A. Sequences 1. Given that a2 = 6 and a6 = 96 are terms of a geometric sequence, find a4. 2. Given that a10 = 78 and a25 = 198 are terms of an arithmetic sequence, find an. 3. 6, 10, 16, 24,... Find the explicit formula for an, where n ≥ 1. -2 1 4 7 4. Find an, where n ≥ 1. 5 10 15 20 5. 5, 8, 17, 44, 125,...Find the recurrence formula for an, where n ≥ 1.

Q: (a) Find the quadratic approximation P2 for f (x) = In x at x = 2 (b) Use above to approximate…

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Q: Find the length (magnitude) of a function gradient z(x,y)=√√2+sin(x²)— y² at the point P(√, 1).…

A: The gradient of a function is a vector that points in the direction of the greatest rate of increase…

Q: 50.) Show how to use a line integral to find the area of a circular disk of radius r

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Q: Find the exact values of x and r. (x, r) = 30 30° X

A: Given:  We are given with right angle triangle with 30o   and one side is 30  To find the other two…

Q: 46.) (a) Parameterize S the 1st octant portion of the cylinder y² + z² = 9, 0 <x<4 (b) Use above to…

A: y2+z2  0≤x≤4x=uy=3 cos vz=3 sin vparameterise the surface ass(u,v)=(u   3 cos v   3 sin v)0≤u≤4,…

Q: Consider the solid that is bounded above by x² + y? + z? = 169 and below by z=5. %3D

A: In this question, we have to write the triple integral to find the volume of the solid bounded by…

Q: Attached.

A: To prove the statement,

Q: Evaluate ſſ, Vy² – x² dA where boundary of R is the parallelogram bounded by the four lines

A: In this question, we evaluate the double integral by using the change of variable. The region is…

Q: 4. Let C denote the circle |z – 2i| = 1, taken in the usual counterclockwise orientation. Compute by…

A: Given: Let C  denote the circle z-2i=1 z-2i=1x+iy-2i=1x+iy-2=1 So, Centre of circle will be 0,2 and…

Q: 100 3 7+12 +3 4 D 56 : 8 +3 · 5 · 2-4 5%3D 200 : 25 +8 · 9+6.6%3D %3D

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Q: Does the sequence {an} converge or diverge? Find the limit if the sequence is convergent. a, = 1 +-

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Q: (a) Find the differential dy. y = cos(x)

A: Differentiate the given function with respect to 'x' and find 'dy'.

Q: 39.) Show how to find the surface area of f(x,y) = xy that lies over the unit circle.

A: A detailed solution is given below.

Q: 1 f(2): 1 3 Find a Taylor series for f which is convergent in |2 – 1| < 1.

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Q: e radian measure of the central angle. radians 70 56

A: Arc  S = r.theta        56 = 70(theta)       Theta = 56/70                  = 0.8 radian

Q: 5. Find the Laurent series about zo = 0 for 1 f(2) = e² + 1 2 that is valid in the region |z| > 2.

A: Given that f(z)=ez+1z-2+1z The Laurent series expansion is…

Q: 3.1 Terminology 1. Probability is a measure of the chance (likelyhood) of certain results (outcomes)…

A: Probability gives the measure of the chance of happening an event. Fill the incomplete blanks.

Q: Find f. F"(x) = 20x³ + 12x²+ 4, f0) = 4, ( 1) = -1 Ax) =

A: Let us denote y = f(x). So,…

Q: if A nd B are mutunlly ex clusine, P, 3 and ecrs) = 0.47 find D PCA nB) E) PC Ano). P CA

A: GivenA and B are mutually exclusiveP(A)=0.3P(B)=0.47

Q: 7. Suppose yo 70 is fixed. Find a geometric description of 1 {u+ € R} + iv :x x + iyo that is, the…

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