of the following options is correct? A. lim (x – 1)½|" + lim (x – 1) | B...

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Q: The revenue (in thousands of dollars) from producing x units of an item is modeled by R(x) = 14x – 0...

A: Given: The revenue in thousands of dollars from producing x units of an item is modeled by Rx=14x-0....

Q: Given the taylor series for ex= 1+x+1/2!x2+1/3!x3+...+1/n!xn Find the taylor series at 0 for e2x^...

A: taylor series for e2x2 at x=0

Q: Find the nth Taylor polynomial for the function, centered at c. f(x) - In(x), n- 4, c-4 P(x) -

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Q: -5 dx Evaluate 2х — 10 (а) — оо (c) 1/2 (d) 0 00

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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: Use a graphing utility to graph the function and approximate (to two decimal places) any relative mi...

A: Given query is to graph the function using. Graphic utility and find its relative maxi and minimum.

Q: 8. rix of A using LU decomposition. 4 6 0] 6 12 2 8 4 A = %3D

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Q: 29. Show that sin x rif0<1 <2m.

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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: 2022" + n 2022 (d) lim sin 2022! + n!

A: We have to find: limn→∞sin2022n+n20222022!+n!. We can take the limit inside of sin as the limit is o...

Q: The figure to the right shows the number of full-time employees of a company (in millions) as a func...

A: here y axis = number of employee in million x axis = revenue in company and rate of change of employ...

Q: Calculate the present value of a loan that could be cleared by payments of $3,300 at the end of ever...

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

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Q: Q3) Find the Lagrange polynomial that fits the following set of four poin value of y at x-0: Ans. y=...

A: Given: - The set of four points, x -2 3 1 7 y 5 7 11 34 To find: - The Lagrange polynomial t...

Q: Given the matrix below, determine the following:  a. Cofactor of the element 5 b. Cofactor of eleme...

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Q: 7. Determine f (x) so that | cos(In°x) f (x) dx = sin(In²x) + C 2 In x In x (а) 2 In x (c) - (d)?

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Q: Find the derivative of the curve f(x) = 3x² - 6x + 1. Use the result to find the slope of the tangen...

A: Follow the procedure given below.

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

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Q: Solve for the 35th term, 40th term, 47th term, and 49th term of the Fibonacci sequence. Show your so...

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

A: Using product and division rule for differentiation. 

Q: How to do area & circumference

A: Given query is to describe how to find area and circumference.

Q: Find g' (3) given that f(3) = -6 and f'(3) = 4 %3D (a) For g(x) = 3xr² – 5 f(x) %3D 1 g' (3) = %3D 2...

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Q: 3 5 Consider the sequences, Which of these statements is correct? 2 5 8 11 A. The sequence converges...

A: Analysing this sequence we write the general term of the sequence as:                        an =   ...

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: Use the table of values to calculate the derivative of the function at the given point. 1 4 6. f(x) ...

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Q: A rain gutter is formed by bending up the sides of a 40-in.-wide rectangular metal sheet as shown in...

A: Given problem:-

Q: Find the derivative of the following functions using the definition of the sine and cosine function....

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Q: How much money should Bryan invest today into a fund that earns interest at 5.75% compounded quarter...

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Q: y(x^2+y^2-1)dx+x(x^2+y^2+1)dy=0 solve using integrable combinations

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Q: e) Explain how one can use differentiation to analytically determine the slope of a curve

A: If cost revenue given , we differentiate it so we give marginal revenue. 

Q: Find the nth Taylor polynomial for the function, centered at c. 1 f(x) x2 п %3D 4, с %3 3 %D P4(x) =

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Q: 5. y = - 5 log , (11x - 4) 6. y = 2 log e 4x°3 7. y = 12x² log 8x 8. y = In 25x 5x3

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Q: 16. u du Form Answer .Given: S 10% -dx а) 3 | а" du Find: formula b) | a"du c);| a*du d) =| a"du

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Q: Evaluate the function h(x) = [[x + 9]] for x = –4.

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Q: Find the radius of convergence of the power series. (If you need to use o or -0o, enter INFINITY or ...

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Q: show that y=seclx) is a solution to and use reduction y° -2tanGe)y'- of order to find a second, line...

A: see below the answer and calculation

Q: 1 с) у- d) y= x 2** e*

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Q: Evaluate the integral dx ,2 2x x - 3x X

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Q: III. For each of the following functions, find the indicated derivative using the definition. Show s...

A: As per our guideline if multiple questions are posted we are supposed to answer only the first one. ...

Q: Kelly received a $39,650 loan from a bank that was charging interest at 4.50% compounded semi-annual...

A: Given : Principal Amount (P) = $39,650 Interest Rate (r) = 4.50 % = 0.045 Compounded Semi - Annually...

Q: Evaluate the integral S 4x4 – 12x² + 7 xdx (2x2 – 3)/4x4 – 12x² + 7 + 2ln|2x² – 3+/4x+ – 12x² +7]} +...

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Q: In Exercises 39-42, the velocity v(t) of a particle moving in the plane is given, along with the pos...

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Q: f(x) = x'- 12x + 2 3

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Q: Sketch the curve of y= 3x-10x³-12x²-7

A: The objective is to sketch the graph.

Q: A contract requires lease payments of $900 at the beginning of every month for 4 years. a. What is t...

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Q: 11. What is the lim (5x? – 4x + 3)? x-2 А. 13 В. 14 С. 15 D. 16

A: 11.limx→2(5x2-4x+3) Recall: polynomial p(x) then limx→ap(x)=p(a) Soln: let p(x) be 5x2-4x+3 therefor...