Determine X(S) expressed as a rational polynomial with simplified numerator and factored denominator a. x(t) = {t2 +2e-2t + sin(3t)} u(t)

Q: 1. Find the domain of the vector function r(t) =

A: 1. Given Vector Function,rt = lnt+2, t1-t2, 2tt2 -4

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A: To determine whether the following statement is True or False.limx, y→0, 0 2x2 sin x+3y33x3+2y2if we…

Q: 12. If eie + 1 = 0, what is 0? A. 0 B. π 2 C. T D. 2π E none of the above

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A: Here we have to solve the integral.

Q: 4. If z = x + iy = (x, y) then the Re(iz) A. Imz B.-Rez C. -Imz D. Rez E. none of the above

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Q: Question 1 f(x, y) = 4xy 2x²+5y² Consider the function a)!* s Find the domain of f. b) [₁ Show that…

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Q: Find lim PHEL x² + 100-10

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Q: 10. Given the complex function 1+z z² Evaluate f (₁¹) A. 1 + 3i f(z) = B.-1-3i = C. 1-3i D. -1 + 3i…

A: Given that a complex function - f(z) = (1+z)/z. And we find f(1/(1-i)). Here i = "iota" that is an…

Q: If p = (7, 2), then find -2p.

A: If p=7, 2, then to find -2p.

Q: Use the First Fundamental Theorem of Calculus to find F"(x) if = [*_ sinh√/1 +ť² dt. F(x) =

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Q: Consider the following all-integer linear program. Max 1x1 + 1x2 s.t. 5x1 + 7x2 ≤ 37 1x1 + 6x2 24…

A: As per the instruction, we will be answering the first one. Kindly post again for others. Given:

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A: The solution is given below

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Q: and x = = z = e-22 In (2-y), Select one: O True O False - 6t, y = t-s, then the value of 3 is equal…

A: In this question we have to find whether the given statement is True of False.z=e-2x…

Q: Work problem 2 (1 Let w(x, y) = 5x - 5y - x² + 5y³, x = cos(t) and y = -sin(3s). Use chain rule to…

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Q: Question 1 function r(t) = (tª In 1, ¹2³, −3e¯³¹). a) Find the integral r(t)dt. b) Find parametric…

A: Here, r(t)=t4ln t, t-32,-3e-3t

Q: 2. y²dx + (x² − xy - y²)dy = 0 [Answer: (x - y)y² = c(x + y)]

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Q: cose 00 2r sin 0 dr de

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Q: π/4 [sin (√x) dx 0

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Q: π sin" g 2. So cos² g dg

A: The given integral is;  Sin5g/Cos2g, limit from 0 to pi.

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Q: A y=1 x=y² B y=x² C (1, 1) X=1 X (0,0) Region A is bounded by the parabola x = y², the line y = 1,…

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Q: 1 √√1/₂ 1/² y+4 y² + y fip C

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Q: give an example of derivative

A: We have to give an example of derivative

Q: 1. Let f(x, y) = y³ + x³ - 2/1y²-3x+30y. (a) Find all the critical points of f. (b) Determine…

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Q: r(t) = (−2 cos (2t), 3 sin (3t), In (2t)), then the fr(t)dt is equal to 3 Cos cos 4 where C is a…

A: Given:    rt=-2cos2t,3sin3t,ln2t then  ∫rt dt =∫-2cos2t,3sin3t,ln2tdt…

Q: 4. Evaluate (²52³Vl-Pax

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Q: Choose the correct answer for the following limit: Select one: Ο Α. 0 O B. Does not exist. OC. None…

A: According to question,Given Limit,Let l = limx, y→0, 0x3 + 6y25x3 + y2

Q: Region R is bounded by the graphs of C₁ : x = y + 1 and C₂: x = 3 - y² as shown in the graph below.…

A: Given: Region R is  bounded by the graph x=y+1 and x=3-y2 as shown in question. USE: cylinders…

Q: Which of the following theorems does not require the differentiability of the given function? a.…

A: We can check in which theorem , the condition of differentiability of the given function does not…

Q: If and x = 2t, y = 5t, then the value of equal to 12. z = x - 2y, Select one: O True O False dz dt…

A: Given that , z=x-2y and x=2t , y=5t find dzdt at t=3.

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Q: The area bounded by the x-axis, y = x², and y = 2 - x.

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Q: If f(x, y) = √6xy - 4x + 30y then fa = Select one: O True O False -4√6xy+3y √6xy

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Q: Find the general solution of the following differential equation. y” + 5y′ − 14y = 0 NOTE: Use c₁…

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Q: If In (x² - y) -x+y+1 then the domain D of the function f is given by the set Select one: f(x, y) =…

A: Given function:- f(x,y)=lnx2-y-x+y+1  find domain of f(x,y)

Q: What is the value of the derivative of f(x) = (x-2)(x² +1)³ est x=1?

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Q: 2 2 If z = f(x, y), where x = s² - t² and y = t² s² and z is differentiable, then - Select one: True…

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Q: Using Linear Approximation, estimate Af for a change in x from x = a to x = b. f(x) = ln (x), a = 1,…

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Q: Question af If f(x, y) = xy² - x ln(y) find Ət if x(t, s) = s² - st³ and y(t, s) = e-st²

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Q: r(t) = (−2√√ť² – 4, 3 sin (4t), 3 ln (−5 – 2t)), then the domain of r is given by the interval…

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Q: Evaluate et +2e2t-et e2t +1 dt.

A: Given that a integration problem and we solve this problem by using general property of integration.…

Q: Which of the following is the partial derivative with respect to x of the function f(x, y)= 4xy + 7x…

A: Given problem:- f(x, y) =4xy+7x+6y-ln(9xy)   To find :- fx(x, y)

Q: 18. If A = 6 a. d. 14 5 0 10 10 1 14 0 01 7 0 b. 0 11 16 C. 8 9 12 14 3577 NOV00 7 572 7 6 7 1 2 61…

A: In this question we have to multiply Matrix.

Q: Find the horizontal asymptote(s), if any, of the curve f(x) = (x-x+) -16 Select one: Ⓒ x = 4, x=-4 O…

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