. Find the arc length of a point that moves with a constant speed of 60 mph along a circle in 15 minutes. 40 miles 60 miles 15 miles 90 miles

Q: Integrate تلد ا - تم( فیگ S (a² – v²) * 22)* dv where " a" is constant

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Q: The derivative of the function y = tan(In(vx² – 6x + 1)) is: 2 -

A: Chain Rule : (fg(x))' = f'(g(x)).g'(x). d(ax+b)ndx = n.a(ax+b)n-1 dtanxdx = sec2(x)

Q: The function h (x) 22 -5x+4 at-1 has a removable discontinuity. To make it continuous at all real nu...

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Q: Find an equation of the plane containing the points A = (1,0,2), B= (– 1,1,2),C=(5,0,3).

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Q: 8n5 + 3n Let an no +7 (a) Determine if the sequence an is convergent or divergent. O Convergent O Di...

A: Here, an=8n5+3nn5+7

Q: Using the tabular approach, evaluate lim X-1+ Inx

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Q: Use the limit comparison test to determine whether the series converges. Σ 3k +4 k=1 The series

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Q: Find the maximum or minimum value of the quadratic function g(x) = 2x + 6x + 3.

A: Given,           gx=2x2+6x+3To find : The maximum or minimum value of the quadratic function.

Q: Verify that the indicated function is an explicit solution of the given differential equation. Assum...

A: We have to verify that y= e-x/3is the solution of differenital equation 3y'+y=0  

Q: Sec2X Q1) A) Evaluate the following integral: S V1-tan2x B) Find the slope of the line tangent to th...

A: A) the given integral is sec2x/√(1-tan2x). B)y=Sin5x ; x=π/3.

Q: Find the domain of the vector-valued function. r(1) =In(1– 1)i+v4-1j O (-1,4] O 14,-1] O 1,4) O (1,4...

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

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Q: Use the formula for the binomial series: m(m-1)2 + 2! m(m-1).(m-k+1),k + .. (1 + x)" = 1+ mx + ... k...

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Q: ) Graph the curve Y = x (x +5)(x -3) between the value of x [-5, 3], then find the area of the finit...

A: Area under the curve =∫ab(upper curve -lower curve)dx  

Q: dx x²Vx² – 49 FOTE: Enter the fully simplified answer with no fractions under the square root and wi...

A: We will find the integral. 

Q: Question * Using integration by parts, the integral Sxsec(2x) tan(2x) dx is equal to:

A: The integration of the integral is xsec(2x)tan(2x).

Q: Evaluate the following integral: J Sec?x -dx V1-tan2X

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Q: Q5) A) Graph the curve Y = - 2 x (x - 4)(x + 6)(x - 2) between the value of x [0, 4), then find the ...

A: To graph the curve y=-2xx-4x+6x-2 between the value of x in the interval 0, 4, then to find the area...

Q: Find the nth Taylor polynomial for the function, centered at c. f(x) 1 n = 4, c = 5 P4(x)

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Q: The graph of f(z) is given by {-1.4) (1, 4) (-1, –2) (5,-2) (3,-4) (-4, 5) Determine if f is continu...

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Q: Find the indefinite integral and check the result by differentiation. (Use C for the constant of int...

A: We know that; The Power rule: ∫xndx=xn+1n+1+C ; n≠-1 The chain rule: fgx'=f'gx·g'x   Given: I=∫5+5t3...

Q: 2022x -dx J x2 + 6x + 18

A: Solution of given integration question is written in below steps.

Q: Jse the definition of Taylor series to find the Taylor series (centered at c) for the function. 4 f(...

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Q: sec Hovy long it will tace the bor te ach 99°C I Round the ani wer to one deaimal place ] Tsec

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Q: Write the first five terms of the sequence: (17 ln n +00 n=1 Determine whether the sequence converge...

A: The given sequence is 17ln(n)nn=1+∞. We have to check whether the sequence is converges or not. A re...

Q: SxV16ln? x – 9 1 dx xV16ln? x – 9

A: We put logx=u/4 and differentiate both sides with respect to u and solve it. Follow 2nd step.

Q: Show that the function f(x) = 1 – I - x² is continuous on the interval [-1, 1].

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Q: Use the formula for the binomial series: m(m-1)---(m-k+1),k + m(m-1) (1 + x)" = 1+ mx + + %3D ... 2!...

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Q: sin x dx TT cos2 x + e cos x

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Q: 3 - 2x? +x- 2 Use L'Hopital's Rule to evaluate Support your answer graphically. lim X2 x² +x-6

A: To find: The limit by L'Hopital rule. Given information limx→2x3-2x2+x-2x2+x-6

Q: 4. Find the equation for the line tangent to a. y=x²- 3 x + 5 at the point (2, 3)

A: We will find tangent equation. 

Q: 3.(Straightforward) Determine if each of these differential equations is exact, and if so, solve it....

A: As per our guidelines we are supposed to answer only one question i.e. the question no 3)a). For the...

Q: 1 Use the Integral Test to determine whether the scries is convergent or V3k + 5 k=1 divergent. Reme...

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Q: 2х — 4 f(x) = n = 4 x + 1 P4(x) = Need Help? Read It

A: We will find the mclaurian polynomial. 

Q: Question 3 Determine whether or not each of the following sequences is (i) bounded, (ii) monotone, a...

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Q: Using appropriate substitution, 3 the integral J1 x(3+ln(2x))² dx is equal to: 1 1 1 1 3+ln 2 3+ln 6...

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Q: 4) Find the interval of convergence for the power series Σ (-1)"-1п 2n n=1

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Q: 3. Let y = cot r + (cot a) In(sin a) and y" Show that -3 cot r +2y. %3D csc² r 4. Given the function...

A: Given: y=cotx+(cotx)ln(sinx)

Q: Find the area between the curves y = x2 - 8 and y = 4 - x.

A: Explanation of the answer is as follows

Q: Find the indefinite integral. sin3 70 V cos 70 de

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Q: sin 0 d0 cos? 0 +5 cos 0 +6

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Q: Question * The derivative of the function y = x(tan¬1(3x))² is:

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Q: Compute the multiplicative inverses of the following (if they exist) usin Using the Euclidean algori...

A: Note: Since you have posted multiple questions we will solve the first question for you. If you want...

Q: S sin?3ß cos11ßdß

A: ∫sin23βcos11βdβ ∫ (1-cos6β)(cos11β)dβ/2 ∫(cos11β)dβ/2 - (cos6β)(cos11β)dβ/2 (sin11β)/22 - ∫(cos17β +...

Q: A is an m x n matrix. Check the true statements below: A. The column space of A is the range of the ...

A:

Q: 1 dx x² – 1 C3 5. . J2

A: Since we are given with the multiple number of question and our guideline is solve first question on...

Q: By completing the square, dx the integral S is equal to: (x+5)Vx²+10x+21

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

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Q: Use the function f and the given real number a to find (f1)(a). (Hint: See Example 5. If an answer d...

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Q: Solve the given initial-value problem. The DE is a Bernoulli equation. x² dy 2xy %3D 4y*, У(1) - dx ...

A: Topic:- differential equations