Determine whether the alternating series converges. k +1 E(- 1)*+1. 6k + 1 k=1 O The series converges. O The series diverges.

Q: sin³ydy |1+ cosy The is equal to 1 A.cosy +, cos²y+C 1 B. –cosy +, cos²y + C 1 C.-cosy -, cos²y + C ...

A: ∫ sin3(y)dy/(1+cos(y)) here put the value sin2(y) = 1-cos2(y)           = (1+cosy)(1-cosy) put this ...

Q: _3. The equation of the tangent line to the function f(x)=-- at (-5,) is x-3 7. y = x- 25 1 25 4. Th...

A: Topic:- function and derivatives   

Q: Solve the systems of equation: Equation 1: x + 2y + 3zi = 20 + 5i; Equation 2: 5x - 3yi + 12z(1-2i) ...

A: I am attaching image so that you understand each and every step.

Q: Consider the region R bounded by the line = 42- 8x and the parabola y = 27 – x². %3D To find the vol...

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Q: Find the derivative of the function. y = (2x – 8x²)3 %3D dy dx %3D

A: The given function,      y=2x4-8x23

Q: Find y' and y''. y = lnx + (7+x^2)^1/2

A: We can find y' and y'' as below

Q: V1+x2 dx 3. J 3.s

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Q: d²y = 5x? + 1 dx2

A: First we integrate both sides with respect to x and solve it. Follow 2nd step.

Q: 1. Given y = log3 9. The value of y= 2 2. If log(x + 2) = 4, then the value of a is 9998 1 3. If log...

A: Given problems:- 1. Given y = log3 9 The value of y 2. If log (x + 2) = 4 then the value of x 3.1f l...

Q: Consider f(r, y) = 3r² – 4y and U = cosa î + sin r î. Find the directional derivative of f in the di...

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Q: 75 ft A pole stands 75 feet tall. An angle 0 is formed when wires of various lengths of a feet are a...

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Q: Find an equation of the line that is tangent to f(x) = x and parallel to the line y = 3x + 1 (Hint: ...

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Q: A roasted turkey is taken from an oven when its temperature has reached 185 Fahrenheit and is placed...

A: Cooling

Q: For the function G(x) = 3 – x, find G(-6), G(u), and G(u) . G(-6) = (Simplify your answer.)

A: For the function Gx=3-x2, to find G-6, Gu, and Gu2.  

Q: 4 ース -where do es t have relahive minimums ? the relahi ve minimum is which occuRs at X= where does ...

A: topic- relative maximum and minimum of function  relative minimum is the value of function where fun...

Q: Qs: solve the follow ing differential equations %3D

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Q: 6. Graph the following piece-wise defined functions and state their domain and range: { -2.r for r <...

A: We have to draw the graph

Q: Evaluate [sec^2 (-1-0.1i)][tan(12-36i)]. Express your answer in rectangular form in 4 decimal places

A: The given expression is sec2-1-0.1itan12-36i. We have to find the rectangular form.  

Q: i da

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Q: 1. S[3 + tan(4x²)J²xdx

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Q: f (t) = t5 e(1-t)

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Q: ) Sketch the region of Integration and write an equivalent polar integral. Then evaluate the polar I...

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Q: 5 What is a. lim,-3 f(x) b. lim,-2 f(x) c. lim,0 f(x) d. lim,2+ f(x) e. lim,2 f(x)

A: To find the given limit values for the function using the give graph.

Q: Find a formula for the general term a, of the sequence, assuming that the pattern of the first few t...

A: Given query is to find the general term for the sequence.

Q: Evaluate the following integral * xVx + 1dx 5/2 (x+1)^(2/5) +2/3 (x+1)^(3/2)+c O 2/5 (x+1)^(5/2) + 2...

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Q: 16. What is the derivative of f (x) = e8x+3? %3D a. f'(x) = e8 b. f'(x) = 3e8x c. f'(x) = 8e d. f'(x...

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Q: Pendulum Problem Calculate the speed of the pendulum with respect to the x axis. Show solution using...

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Q: Evaluate the following integrals. dr x²Vx² – 9 13

A: We put x= 3sec(u) and differentiate both sides with respect to u and find the value of the given int...

Q: MATRIX ALGEBRA Find all solutions to the system of equations below, making use of the inverse matrix...

A: First we find inverse. 

Q: yln" (I+ y?) dy I+ y2

A: Given:  Let I=∫y ln71+y21+y2 dy To Find: To evaluate the given integral.    

Q: A. List the first four terms of the infinite sequence with the given rule. 1. ап — п? — 4 2. аn 3 n?...

A: Please refer to the image below

Q: Determine the length of the curve y = In(cos r) betweenI = 0 and r = 1/4. (Hint: if you simplify the...

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Q: The graphs of y = 7, y = g(x) (solid) and y = f(x) (dashed) are shown; the graph is not drawn to sca...

A: Let's find. 

Q: Determine whether g(x) is continuous on the following intervals. 1. (-5, -3) g(x) 2. (-3, -1) 3. (1,...

A: Given :   g(x) is a function that is :

Q: Let a, = e8/n (a) Does the sequence {a,} converge or diverge? If it converges, find its limit. If it...

A: Given that an=e8n. A sequence an is said to be convergent if it has a limit when n tends to infinity...

Q: EF = (6x – 4y, z – 4x, y – 8z), then V × F = 0.

A: Topic:- application of derivatives

Q: 5. f(x) = 2x2 – x + 6 for all values of x

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Q: 5. xV16-9х2 5. J 16-9х dx XV

A:

Q: Find the nth Taylor polynomial for the function, centered at c. f(x) : 1 n = 4, c = 5 Pa(x) = %3D

A: A Taylor series is given by          f(x) = ∑k=0∞ fk(c)k!x-ck = f(c) + f'(c)1!(x-c) + f''(c)2!(x-c)2...

Q: 3. у %3D In(5 — е**) 4. x = et (cos 2t + 2 sin 2t)

A: Topic:-  derivatives 

Q: need

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Q: For what values of p is the set of ordered pairs {(1,3), (2p, 4),(4,p)} a one-to-one function? A p E...

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Q: PART A) A hyperbola with vertices at (0,5)and (0,-5) passes through the point (11,6). Draw this hy...

A: Find your answer below 

Q: The sin*3udu is equal to 3 А. — и + 1 - sinбu 12 1 -sinбu + 12 1 -sinбu + 12 1 -sin12u + C 96 1 sin1...

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Q: 2. Use the previous item to determine if the improper integ 2x – x3 d.x (x – 1)²(x² +1) 8∞ converges...

A: This is a problem of improper differential equation. First by partial fraction decomposition we will...

Q: .

A: Please refer to the image below

Q: a in togials Evaluate the tollowing ズ du

A: The given integral,                ∫0π41-uudu

Q: 4. Find (a) the gradient of f at P and (b) the rate of change of the function value in the direction...

A: This question is based on gradient of function.

Q: 2 4 -2 where is f'>o ? Vx in the interval where is f'<o? Vx in the interval キ

A: Explained below 

Q: Solve the differential equation (x² + 1)y – 2xy – 2x = 0 using the method of separation of variables...

A: