Let C = C₁ U C₂ U C3, where C₁ is the line segment from (-1, -1) to (0, 0), C₂ is the line segment from (0, 0) to (-1, 1), and C3 is the portion of the circle x² + y² = 2 from (-1, 1) to (-1,-1) traced counterclockwise.

Q: The graph of a function is given. -4 -2 X I 4 2 -21 -4 2 4 (a) Determine the interval(s) on which…

A: We can find the answer as below.

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Q: Evaluate t

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A: Given hyperbola, Centre (h,k)= (0,7) Vertex = (0,4) Foci = (0,2)

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Q: = 5. Prove the identity: cot(A + B) cot(A − B) = cot² B tan² A tan² A cot² B-1

A: To prove cotA+BcotA-B=cot2B-tan2Atan2Acot2B-1

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A: Given that the decay rate for a radioactive isotope is 1.6% per year.Our Aim is to find the…

Q: 7. Solve for cot NI 2 if cos(20) = |L0 5 and P(0) E QIV.

A: Given: cos2θ=-45 To find: cotθ2

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A: Topic:- function

Q: If y = 3u² + 2u and u = √² +5, fip S da would be: (6√2²+5+2)(√) (6 (3u² +2u) + 2)(√5) ○(3√2²+5+1)(√)…

A: We can find the derivative as below.

Q: Find the Fourier series for the following functions: f(t) = |sin t], -1 < t < n

A: To find the Fourierseries for the following functions.ft=sin t, -π&lt;t&lt;π

Q: What is the explicit equation for the nth term of the arithmetic sequence 6, 3.5, 1,-1.5, 4,...?…

A: We have: a1=6 -- the first term   Next, we calculate the common difference d=a2-a1 So, we have:…

Q: 2 8 X2 x4 + x2 dx

A: To solve the given integral.

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A: This question can be solved using the concept of fundamental theorem of calculus part 2 according to…

Q: Given the functions f(x)=√x² + 49 and g(x) = x4 fog would be equal to? O√x +49 O√x¹ +49 Ogof (x²…

A: The given functions are fx=x2+49 and gx=x4

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Q: Consider points P(-1, 3), Q(1, 5), and R(-3, 9). (a) Determine vector 2PQ- 2PR and express it in…

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Q: fa¹e² da dx: Applying the integration by parts technique, let Consider the integral Ա 4 X dv = ex x¹…

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Q: Find the Fourier series for the following functions: {3¹ f(x) -2≤x≤0 0≤x≤2

A: Given functionf(x)=-1     if   -2≤x≤03        if       0≤x≤2

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A: According to bartleby guidelines when student post more than one question then expert must have to…

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Q: III. Consider the power series +∞ n(3x + 2)n n³ +4 n=1 -1. 1. Show that the series is absolutely…

A: Given power series is ∑n=1∞n(3x+2)nn3+4 When x=1, the series becomes…

Q: 3. Find the domain of f(x) = = 1 1 X X 3.3

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Q: 8. Find dy/dx- y = sin (1 + x^2/1-x^2)

A: Topic = Derivative

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A: Question: (a) Find an exponential model for the number of bacteria in the culture after t hours. (b)…

Q: -5 0x2 0<x<2 2 Over what interval is f(x) concave down? Ox<0 y=f" (x) 5

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Q: Find the antiderivative F(x) that satisfies the given condition: f(x) = 4x² +5e"; F(0) = -2. Show…

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Q: Which of the following is a type of inequality sign? > ≥ and ≤ < All of the answers are correct.

A: We know that, In mathematics, the relationship between two values that are not equal is defined by…

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Q: Determine the equation of the normal line to f(x) = x³3.5¯³x at x = -1.

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Q: On Integration of Rational Fractions. Distinct linear factors Repeated linear factors 1² +2 x² +2…

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Q: 4. S dy y³-2y²

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Q: Given f(x)=√x + 2 and g(x)= x³, find ()(x) and write the domain of (x) in in interval notation.

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Q: What is the domain of the rational function(x)=-3x²-16x +48 Oxe 31x*-4,-2.3.4) Oxe 31x*-4, 3, 4) O…

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Q: 11) Find each of the two areas bounded by the curves y=x3-4x and y=x² + 2x Points of intersection:…

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Q: 2. Sketch the solution region of 2x − y − 1 > 0 (x − 5)² + (y + 1)² ≤ 25.

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Q: r³+3x+1 8) (x+1)²(x-2)²

A: The objective of the question is determine the partial fraction decomposition. Note -  As per our…

Q: 2ucot 2x

A: Please see the below picture for detailed solution.

Q: For the following graph the equations and shade the area of the region between the curves. Determine…

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Q: D O O O 59 2 04 Question 16 Evaluate lim N-00 12 01 3|2 • Σ [()* - (-)] ++ N by using it as a…

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Q: 25. The vector field F(x, y, z) = (2xy + tan x)i + (x²-√y² - 1)j is conservative. a) True b) False

A: To determine whether the following statement is True or False.The vector field F→x, y, z=2xy+tan…

Q: Consider the integral fa³ In(a) dæ: Applying the integration by parts technique, let In(x) Ա dv = x3…

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Q: A function is given below. Determine the average rate of change of the function between t = 6 and t…

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Q: 8 1 4-x² 4 x¹ +4.x² dx

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Q: I = [x² -√3 Jo √3-1² z²+y² 2-√4-x²-y² 2y dz dy dx

A: Here we have to use cylindrical coordinates.

Q: This equation is an example of which one of the following? Ax + By > C A two-variable inequality…

A: Since , x and y are variables , therefore given inequality is a  Two - variable inequality. Option…

Q: s) Given the piecewise function below, find h(-5) and h(-4). if x < -4 h(x) = { 6x - 7 √x+8 ifx ≥-4…

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