Sultan Qaboos University Compute the Values Algebra Questions

First one: The value is 3

Second one: The value is 4

Q4 Using appropriate Tests, check the convergence of the series,
∞
1
Σ {³P + 1² P + ( +/+
n²p
n=1
Q5 If Ø(z) = y + ja represents the complex potential for an electric field and
a = p² +
+ (x+y)(x−y), determine the function(z)?
Q6
(x+y)²-2xy
n`
-(1/1/2+₁1) -2²7)
Find the image of |z + pi + 2p| = 4 under the mapping w =
= p√2 (e¹) z.
Q7 Find the first three terms of Taylor series for F(x) = Sin(pâx) + ex-P, about
x = p, and use it to approximate F(2p)
Q8 Find the first three terms of Maclaurin series for
F(x) = In (x+3)(x+3)²
[15]
[10]
[10]
[15]
[10]Q1 Find a formula for the nth partial sum of this Telescoping series and use it to
determine whether the series converges or diverges.
Q3
∞
n=1
Q2 Using the Integral Test, check the convergence of the given series by verifying [15]
the necessary conditions of integral test.
∞
Σ
∞
(pn)-²
2 3
+=+1
n=1
n=1 n² n
pn
Using the Ratio test, determine whether the series converges or diverges :
[Sin²p+n²+ cos² p]
P√n
(³√n²+1)
[15]
P√√(2n)!
[10]