Determine whether the series converges, and if so find its sum. 4k+2 7k-1 k=1

Q: Question 2 12x +1 dxp. (2x- 1)2 (3x + 2)² Evaluate:

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Q: 3. S(x) = (x²/3 – 1)²

A: Given that fx=x23-12c. if f'x>0 then function is increasing.if f'x<0 then function is decreasi...

Q: The diagram below shows points P, Q and R. The coordinates of the points are given by P (2), Q(5, 6)...

A: The objective of the question is determine the equation of line .

Q: Consider the function f :R →R given by f (x, y) = e* In(1+ y) Find Vf. What is the rate of change of...

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Q: Given: / 5x2 tan(3x³) dx. Ifu=3x°, then the resulting integral is Jf(u) A B none of the choices 5 18...

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Q: x2 dx. Which of the following options is correct? Consider 9+x6 A) Arctan + lim - Arctan lim 9. w- 0...

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Q: What is the horizontal shift? y= 2 tan X-180 +3 O 180 degrees O360 degrees O 45 degrees 540 degrees

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Q: 8. What is de x2+1

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Q: 12x +1 dx. (2x- 1)2 (3x+2)? Evaluate: 1 (A (2x- 1)2 (3x +2)² +C B (2x- 1)3 (3x + 2)3 3 + C ⓒ In l(2x...

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Q: 2. Use the Intermediate Value Theorem to show that 2.x - 3 if – 3 0 has a zero on the interval [-2, ...

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Q: / 5x? tun(3x) dx. If u= 3x³, then the resulting integral is Jf(u) du. Find f Given: 5/2 A 18 B none ...

A: This question can be solved using the concept of substitution as used in integration.

Q: x²dx S: 1. 4 – 3 x' dy 2. V16 + y²

A: Let I=∫x24-x2dxI=∫x222-x2dxPut x=2sinudifferentiate dx=2cosu.duI=∫22sin2u22-22sin2u2cosu.duI=∫4sin2u...

Q: Is the series divergent or convergent? Show solution and explanation. +oo In n E(-1)": n2 n=2

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Q: 2) y'+2xy = 0

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Q: sing u-substitution, the integral Jf(x)dx reduces to a new integral J glu) du. If g(u) = , evaluate ...

A: Topic:- application of integration

Q: For x, y > 0, the function f is given by ƒ (x, y)=2In| Find the partial 1. derivatives f, and f..

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Q: Please see the attached image to see the given. thank you  (a.) the critical numbers of f (b.) all ...

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Q: rectangular prism with dimensions 6 m × 4 m × 8 m (l×w ×h) is shrinking. a)  Assume that the length...

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Q: The graph shown below is f(x) = x2. If g(x) = f(t)d t, find g(3). AY 8 6+ 21 X 4 O g(3) = 9 O g(3) =...

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Q: The graph shown is f (x) = sin x. If g (x) = / f (t)dt, find g' (7). %3D AY 6.28 -3.14 3.14 6/28 -2 ...

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Q: f(x) = 3√3x^2 + x + 1  take note: fuction of x is cube root of 3x^2 + x + 1 (a.) the critical numb...

A: As per bartleby guidelines we only give first three suparts  question answer.

Q: Consider the following sequence: 5" {an} = n=1 An+1 Use the ratio to show that the given sequence {a...

A: Given sequence an=5n2n2n=1+∞

Q: Classify the series as absolutely convergent, conditionally convergent, or divergent. 00 k+1 Σ (2k –...

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Q: 6 du Consider dx. Transforming the integrand, the result will be where k is a constant. What is u an...

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Q: 1. Consider the relation R1: R2 - R such that (r1, y1)R1 (x2, y2) if and only if both points are on ...

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Q: Use sigma notation to write the Taylor series about z = 1, for the function. 3 In z; z9 = 1 k =

A: The given function is 3ln(x);x0=1.

Q: 7 1 Calculate the following limit. Let an = Vn + In (n) and bn Vn (Give an exact answer. Use symboli...

A: Let's find. 

Q: EC an

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Q: When the numerator has a higher degree than the denominator, we have to start with long division. Af...

A: It will be covered in step 2.

Q: uestion 9 x2 dx. Which of the following options is correct? 00 onsider 9+x6 (A Arctan 3 + lim Arctan...

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Q: The number of yeast cells in a laboratory culture increases rapidly initially but levels off eventua...

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Q: Is the series convergent or divergent? Prove in no more than two sentences. +oo - n T1-n n=1

A: ∑n=1∞ (πnπ-1n3)(series with increasing terms)limn→∞(πnπ-1n3) =∞-0  =∞   

Q: 2. Find the indicated limits of the following algebraic and trigonometric functions: x' -1 а. lim. -...

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Q: Solve the following ODE. y" + 2y" – y- 2y = 9 - 123 NOTE: Write arbitrary constants as c1, Cg, and c...

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Q: II. Determine the derivative of the ff. logarithmic functions 1. y = 25 In 5x 2. y = -10 In 3x4 3. у...

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Q: 1. Find the tangent to the curve given by the parametric equations: X = 1/t; y= VE e-t

A: Appliaction of derivative problem  

Q: Why is there a need to solve for integrating factors?

A: We solve easily by using integrating factors. 

Q: Inz Let U = ry ,x= Vst, y = s? - 1². Use the chain rule to find when s = 1, as 4. -. t = 2.

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Q: Solve the equations: 8х - 2у - 13 -2x +5y- 8.

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

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Q: Question 5 5 Given: dx. Using u-substitution and transformation of integrand, what is u and du? 3/x ...

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Q: dx The integral can be re-written as (A) (2-2 V1-m ) lim m- 00 B none of the choices lim (-2+2 /1-m ...

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Q: sin(In x) In(sin x)" Use Squeeze Theorem to evaluate lim

A: limx→ 0+sinlnxlnsinx

Q: x'- 36 lim 16 x+6 (a) Vx+11-4 lim- (b) х -5 (c) lim- +2 2-x

A: Since the student has posted many sub-parts of the question and does not mention any specific part, ...

Q: d) If the coefficients are rounded off of 0.31x + 2.73 find the absolute and relative in y x + 0,35 ...

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Q: 7. What is dx (x six(x)?

A: Since you have asked multiple questions in a single request we would be answering only the first (7t...

Q: 2. (a) Prove the following inequality n(n- 1) ,2, 120 (1+ 1)" 2 1+ nz + 2 for any n 2 1. (b) Show th...

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Q: f(x)= (x-2)/(x^2-x+1)^2the intervals on which f is increasing or decreasing (d.) the intervals on wh...

A: Given functionfx=x-2x2-x+12We will answer sub-part c, d and e(c) the intervals on which f is increas...

Q: Find the nth Taylor polynomial for the function, centered at c. f(x) = In(x), n = 4, c = 4 %3D P4(x)...

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Q: Use the formula for the binomial series: (1 + x)" = 1+mx+ + 21 = 1+ £in to obtain the Maclaurin seri...

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