P-3 Check whether function is even or odd and then expand the given function in an appropriate sine or cosine series a) -2

Q: Does e + z? have "fenetely mony gores in E explain.

A: Since you have posted a multiple question ,I will solve the first question  for you. To get…

Q: 1. Consider the harmonic series: a. Draw a graph of the function f(x)= ! on the domain [1, o). b. In…

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Q: For x ≥ 0, find functions f,g,h so that fogoh (x) = (2√ Oh(x)=x4, f(x) = 2x+x², g(x)=√x g(x)=x4,…

A: Given: The function is fx=8+x+tanxπ2. To find: The value of f-18.   Formula used: tan0=0

Q: Given, sequence of functions {f()} given by f₁ (~) = n for ^+ [0,1] and O otherwise

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Q: Sketch the graph of the parametric equations x = sint, y = 2 cos(3t), π ≤ t ≤ 27. Clearly label the…

A: We are to sketch the graph of the parametric equationsx = sint, y = 2 cos(3t), π < t < 2π.…

Q: Using Taylor Series, show that sinr can be approximated by x-x within 0.01 on the interval [-1, 1].

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Q: 5.) Ms. Cyrus has 64 songs on her phone. Two- fifths of the songs are R&B songs. The rest are jazz.…

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Q: If a function is of the type y = A sin(B(x - C)) - DMath output error and the amplitude is 3, there…

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Q: C) Use a known series to express f(x)= sin(x²) X as a Taylor series.

A: Given function is f(x)=sin(πx4)x As, we know  sin x = x-x33!+x55!-x77!+…

Q: Exaumple- Find the half pervodic Punetion which dé finition in rary expansion for the period as :.…

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Q: Find the Fourier series on the given interval f (x) = x?,-1 <x <1

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Q: Use series to evaluate lim X x-0 (D x 1 et - 2x x - sin x

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Q: the positive Let Ź ak canverge with term. ヒニイ In this casei examine E the character f series 1+ sin…

A: we have given the series converges with the positive term series . We have to determine whether the…

Q: Let (fn) be a sequence of real valued functions defined by cos(x) fn(2) = n By definition, show that…

A: Given  fn(x)=cos (x)n

Q: Power Series 1 f(x)=√√2 + x about x = 1

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Q: х Prove that 1 < < sin x for all x e (0,5). - ド|N

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Q: 10-9 8-7-6-5 -# -3 -2 -1 2345678 13. The intervals for which f "(x) < 0 are:

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Q: X Estimate the error if P3(x)=x- is used to estimate the value of sin x at x = 0.7. 6

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Q: (a) For f(x) defined on the interval (0, 2), graph the function to which the Fourier Cosine series…

A: Given that  in interval 0,2, we have to define a fx For cosine series, we will extend fx in…

Q: Using Maclaurin's theorem to show that 0 < 1/108. (ex=1)< <1

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Q: d) Sketch the graph of the function to which the Fourier cosine series con- verges on -6 ≤ x ≤ 6.…

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Q: Use series to evaluate the limits

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Q: ProveWithoutLopital or Series : eae sin(tan x)-tan(sin x) lim -0 2x cos(tan x)- 2x cos(sin x)+x 5…

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Q: 1. Given that n=0 power series which converges to (1-x)-2 on (-1, 1). converges to (1-x)-¹ on (-1,…

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Q: Sigma( 2+√k)÷((k+1)^3-1)check whether the given question is convergent or divergent by limit…

A: Given

Q: Apply the theorem: /Let (XN) be a sequence of positive real Numbers such that Li 2:= lim (XN+1/XN)…

A: Given sequences: (a): (b): (c): (d): where  and  satisfy We have to find the limit of the given…

Q: Question 6 Suppose that f(x)-e) for 4 <x. Determine the (b) P(2=X<5) (d) P(8 < X < 12) following:…

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Q: Which of the following is the domain set of the function f(x.y)= arccos(x² + y² - 3)+In(x² +y² -3) ?

A: In this question, we evaluate the domain of multivariable function and in second part we check the…