1. Determine the domain and range of the following functions: (Note that each square is 1 square unit) Domain: Range: Domain: Range:

Q: (3) Find the radius of convergence of a) infinite b) 1 not defined 0 infinite X Σ₁ F

A: The given series is: ∑j=1∞xjj2 Let, aj=xjj2; j≥1

Q: 3) Find the divergence and curl of f3xi+ 5x} j + 2y²k, at the point (1,2,3)

A: Solution is done in step 2

Q: Find point D where D is a point on AB where AD 1 CD. Then compute A = |AB||CD||

A: See the details solution in below

Q: 393. lim x → xl/x 0+

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Q: 1. Find the following limits proving whether they exist or do not exist y² sin x X E) F) lim (x, y)…

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Q: The probability a machine has a lifespan of more than 5 years is 0.8. Ten machines are chosen at…

A: This is a problem related to probability. Please follow the procedure given below.

Q: .. Find the constants a and b, such that the function is continuous on the entire number li 2, x≤ -1…

A: Topic:- calculus

Q: Find a plane containing the point (1, 3, 3) and the line of intersection of the planes - 2x - 3y -…

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Q: Express the following functions in the form U+iv f(Z) = ln (1+z) ●

A: The given function is fz=ln1+z.We need to write it in the form u+iv.

Q: The random variables A and B have variances 0.3 and 0.4 respectively. Let T= 5A-2B. The variance of…

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Q: 11. A = {a, e, i, o, u} 12. B = {2, 3, 5, 7, 11, 13, 17, 19, 23,... } 13. C = {1, 3, 5, 7, 9, 11,…

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Q: There is a ready polar formula for negative one (-1) and also a ready polar formula for negative i…

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Q: nts. The results of 120 parts are summarized as follows. Length Excellent Good 84 12 15 9 Surface…

A: We  are asked to find the probability that the length is not excellent.

Q: 2x²12-59 P₁ = (x, y) 2 y = 4x P₂=(x, y)

A: See the details solution in below

Q: The tortoise versus the hare: The speed of the hare is given by the sinusoidal function H(t) =…

A: The speed of the hare is : H(t)=cos(t) The speed of the tortoise is : T(t)=12t

Q: Make a table of values for the equation. y = 9- |x| X -4 -2 2 4 у Sketch a graph of the equation.

A: To make a table of values for the equation. y=9-x   x y -4   -2   0   2   4   To…

Q: The graph is a transformation of one of the basic functions. Find the equation that defines the…

A: We need to find equation.

Q: DUE NOW. Please answer all the script part as the same as the process on what's in the sample…

A: The objectives are: Now we have to make a script as the following;

Q: A. Find the limits of the function f(x,., -2 2 1. lim f(x)= x--1+ 2. lim f(x)= X-4- 3. lim f(x)= 4.…

A: The graph of the function is  To evaluate:  1. limx→1+fx2. limx→4-fx3. limx→4+fx4. limx→1-fx5.…

Q: Evaluate the difference quotient for the given function. Simplify your answer. f(x) = f(a) f(x) = —…

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Q: Find Domain and Range y=- ex-1 The domain is (-00,00) and range is (-00,0) The domain is (0,00) and…

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Q: Question Consider the region, R, bounded on the left by the line g(x) = x, on the right by the…

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Q: 5. lim -00 2-1 5

A: limx→-∞x2-x45

Q: Find the average value of the function over the given interval. (Round your answer to four decimal…

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Q: Q1:/Verify that the given function is harmonic and find it is harmonic conjugates so that f(z) = u +…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: 1. Find the limit if exists or show that the limit does not exist 1-cos(x+2y²) (x+2y2)2 (a) (b) lim…

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Q: Find the sum of the following geometric series: 3 Σ an=64n

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Q: Solve

A: We have to find the value of the given following conditions according to the given information

Q: Q3: Solve the differential equation subjected to the condition y(e)=e² and give the result in…

A: Let's solve given differential equation.

Q: Find the roots of Z₁ + 1 = 0 Hint i = 1/2 e

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Q: Two cars travel toward each other from cities that are 427 miles apart at rates of 64 mph and 58…

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Q: Find the equation of the tangent line to the space curve r(t) = 2cos (t)i + 2 sin(t)j + tk at the…

A: The curve is given by: r(t)=2cos(t)i+2sin(t)j+tk

Q: If y = arctan (4x² + 4x + 5), dy dx

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Q: 5πT 4 Convert the angle from radians to degrees: 5πT 4 O

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Q: 22 e 1-§ 2(2-21) ² c: |z_11 = 1/2, 17-11-2

A: The given integral I=∮Ce2zzz-2i2   ;  C=z-i=12, z-i=2 Cauchy integral formula:   suppose that C is…

Q: (c) If b = 1, what is the range of this function? (Enter your answer using interval notation.)

A: Topic = Function

Q: . Test the equation for symmetry. (Select all that apply.) y = 7x4 + 2x2 a. The graph is symmetric…

A: Topic = Function As per guidelines , At a time only one question with three sub-parts can be…

Q: Wrong answer

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Q: Find the missing element in the sample space S = {x|x³x² - 17x - 15 = 0} where S = {-3,-1,__}.

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Q: Solve the homogenous diff equation of; y' = y sec x

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Q: Extra Problem 1 The table gives values of a continuous function. Use the midpoint rule (n = 3) to…

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Q: 4. Perform the indicated operations. Use principal arguments throughout. (a) [22(x/3)].[32(x/2)] (b)…

A: (a) We have to evaluate 2∠π3.3∠π2

Q: Let Fib(n) be the nth term of the Fibonacci sequence with Fib(2)= 1, Fib(3) =1, Fib (4)=3 and so on,…

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Q: 380. lim (x + 1) ¹/x x → 0

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Q: 1. If y=tanx, prove that y=2(y² +1)(3y² +1).

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Q: Please find attached

A: To sketch the graph of the equation given.

Q: If you count from 1 to 100, how many 7's will you find along the way? Answer in numeric format only.

A: if you count from 1 to100,how many 7's will you find along the away?

Q: [ 0 y-y² y-y² (y - y² - x²) dxdy

A: Given equation: ∫01∫-y-y2y-y2(y-y2-x2) dx dy

Q: Function 1 t h(t) = sin t+=e 5 Point πT 1 I, -e 5 (a) Find an equation of the tangent line to the…

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Q: The probability distribution for the random variable, x, is x:2, 2.5,3.0,3.5,4.0 ,4.5 and P(x):0.07,…

A: This is a problem related to probability distribution function. Please follow the procedure given…