Exercise 11. iz Let f(z) and CR be the upper half circle with center (0,0) and radius R z5+1 taken in the counterclockwise direction, Then lim ſr f(z) dz is R00 CR a. 0 b. does not exist c. None of these

Q: 8. The rectangular function is defined by: A, (0) - {₁ T - sts Plot the following rectangular…

A: All the graphs are plotted below.Explanation:Here are the plots:

Q: sin'y 11) lim y--TT 1+cosy •TE1+cosy

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Q: 8.) Let fx)= 2x³+3x +4 Use the limif definition of the derivative to calculate the derivative of f:…

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Q: Pls help

A: We have to find the horizontal asymptote.

Q: a) Write down the definition of the derivative in terms of limits. Using this definition find (x² –…

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Q: (b) Sketch the graph of the function y = 1+ /16 – x²2 for -4 < x < 4. Hint: x2 + y? = 16 is the…

A: Consider the equation of the circle The graph can be plotted for the circle as

Q: Graph these parametric equations on the TI and include screenshots x = 2t – 2 sin t, y = 2 – 2 cos t…

A: In the Cartesian coordinate system, the parametric equations use a third variable(usually "t") to…

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Q: a) estimate fx (1,0) and fy (1,0), explain b) estimate fx (0,0) and fy (0,0), explain

A: The contour map of a function is given as follows, where the level curves are labelled by the…

Q: Evaluate using the result of Exercise 54

A: We use the half angle formula

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Q: Let y = f(x) be defined parametrically as y=t+tt, x = 2t -t, te R. Find f(x) and discuss its…

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Q: -3. 3) to the curve given by f(x) =

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Q: x² sin x (x, y) (0,0) x² + y² Determine whether lim exists.

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Q: 3. Prove properties (3) and (4) analytically, by making x = -t in the part of the Integral from -a…

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Q: |z²–1| 2 1) Use a tble of functional values to evaluate: lim I-1

A: The tables containing the functional values are very useful to approximate a limit. The tables are a…

Q: 1. a.) Use use the L’hospital rule lim(1+* dy b.) Use Devirative Rule to search dx from the equation…

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Q: tan(1 – x) limx→1 2 2x +x – 3,

A: Limit

Q: の3 Find lim メy <xiy)-s(0,01 x+y² along the curve y=x²

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Q: a- Find the limits of the functions below: 7x3 - limx→0 3-3x²-6x x+2 limx--2 Vx²+5-3

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

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Q: Give a pair of functions f: R →R and g : R →R such that g is not tangent to f at 0 and yet lim,0…

A: To give a pair of function f : ℝ→ℝ and g : ℝ→ℝ such that g is not tangent to f at 0 and yet limx→0…

Q: An swer the po llowrng lim f (x) xータ-2f 2. Im t(x) Inn

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Q: o let fon= (x-1)? +2; xzl a find f-(x),domain range b) confirm fof cigraph t Uning yix using…

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Q: Find lim R→∞ -R ex/6 e + 1 dx using the rectangular contour (explain in detail)

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Q: Let C1 be the curve r(x)= (x − lnx )i + (x +lnx )j, 1<=x<=e, and let C2 be the curve of y=et,…

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.