Find the arc length of y = 7r +1 over the interval [0, 2]

Q: If sequences (a,) and (b) converge to limit gand , respectively, then which of the following stateme...

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Q: Evaluate the integral cot 2x S- Vcot2 2x – 15 V cot? 2x

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

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Q: One of the following is an improper integral. - In 3 e* dx JIn 2 V4 – ex dx xV16 – In x - dx · In 2 ...

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Q: 1. An inverted conical tank with 14 m height and 6 m radius at the top is full of water. Calculate t...

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Q: Evaluate the integral dx 2xx - 3x?

A: To find: The integral ∫dx 2xx3-3x23 Concept used: ∫1-v2+1dv=lnv+12-lnv-12

Q: Given F(s) = L(f), f(t), a, b, L, n are constants. Show the solution. 12 228 1) s4 $6 2) L²s²+n²n²

A: find inverse laplace transform ?

Q: Use the binomial series to find the Maclaurin series for the function. 1 f(x) (1 + x)4 Σ f(x) = n = ...

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Q: Determine if the series is conditionally convergent, absolutely convergent or diverges. M-1)"- n =1 ...

A: The given series is: ∑n=1∞(-1)nnn3+4...(1) The absolute value series is: ∑n=1∞nn3+4 Let, an=nn3+4=nn...

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: 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: 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: 2. The seventh term of a geometric sequence is -2 and the tenth term is 128. Find the fifth term. 3....

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Q: Which of the following integrals represents the length of the curve y = cos(x), 0 < x < 2n? А. 1+ si...

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Q: Graph the line x=-1. 8- 12

A: We will graph the function. 

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

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Q: 1. One of the following is an improper integral CA In 3 cIn 2 dx xp 4 – ex 2x + 1 JIn 0.5 ' In 2 dx ...

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

Q: Evaluate the integral V4x4 – 12x2 +7 xdx

A: Using integration of square root of x2 - a2 and follow step 2nd . 

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

A: The given question can be solved as shown in step2.

Q: dx be given . If u = e* + 1, then the resulting integral is 2. Let | f(u) du. Compute f(3). (a) 2/3 ...

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Q: Consider the sequences Which of these statements is correct? 8. A. The sequence converges to 0 O B. ...

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Q: Give a power series Cnx" such that it is =1 convergent if |x| 1 of x = -1.

A: A series of the form {\displaystyle \sum _{n=0}^{\infty }(-1)^{n}a_{n}=a_{0}-a_{1}+a_{2}-a_{3}+\cdo...

Q: 3. The integral of an t dx is b In|sec(In(2x)ª)|. What is b? A. 1/2 В. 1/4 с. 2 D. 4

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

A: The objective is to sketch the graph.

Q: What is the accumulated value of periodic deposits of $4,500 made into an investment fund at the beg...

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Q: Learning Task 3: Find the equation of the tangent line to the following curves at a given point 1. y...

A: we need to find the tangent line of y=x2-6x+9 at x=2

Q: Find the interval of convergence of the power series. (Be sure to include a check for convergence at...

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Q: Answer this question by showing all work and formulas uses to solve: Determine f'(2) for f(x) = g[h(...

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

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Q: 2 dxdy

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Q: Find the Maclaurin polynomials of orders n = 0. 1.2.3, eand 4 and then find the nth Maclaurin polyno...

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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: 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: 11. y = coS x COS X -2 tan x 12. y = x? sin x tan x 13. у %3D 1 14. y = --3 sin x 15. y = x cot x

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Q: c) TR = (/Q5).(InQ)

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Q: Find two functions f and g such that (f ∘ g)(x) = h(x). (There are many correct answers. Use non-id...

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Q: The function s = f(t) gives the position of a body moving on a coordinate line, with s in meters and...

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Q: Set up an integral that represents the arc length of the function g(x) = sin x for the interval [0, ...

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Q: Find the laylar polynomials of orders = 0,1,2,3, and 4 about x = No, and then find the nth laylor po...

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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: 2. Let dx be given . If u = e* + 1, then the resulting integral is f(u) du. Compute f(3).

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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: Use the definition of Taylor series to find the Taylor series (centered at c) for the function. f(x)...

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Q: Let f(x) = (4x – 6)(x² – 5). Find all the values of x for which f'(x) = 0. Present your answer as a ...

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Q: Solve of AABC. 2. ABCD is a square of side 6 cm. If a rectangle of length (2x- 1) cm and width (x + ...

A: Area

Q: Evaluate the integral [/4x4 – 12x² +7 xdx (2x2 – 3)/4x4 – 12x² +7 – 2ln|2x2 /4x4 – 12x² + 7|} + c -3...

A: Given that, The integral is following, I = ∫4x4-12x2+7xdx We have to solve this integral.

Q: ²+2x 5. Sketch the curve: y? x-1

A: The graph of the given function is plotted below.

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

A: see below the answer

Q: Consider sequences n+1 n+2 (1) tan 2n (i) n+ (- 1)". Which of the above sequences are monotonic: A. ...

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Q: I. Determine whether the series converges using any appropriate test. Identify the test for converge...

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