convergent or divergent. Please provide detailed solution. a) : E 10" n=1 (n + 1) 52n + 1 00 -5n 2n b) ):E

Q: Choose the right description for the given differential equation 3 Sm :) + 8 m бр? COS m + Т. %3D O…

A: The given DE is: δmδn2+δ2mδp2=cos m+T

Q: Ge + C2x e* + C3 x*e*

A:

Q: 9x2 dx Vx3+2

A:

Q: dy Use implicit differentiation to find dx 2x - 5 3y? 2x +5 dy dx

A:

Q: 3. (1 + e**) + e (1-- 0 Ans. x + ye*/y = C

A: To differentiate.

Q: P1:

A: Solving

Q: Find the absolute maximum/minimum value for f(x)=x² – 4x+1 on the interval [(-3, 3] 9.

A: Given: fx=x2-4x+1 and x∈-3,3   The Power law: ddxxn=nxn-1

Q: sove the fowowing, using Lagrange Multipiiers: Maximize flR, Y. 2) solaject to x2 + Ax + a4 t 2 + 2…

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Q: Asec24xdx

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Q: 4x 9. sech(2x) dx e

A:

Q: 1) Use the Integral Test to determine whether the series > 1 is convergent or divergent. n=1 (3n–…

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Q: 元 店sit sin? 4x cos² 2x dx

A:

Q: 3 1 - dx 2 2. cos sin X

A: solution:-∫cos4xsin3x1x2 dxlet 1x=t-1x2dx=dt=-∫cos4tsin3t dtWe know that the formula  2cosAsinB =…

Q: EXERCISES Solve the following differential cquations 9. y(x*y + e*)dx e*dy = 0 x ex Ans. =C

A:

Q: dy into 11. The rationalizing substitution y = u° transforms J 7(1+ В. 6 f и du D. 6J TFu² du С. 6 /…

A: Given problem:-

Q: Find and b such that the following function is continuous at x=( [x] – 2a x 0 -

A: To find the values of a and b

Q: Solve [æ – y cot ( ) dæ + x cot () dy = 0 ; y (5) = 1

A:

Q: x-1 y = log, x+1

A: We know, ddxlog(x)=1x ddxu(x)v(x)=v(x)u'(x)-u(x)v'(x)v(x)2 log(ab)=log(a)-log(b) log(a)n=n*log(a)

Q: Simplify the complex number. Express your answer in a+ bi form and include each step necessary in…

A:

Q: Use the chain rule to find the derivative of f(x) = 6/3x + 5x10 Type your answer without fractional…

A:

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: Which of the following equations is a homogenous DE? O (xy? + x)dx + (x²y- y)dy=D0 O (x- y)dx+ (3x+…

A:

Q: Step 1 To find the definite Integral 9 dx by the limit definition, divide the Interval [2, 7] Into n…

A: For the asked steps we can solve as follows.

Q: Q5: Find equations for (a) the tangent plane and (b) normal line at the point P, on the given…

A:

Q: 4. Given a function, fix), such that f(x)dx = 10, calculate: a) - r(«)dx b) S rx - 2)dx d) Stsx) +…

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Q: The graph given below is graph of f '. Determine where f is increasing, decreasing, concave up,…

A: Let's find.

Q: Use Lagrange multipliers to find the point on the plane x – 2y+ 3z = 6 that is closest to the point…

A: Let, the point be (x,y,z) then the distance between (x,y,z) & (0,1,4) is:…

Q: 2. A bushfire spreads with burning area according to the following function, A(t) = 160t – 40t2 (in…

A: Let's find.

Q: is this statement true or false   The probability of any possible value in a discrete in a…

A: Here is the solution.

Q: csch 3x – 5 [3х — 10. dx V3x – 5

A: 10) To evaluate: I=∫csch43x-53x-5dx Substitute 3x-5=u⇒123x-5(3) dx=du⇒13x-5dx=2du3 ⇒I=∫csch4u2du3…

Q: 3 y = Vx and y = x³

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

Q: Find the volume by revolving the region of the curve xy = 6 from x = 2 to x = 4 about the x-axis.

A: Given xy=6        x=2 to x=4To find volume:

Q: Given: a= 22, c=24.1, zB = 67 C A Solve the triangle. (Do not round until the final answer. Round…

A:

Q: Select all that apply. For the quadrant in which the following point is located, determine which of…

A: Given query is to find function , which are positive for the point.

Q: dz and dy dz Suppose z is a function of x and y, and tan Vy² + x2 = 2"e®y_ Solve for

A:

Q: Write z1 and 22 in polar form. 21 = -36, z2 = V3 +i Z1 Z2 Find the product z1z2 and the quotients 2…

A: Let's find.

Q: Let F(x) = f(æ*) and G(x) = (f(x))*. You also know that a' = 3, f(a) = 2, f'(a) = 8, ƒ'(a*) Then…

A:

Q: 1 2 3 4 f(x) f'(x) g(x) 4 1 2 3 2 4 2| 3 (x),6 2| 1 4 1 4 3 h'(4) if h(x) = f(x)•g(x) f(x) h'(4) if…

A: Our Aim is to find h'(4) with the help of table and three conditions given below:-(i)…

Q: X = -y A y 2Fx = 2- y² -2

A: Recall: Formula Area=∫abf(y)-g(y)dy  We have,  f(y)=2-y2, g(y)=-y

Q: Stan@ -1}de

A: ∫ tanθ dθ = -lncosθ+C ∫sec2θ dθ = tan θ +C.

Q: Use the graph of y = fx) shown at right to determine whether fis continuous at 0. (-6,4) 41 94) Is f…

A: We can solve this as follows:

Q: re' dy + +1 dr =0 O (y – 1) e + + In z = C 2. O-(y+1) e + Ine =C 2 O (1- y) e + 1. O 2y - e + +In=C

A: To solve given differential equation

Q: 1 Integrate

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Q: Show that the function f defined by (r, y) = (0,0) f(x, y) = { 22 + y (r, y) # (0,0) x + y

A:

Q: Solve the second derivative(y") of the following

A:

Q: After substitution is performed, which of the following is equivalent to xV4x² + 9 dx? 25 du 8. 25…

A: Here is the solution:

Q: 0 14 (x² + 4y) dæ dy 4

A:

Q: If f(x) = 4 Tln(x), find f'(x). %3D Find f'(2). Submit Question

A: Differentiation

Q: -3 -8- -

A:

Q: Solve the equation (2xy - tan y)dx + (x^2 - x (sec y)^2))dy = 0

A: