Write the first five terms of the sequence whose nth term is an = (-1)n/(n2).

Q: If sin x = siny = a and cosx = cosy = b, then cos(x-y) is Select one: O a. z2 + a² O b. 2b + 2a O C....

A: Given  sin x = sin y = acos x = cos y = b Use cos (x-y) formula cos(x-y)=cosx cos y + sinx sinysin x...

Q: What is the domain of ƒ1x2= logb x2? What is the range of ƒ1x2= logb x2?

A: Given: fx=logbx2 we know that domain of logx is x greater than zero similarly, domain of given funct...

Q: 3. P(x) is a polynomial of degree 6 with real coefficients and zeros x= 2 and x = 6i . The zero x = ...

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Q: A firm has an average cost function A(q)=125/q+q/16-4 where q is the firm's output. Determine the le...

A: Given,         A firm has an average cost function Aq=125q+q16-4; where q is the firm's output.

Q: a. Find the open intervals on which the function is increasing and those on which it is decreasing. ...

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Q: Find the power

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Q: Find the domain and the range of f. Find the range by finding the domain of f1. (Enter your answers ...

A: Follow the steps.

Q: Write the partial fraction decomposition of the rational expression (2x2 - 18x -12) / (x3 - 4x).

A:   The given rational expression is 2x2-18x-12x3-4x. Rewrite the given rational expression as follows...

Q: 3x2 − 2y2 + 18x + 8y + 13 = 0 directrix:

A: Given equation is 3x2-2y2+18x+8y+13=0. Given equation can  be written as: 3x2-2y2+18x+8y+13=03x2+18x...

Q: What is the probability of a family having five boys born in a row?

A:   What is the probability of a family having five boys born in a row?      

Q: The amount of carbon-14 present in a paint after t years is given by y yo e00KK12 The paint contains...

A: y=y0 e-0.00012t

Q: Assume the point (6,2) is on the graph of y=f(x). Determine the value of nn in the following situati...

A:   Assume the point (6,2) is on the graph of y=f(x). put x=6 and y=2 f(6)=2 We have to determine the ...

Q: 1. Determine whether each of the statements below is true or false. Circle the appropriate answer an...

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Q: dx +ズ12

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Q: In Exercises 11–28, calculate the derivative with respect to x of the other variable appearing in th...

A: Given Equation:                                              x2y+2x3y=x+y   To determine:           ...

Q: 99-100 - Inverse Functions from a Graph A graph of a func- tion f is given. Does f have an inverse? ...

A: Since you have posted multiple questions, we will answer the first question. If you want the remaini...

Q: Solve 2(x² + 3x)² – 5(x² + 3x) = %3!

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Q: Find the linear equation of the plane through the point (2, −2, 6) and with normal vector j+2k.

A: Explanation of the solution is given below...

Q: f(x+h) – f(x), Use the definition of the derivative (that is, f'(x) = lim h0 3 = 3r2. dr to show tha...

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Q: 18. Sx²Vx3 – 4 dx a) Let u =x^3-4 b) Find du c) Find dx d) Evaluate the integral (2/9)(x^3-4)^(3/2)+...

A: a) Let u=x3-4So, du=3x2dxor, dx=du3x2

Q: Calculus Question

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Q: Using trig. substitution. Please detailed prodecure. Thank you!

A: ∫13x2x2+9dx Put, x=3tanθ⇒1=3sec2θ·dθdx⇒dx=3sec2θ·dθ

Q: 2(-1)n - 1_3" 2"n3 n = 1

A: Given series is ∑n=1∞ -1n-13n2nn3. Consider an=-1n-13n2nn3. Then an+1=-1n+1-13n+12n+1n+13=-1n3n32n2n...

Q: 1. I'm planning to build a rectangular garden with a fence enclosing it. I have 56 feet of fencing. ...

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Q: In 2011, the population of a colony is 19000, and is decreasing exponentially at a rate of 6.3% per ...

A: Given  In 2011, Population = 19000 Decreasing at a a rate of 6.3% per year   

Q: True or false?

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Q: Find the interval convergence

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Q: I need help finding a number

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Q: The average cost per item to produce  q  items is given by           a(q)  = 0.3q2 -0.7 q + 11 for q...

A: Given,         The average cost per item to produce q items is given by            aq= 0.3q2-0.7q+11...

Q: Decide what values of the variable cannot possibly be solutions for the equation. Do not solve. %3D ...

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Q: ,determine the general solution to the given differential equation. Q. (D2+4D+4)(D−3)y =0

A: the given differential equation is: D2+4D+4D-3y=0 we have to find the general solution of the given ...

Q: Two polynomials P and D are given. Use either synthetic or long division to divide  P(x) by D(x), an...

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Q: C) It is given that f(x) = tan¯*(1 +x). 1 Find f(0) and f'(0), and show that f "(0) = 2 (i)

A: Given:                           f(x)=tan-1(1+x)   To determine:                            f(0) and...

Q: The rate of expenditure for maintenance of a particular machine is given by M'(x) = 12xx +5, where x...

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Q: i. Your friend claims you can use the change – of – base to write the expression (In x) as a common ...

A: Part (i) The equation to convert natural logarithm to common logarithm is, logx=lnx×log(2.718) This ...

Q: Describe a translation of the graph that will result in a function with (a) four distinct real zeros...

A: Solution:-  The given functions is  f(x)=x4-4x2for zeros put f(x) =0x4-4x2=0x2(x2-4)=0x=0; x=0;x=2; ...

Q: The function f(x) has its fifth derivative continuous on (−∞,∞). (a) If |f(5)| < 6 on the interva...

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Q: 11. A gardener with 1200 feet of fencing wants to enclosc a rectangular field and then divide it int...

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Q: Need help with finding the work required.

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Q: Write an equation of the line with the given properties. Your answer should be written in standard f...

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Q: f f(x) = sin¯' (x² – 2), what is f'(x)? o f'(z) = 2z o f'(z) = 2z V1-(2²-2)² o f'(z) = f'(x) 2z V1+(...

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Q: Write the first four terms of the sequence whose nth term, or general term, is given: an = 3n + 4

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Q: Write the equation that defines two differentiable functions?

A: The functions which are differentiable in the defined limits are said to be a differentiable functio...

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.