If the integer n > 1 has the prime factorization n = p' p establish the following: pr, use Problem 3 to ... (d) Eain dµ(d) = (1 – pi)(1 – p2) · · · (1 – p,).

Q: Determine the values of n and h required to approximate e²x sin² (3x) dx to within 10-4 using (a)…

A: Given the integral We need to find the values of n and h such that the error is within 10−4.(a) The…

Q: 2) Use the false position method to find a root of the equation ex + 2-x+ 2cos x = 6 in the interval…

A: Solution :_

Q: 2. Consider the equation 2x³ + 5x – 4 = 0, 0 < x< 1. i) Show that by using Newton's formula, the…

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Q: Show that 1 Σ (z – n)2 cosec² (z) 8.

A: As we all know the theorem which states that, For z∈ℂ\ πℤ 1sinz=∑n=-∞∞-1nz-nπ=1z+2z∑n=1∞-1nz2-n2π2…

Q: 1 s(s+1) 6) L'

A: Given: L-11ss+13

Q: If sin\theta =-(1)/(2) and 3\pi <\theta <(7\pi )/(2), then

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Q: Suppose that P(Xi = 1) =pi = 1-P(Xi = 0), i=1,2 If p1>=p2 , show that X1 >= X2.

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Q: 1. Find the smallest positive root of the equation x In x = 1 correct to the three decimal places by…

A: Firstly we solve given equation xlnx-1=0,  (a) Using method of false Position, And then we solve in…

Q: Show that L-1{ = (sin hat sin at) s4+4a4, 2а2

A: To find Inverse Laplace transform of ss4+4a4: write ss4+4a4 as  ss2+2a22-2as2 Then the denominator…

Q: 4.) x : 12 required:a) find the value of x if y = 1/2

A: Given, x=-112y142y-y214We need to find value of x when y = 12

Q: 1. Solve for P given P' = 6t√P √² +3 with P(1) = 25.

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Q: Q3) Choose the correct answer for the followings: i. if 0 = T/12, z = i + sin(60) then |z| =

A: We find absolute value of z

Q: 7. Show that I (A)(3)(2)("-") = 1 (2π)(m-1)/2 m

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Q: 1. D, [3x²y+In(xy²)] За + In(xg In(xy³)]

A: Given,

Q: 1. a. Let In = exp (nx) sin (exp (x)) dx. By making an appropriate substitution, or otherwise,…

A:

Q: . Find the real coefficients a and b such that the function u = 4r +4r'y+ar y² -4ry+by is harmonic…

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Q: If y = ((5z² + 8z)³ – 5-)°, then dy/dr is:

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Q: If the nth partial sum of a series > an is n = 1 n - 7 Sn n + 7 find a, and > an n = 1 1 a1 = 4 14…

A: When you put n = 1 in an That will be incorrect as it states that for n ≠ 1 that's why your answer…

Q: 5. 1/2 cos² Itsin -dx ANSWER: л/2-1

A:

Q: Show that in (5.2) the average values of sin mr sin nx and of cos mI cOs na, m+ n, are zero (over a…

A: Given problem is :

Q: 5. Find dy dx of √xy + 2x = √√√y

A: Topic = Derivative

Q: 2. L{sin² = nt} 7² a. S³+π²s π² b. 772 2s3-2π²s π² C. 772 2s3+2π²s π² d. S³-π²S

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Q: 16. There is a very quick way to compute £-, 2'(-1)ª-' (); do use it. l=D0

A: Introduction: The binomial theorem is very important in mathematics. For any real numbers a,b with…

Q: 7. The square of the distance from a point on the curve y = In(x) to the origin is given as S=+ (In…

A: Let's find.

Q: Ex: the function f(x) = 2 * sin(x) = 2/4-1 is Zero for two values near x=-5. use bisection to find…

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Q: 14. Find four solution of z=3-4i to three decimal places

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Q: 1. Using a Venn diagram or otherwise, given that P(A'^B) = ½², P(B) = ³½³ and P(A' ^ B') = 3/3 3 5 1…

A: The given data is as follows: