2-28 Determine whether the series is absolutely convergent. conditionally convergent, or divergent. (-1)" n In n 22.

Q: Find the solution of the differential equation (x+ Vy² + 1)dx – (y - ху dy = 0 %3D Vy2+1,

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Q: Solve the differential equation (y /x² + y²) dx - xdy = 0. If y = 1 when x = /3, determine y whe +

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Q: a) Queen Beyoncé's yacht will be leaving from Port Destiny and traveling on a straight line to an is...

A: Each part of the problem is solved below in detail.

Q: 4. Show that In x lim x→1 x – 1 1. (Hint: Note that In In x-ln 1 x-1 and interpret the limit as a de...

A: Given: To prove that limx→1 ln xx-1=1 using the limit as a derivativeFormula: f'(a)=limx→af(x)-f(a)x...

Q: 1. Let f(r, y) = arctan(ry). (a) Find the unit vector in the direction where the directional derivat...

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Q: know what the derivative of e^(g(x)) is and what the derivative of In(g(x)) is. I.e. the chain rule ...

A: From chain rule  If g(x) is a differentiable function, then the derivative of eg(x) is g'(x)*eg(x) ....

Q: 3. Find the exact value of each trigonometric function. cos-1 cot

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Q: Find the exact value of each exp V3 sin 2 Si

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Q: ese()2 TT csc 6 ? What is the exact value of

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Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given point...

A: Given: ysin16x=xcos2y Equation of a tangent at point a,b with slope m is defined as  y-b=mx-a

Q: Variable Separable (6) (xy - 3y + x – 3)y' = xy + 2y – x - 2 (7) y' kM – ky; Provide the explicit so...

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Q: (s+1 if s 1 (a) Find lim f (s) (b) Find lim f(s) S-1 s--1 2t +3 if t 1 2. g(t) = Find lim g(t) %3D ...

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Q: Question Evaluate the following limit using L'Hospital's rule. lim (x+ 6) In ( (æ + 6)² ) z-6+ Provi...

A: if the limx→af(x)g(x) is of the form ∞∞ then by L'Hospital rule the limit is equivalent to limx→af(x...

Q: (vz-i, »). a Let 7(t) = (/2-i -1+e' In(t + 1) (i) The domain of 7 is [a] (input a number from below)...

A: The domain of a vector function is the set of all t for which all the components of vector are defin...

Q: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of...

A: Given that: ∫x2+1(x-3)(x-2)2dx

Q: Find the general solution of у" -у - бу %3D 6х3 + 26 sin 2x

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Q: The curve C is the portion of the graph of y = 16* for 0 <z < 2 (distances measured in m). The curve...

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Q: / (3cosh m 2 cosh m sinh mdm +e°

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Q: 8. Find the exact value of each expression. 3V34 tan cos 34

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Q: 1- Solve the following equations using Grammar's rule: b) 2x + y - z = 2 x - y +z = 7 2x + 2y + z = ...

A: Given system of equation2x+y-z=2x-y+z=72x+2y+z=4We know that for system of equation a1x+b1y+c1z=d1a2...

Q: Find the total mass of two turns of a spring with density p in the shape of the circular helix below...

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Q: Evaluate the given function ſ sec5xtanxdx a. sec*x + C b. sin*x + C c. cosx + C d. 금esc5x + C

A: topic - indefinite integral

Q: OBTAIN A FAMILY OF SOLUTION 2. (x - yny + y In x ) dx + x CIn y - In x)dy =0 3. [x - yarctan (y/x)]d...

A: This question is related to differential equation.

Q: Describe how the graph of the following function can be obtained from one of the basic graphs. g(x) ...

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Q: Find the integral. e4X cos 3x dx + C

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Q: A pyramid of height 500 ft has a square base 800 ft by 800 ft. Find the area ? at height ℎ....

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Q: Given points P(2, 4, 3) and Q(1, -5, 2) in the rectangular coordinate system. What is the resultant ...

A: Given points P2,4,3 and Q1,-5,2  in the rectangular coordinate system.We need to find the resultant ...

Q: 1. Find the limit of the following: x° – 11x +37x* +6x' – 297x? +621x – 405 lim. x* —11x* +47х* -114...

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Q: to, thenk is15 not a - andly-k) 5/15 not a If fQ) =0,thvnk 5/5 not cs ond Oxok) Is/15 not a

A: The Remainder theorem says that if a polynomial P(x) is divided by (x-a) then remainder obtained is ...

Q: QUESTION 4 Given f(x) = 8x3 + 2x. Estimate the value of f(2.01) using differential.

A: Given that: f(x)=8x3+2x

Q: Let f (x, y) = 3y O 1 x/3 1/(3у) (1/3)y

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Q: Find the domain of the vector function r(t)=⟨ln⁡(19t),sqrt(t+8),1/sqrt(7−t)⟩ using interval notatio...

A: Given vector function isrt=ln19t,t+8,17-tfind the domain.

Q: A. Find the differential equation: (1) whose general solution is y = c,e-2x + Cze3x (2) by eliminati...

A: To find the differential equation.1 whose general solution is y=c1e-2x+c2e3x.2 by eliminating B and ...

Q: the given position vectors r(t) compute the unit tangent vector T(t) for the given value of t . A) ...

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Q: 2. What is the egnation of a line to Seyment from = <8,0,47 to P =<-5, 2 17 .

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Q: The average change of a function f over an interval [¤1, x2] is f(x2)-f(x1) First find the average r...

A: We can find the instantaneous rate of change as below

Q: if 2 and gcx) -X and h =1-2X %3D Find, fog fog, gof, gog, gofoh, fof > fof .

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Q: 1. Using tables of values, determine the limits of the following. (i) lim (x° + 1) x→1 (i) lim(1 – a...

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Q: Find the parametric equations for the tangent line to the curve x=t^2−1,y=t^4+1,z=t^4 at the point (...

A: Given: x=t2-1, y=t4+1, z=t4 Point 8, 82, 81, is for t=3 as you can see substituting it in the three ...

Q: dy 2у _ (x+2)² 9. dx'x -4 r² – 4 +

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Q: Given that f(4) = -8 and f'(4) = –6 , find an equation for the tangent line to the graph of y = f(x)...

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Q: Consider the surface given by the equation z - y = x2. Draw a total of at least 3 traces in at least...

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Q: Find the open intervals on which the function f (x) = x + 6v4- r is increasing or decreasing. If the...

A: Solved below

Q: Find the values of 'a' and 'b' that make the following piecewise function differentiable everywhere....

A: We have to find value of a and b for given Questions.

Q: The height (feet) of an object moving vertically is given by s = - 16t2 + 144t + 108, where t is in ...

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Q: sec?xdx Evaluate the given function ſ V1-4tanx a.글(1-4tanz) +c ·극(1-4tanx)i + C c.(V1 – 4tanx)' + C ...

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Q: Find the value of the line integral given below. (Give your answer correct to 2 decimal places. Hint...

A: Given: F(x,y)=yexy i+xexy j

Q: 9. y(x) = V + ti dt

A: Fundamental theorem of calculus 

Q: Consider the vector function r(t)=⟨t,t^2,t^4⟩ Compute r′(t)=⟨  ,  ,  ⟩ T(1)=⟨  ,  ,  ⟩ r′′(t)=⟨  ,  ...

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Q: Problem 1. Set 2x f (x) = | V16+ t+dt. (a) Show that f has an inverse. (b) Find (f-1)'(0).

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