Find the curve length of the function 1 1. f(x) = ;x² 0 < x < 3

Q: 22. Sketch the region bounded by f(x) = Vx -1 and g (x)=x-1 AND find the area.

A: Sketch

Q: What is the solution of D.E y"- 2y' = e*sinx when solved using the method of undetermined…

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Q: In(n+24)158 In(103+12 n)200 The sequence is and its limit is

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Q: The particular solution y, of the differential equation y" + 4y' + 4y = 3x? + 1 is (1/8) (1-2x+6x^2)…

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Q: 21 x² +4x+3 4. Find lim x→1x -5x+6

A: Given query is to find the limit of the expression.

Q: Express the series using sigma notation 6m + 3m + 0 + (-3m) + (-6m) ...

A: Consider the series 6m + 3m + 0 + (-3m) + (-6m) ...

Q: The technique used to prove that x4 x3 , dx =- 2x + 2vZtan- ( 2/2tan + C x2 + 2 3 is Long…

A: We have to find the method

Q: Let u = and v = Find each quantity: a) (u)(v)  b) (u)(u)  c) (v)(v)

A: Given: u =&lt;4,-3&gt; and v =&lt;-2,7&gt;

Q: g. -3+i

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Q: Using the Nth term test for divergence, V5n-2 n2 n=1 diverges since lim V5n-2 n² is equal to n→∞ 8.

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Q: Which of the following is the particular solution of a nonhomogeneous differential equation…

A: As per the company's guidelines, we are supposed to solve first question for you, kindly repost the…

Q: 3 y = Vx and y = x³

A: We have to find the area by using definite integral

Q: Determine s) for $) = 31 + 212 1 s'() = 41 + 3 Os') = 41 + O s'() = 41 - %3D s'(t) = t+4t %3D

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Q: Find the surface area of the plane ( 15x- 5z+20y=35) if it is in the first octant

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Q: dy find the dx +Ince 义 9 = sin In Cl+e)

A: The given problem is solved below in detail.

Q: Find a series solution about the ordinary point 0 of the differential equation y" + 8xy'-4y-0 O None…

A: The given differential equation is:y''+8xy'-4y=0We need to find a series solution about the…

Q: Nathan invested $2,870 for 219 days at a simple interest rate of 2.75% p.a. How much more or less…

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Q: Q2/ Find the second derivative of the following: 1. 2 Va 2. (x-1)(x2-2x)

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Q: Express the limit as a definite integral on the given interval. lim n- 00 [4(x;)³ – 4x;"]ax, [(2, 7]…

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Q: A test has multiple choice questions with 3 choices for each answer; only one answer is correct for…

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Q: Using appropriate substitution, sin³ (3x)cos*(3x)dx is equal to -cos"(3x) + cos"(3x) + c - cos (3x)…

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Q: (a) Evaluate the triple integral dV, where E= {(x,y,z):0<x< 3, 0<y< 3, 0<z3 2). %3D (b) Evaluate the…

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Q: Using decomposition into partial fractions, 4x2 + 2 -dx x(x² + 2) is equal to In|x (x? + 2)| + C…

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Q: Given y, (x) = x? is solution for the differential equation x²y"-3xy' +4y= 0 Using the reduction of…

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Q: Solving by variation of parametery"-4y' + 4y = xe2x, the value of Wronskian W is: xe^4x O None of…

A: We can solve this as follows:

Q: Consider this function: y=-5 sin(3x+x) (Continued from previous question.) Imagine the graph of this…

A: We will find the 5 points.

Q: Find the first five terms of the Taylor series for the function f(x) = lnx) about the point a = 2.…

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Q: Express the series using sigma notation -5 + 10 - 20 + 40 - 80.

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Q: For some constant a, the following improper integral a | (x² + 1)e2×dx

A: We have to solve given improper integration

Q: 2) z= (1+t²)(3 - 2y); z' Ans: z' = -2(3t? + 3t + 1)

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Q: II. Find the equations of the tangent and normal lines at the point indicated. a. 7x - 6V3ry + 13y -…

A: Solution is given below:

Q: For items 5-10. Solve inequality for y. 5. 84x+7y2 70

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Eliminate the arbitrary constants on the given equation: y= Ae" + Bre 2y +y=0 O y =-y" + 2g

A: To eliminate the arbitrary constant.

Q: Test the series for convergence or divergence. (If the quantity diverges, enter DIVERGES.) (-1)"-1…

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Q: 6. The equation 4 (x – 1)2 + 4 (y+ 2)? + 4 (z – 3)² = 1 represents a sphere. %3D 6.1. What is its…

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Q: |y = xx² – 4)

A: This is a problem of area calculation by region given. Based on the general formula and concepts we…

Q: sin x 2. Find the derivative of y = 3+2cos x

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Q: these O 6) Eliminate the x = t , parameter and find à corresponding rectangular equation: y = 2 –3 t

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Q: (zxャy)dx->xy dy =。 2-

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Q: Given the geometric sequence where a, = 2 and r = 2 Find a10-. 32 256/2 32/2 256 O O

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Q: For the number 70260.011000 What is the number of significant digits and what are the significant…

A: Number of  Significant digits = 11

Q: Q3: Find gradient of the following function at given point 1) f(x, y) = y –x, (2,1) 2) g(x, y) = y –…

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Q: The technique used to prove that x4 x3 - 5x + 5V5 tan¬1 3 x² + 5 dx + C - - is Long (Euclidean)…

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Q: Some values for a relation are given in the table. Is the relation a function? Find the domain and…

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Q: 5. (1 + e*/") + e*/ dy

A: Solution

Q: 6 What is the recursive formula for the sequence 3, -12, 48, -192, 768,...? a 1 = 3, a n = (a n -…

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Q: testonvergence and divergene h.

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Q: 26 Select the correct answer. Which matrix can be multiplied to the left of a vector matrix to get a…

A: The given problem is solved below in detail.

Q: For the differential equation (x -4)y" + (x- 2)y'+ 2y 0, the singular points are: O None of them x-3…

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Q: Prove: If s S6sn for all n EN and if both sn Land un+ L, where LE R, then t - L asn- 0 as well. That…

A: We are given that sn≤tn≤un  for all n ∈ℕ and both sn and tn converges to L∈ℝ.We need to show that tn…