Consider the integral cot(0) · In(6 sin(@)) d0: This can be transformed into a basic integral by letting and du do After perfroming the substitution, you obtain the integr du

Q: 1 1 + 25 1 +. 125 Given the series 1+ Does this series converge or diverge? converges O diverges If…

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Q: 524–121x4 lim x00 62xº+24x4+234x³+11x2+169 ||

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Q: Find the indefinite integral. (Use c for the constant of integration.) (4t³i + 6tj – 6ik) dt

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Q: 465.98 23.98 2.789 56.09 ATATA TTA TA

A: Rounding up

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Q: letter b

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Q: Describe the graph of the equation. r = (7 – 21) i+ 101j O Itis a line in 2-space through the point…

A: Equation

Q: 5. Given the General Solution the DE, Identify the roots * y = C1e¬2x + C2cos2x + C3sin2x O A) m1=…

A: Here, the solution to the DE is: y=C1e-2x+C2cos 2x+C3sin 2x...(1)

Q: On what intervals is the function f(x) = continuous? x(x - 1)(x- 2) 1. (-00,0) 2. (0,1) 3. (1,2) 4.…

A: First draw the graph Uasing limits and the check the countinity of this function

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly.…

A: Here , we have given an integral and we have to integrate over a rectangle whose vertices are given…

Q: 13) Determine the lim X--9 + 169 く+9

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Find div F and curl F if F(x, y, z) = x*i – 5j + yzk. - div F= curl F=

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Q: Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series…

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Q: x+2x+3 If A = S dx then (x-6)(x²+4) I tan- 7 A is equal to 40 Inlx – 6| - In(x? + 4) + C - Inlx – 6|…

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Q: Find curl (7z i + 8x j + 9y k). curl(7z i + 8x j + 9y k) = ( i )i + ( i )j + ( i )k

A: This question is related to vectors, we will solve it using given information.

Q: #1 Evaluate F• dr. F(x, у) — хі + уј C: r(t) = (9t + 2)i + tj, 0sts1

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Q: Use the formula «(t) = F () ×F (51 to find k(t). ||r(t)||* r(t) = t²i+t°j K(t) = %3D

A: We have t find κ(t) for the given vector r(t) = t2i + t5j The given formula is κ(t) =…

Q: E(-1)" n n=1

A: Series

Q: Q6 Find dy, if y= +++

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Q: INSTRUCTION/S: Evaluate each limit by two methods. TOPIC: INDETERMINATE FORMS FIRST METHOD (Partial…

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Q: Find the general solution of y’= y sec x.       y = c ( sec x – tan x ) y = c ( sec x + tan x ) y =…

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Q: Use the divergence theorem to calculate the surface integral F. dS; that is, calculate the flux of F…

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Q: Find the area bounded by the curve x = y² + 2y and the line  x = 3.

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Q: 4.)(4D3 + 28D² + 61D + 37)y = 0

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Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) x r"(t). r(t) = – 2tj %3D

A: 1st derivative, 2nd derivative, dot product and cross product are evaluated.

Q: A swimming pool full of water is in the form of a rectangular parallelepiped 5 m deep, 25 m long and…

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Q: -2 12) Find the sum of the Series 2".30" A C) D) 2 E) 9

A: Let    I= ∑n=1∞2n3-n-2Rewriting 2n3-n-2=2n3-n3-2                                  =2n3n×132…

Q: Question 2 of 4 (x² – 1)(x + 1) (x2 – 2x + 1) :- f (x) =

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Q: Set up (but do not evaluate) an iterated triple integral for the volume of the solid enclosed…

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Q: 2. If the acceleration function of a certain particle is given by a(t) = sech () tanh () – ež, find…

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Q: 3.) ž sin'(x)dx

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Q: 3. A tank contains 200 liters of fluid in which 30 grams of salt is dissolved. Brine containing 1…

A: Given problem:-  A tank contains 200 liters of fluid in which 30 grams of salt is dissolved. Brine…

Q: Find curl (2z i + 3x j + 5y k). url(2z i + 3x j + 5y k) = ( i )i + ( )j + ( 3 )k

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Q: INTRODUCTION TO MATRICES Answer the following questions: Given the Matrix A below. 3 12 21 A- 17 15…

A: This is a problem related to matrix . Based on the general formula and concepts we will answer the…

Q: Express the integral as an equivalent integral in which the z-integration is performed first, the…

A: Integral

Q: 26) In Problem 26 and 27, given f(x)dx= - 1 J g(x)dx= 2 and S f(x)dx= 3 a a d. Find f" f(x)dx + S*…

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Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) x r"(t). r(1) = i – 26j + %3D (a) r(t) 3ti- 2j + 2 k (b)…

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Q: The position vector r describes the path of an object moving h space. Find the velocity v(t), speed…

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Q: Determine the exact area between the x-axis and the curve defined parametrically by ¤(t) = ;t2 1…

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Q: 2. dy dx

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Q: 1 for convergence, you can use the P-test. (You k2 k=1 To test the series could also use the…

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Q: 91 (x). いz 16 モtuて X ultブ -(り+ X uft-) こtれてXutラ =()(つ 3-(x)ナ( zn+1 (6トフ3×マ A) flx)= x?m 167x2 power…

A: Let's find.

Q: Given the function f(x) = Which f the following is/are true? (x- 1)(x + 1) 1. lim f(x) = +00 2-1+ 2.…

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Q: Answer is incorrect

A: Apologies for the inconvenience. In the second last line there was a calculation mistake.

Q: 47. f(x) = V(3 – x) on [1,3]

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Q: Find div F and curl F if F(x, y, 2) = 4y®z'i – 14.x°2®j – 7xyʻk. div F= curl F=

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Q: d. | x In(x + 2) dx

A: This question is related to definite integration, we will solve it using given information.

Q: 2. SET-UP the definite integral that will give the area of the region specified using (a) x as the…

A: Area

Q: Find V x (V x F) if F(x, y, z) = 5xyj+ 9xyz k. V × (V × F)

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