Find the exact value of the expression. sin sin 16 CoS Cos 16 16 16

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

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

Q: You want to find the average value of z = 4x²y over region bounded by y = x´ and x + y = 6. Set up…

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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: (More problems in Problem Set 9.4.) Is the given set, taken with the usual addition and scalar…

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

A: Let us denote y = f(x). So,…

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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Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.