π Find the area of the region enclosed by y = sin¯¹(x), y = and the y-axis without using integration 4' by parts.

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: 4. Identify the focus of A. (0,3) -(y - 3)² = (x-2). B. (4,3) C. (2,1) D. (2,5)

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Q: Wants to know what will be the Maclaren series of g(x) = sin(x) is ?

A: Maclaurin series of function fx is a Taylor series of function fx at: a=0…

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A: The given trigonometric function is f(x)=sin3π2-x

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Q: Evaluate

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Q: Consider the two-dimensional vectors a and b. a = (3,-1), b = (-5, 0). (a) Find the measure of the…

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Q: The base of the solid is the triangle enclosed by x + y = 11, the x-axis, and the y-axis. The cross…

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Q: 21. Find div(F), where F(x, y, z) = xyzªi+x²zªj +4x²yz³k. a) -4xyz³+xz4 b) x²y+xz4 c) yz + 3x²yz² d)…

A: Topic = Algebra Correct option = d

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 2x log 2x dx

A:

Q: Question 6 Find the limit, if it exists. lim (e²r + x) = 1-0+ 01 O e² 0 3 02

A: Given    limx->0+{e^(2x)+x}/(1/x)

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Q: Let y(x)=−3/x^2. Find y′(−3). Enter the exact value, i.e., no decimals

A: given  y(x)=-3x2=-3x-2

Q: Consider points P(-1, 3), Q(1, 5), and R(-2, 8). (a) Determine vector PQ and express it in component…

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Q: If what does the following integral equal? - 14 73 [6f(x) + 3g(x) - h(x)]dx = - 14 f(x) dx = 11 and…

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Q: Given the function graphed below, evaluate the definite integrals. -1 4 3 2 1 1 -1 -2 -3 -4+ […

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Q: Determine if the series  ∞ (−1)n − 1e8/n n = 1  converges by the Alternating Series Test. If the…

A: We have to test to determine if the series converges or diverges.

Q: The function h is defined below. h(x) = Find all values of x that are NOT in the domain of h. If…

A: Given function is h(x)=x-5x2-6x+8 We have to find all the values which will not be part of the…

Q: Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of the…

A: PLEASE LIKE .

Q: Consider the region bounded by x=4-1², the y-axis and the x-axis. N 1 1 2 3 4 The volume of the…

A: Given problem:-

Q: 17 0 dx √|x-1|

A: The objective of the question is evaluate the definite integral.

Q: Onsider the function f(x) = -4x²+7x+6. Interpret the e average rate of change from x = -7 to x = 7…

A: Topic:- application of calculus        Definition :-  The tangent represents the instantaneous rate…

Q: D O O Question 8 Evaluate the limit limo 04 0 2 00 0/1/201 3 tan (+h)-tan (3) h by recognizing it as…

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Q: 2. S (x+1)dx x²(x-1)

A: We can find the answer in the following steps.

Q: Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of the…

A: Please see the below picture for detailed solution.

Q: The slope of the tangent line to √x+y+√√xy = 2y at the point (2,2) is:

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Q: 2 8 X2 x4 + x2 dx

A: To solve the given integral.

Q: By an appropriate trigonometric substitution, Choices: √ √10 sin sin 0 cos de cos √10 sin 0 1 /10…

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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

Q: 5) Integrate 2x cos (x²-5) with respect to x.

A:

Q: Find the volume of the solid generated by revolving the shaded region about the given axis.

A: We need to find volume.

Q: Let an 4n 7n + 1 (a) Determine whether {a} is convergent. convergent divergent = 8 (b) Determine…

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Q: Which linear equation has the solutions (2, 4) and (-2, 6)? y = 2x + 8 y = (1/2)x + 3 y = (-1/2)x…

A: The given problem is solved below in steps.

Q: Which of the following statements proves the series-128+96-72+54- O 2 is geometric?

A:

Q: PART D: Solving problems involving rational function, equations and inequalities. 1. Suppose you…

A: Disclaimer:  “Since you have posted a question with multiple sub-parts, we will solve the first…

Q: Praw the curve r= 4 + 8 case and find the area outside the inner loop of the curve

A: Given: r=4+8cosθ

Q: Describe the end behavior of each polynomial. (a) y = x³ - 8x² + 6x End behavior: y → End behavior:…

A: Recall

Q: Use the shell method to find the volume of the solid generated by revolving the shaded region about…

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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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Q: A smooth curve C is defined by some vector function R(t) with R (7) 2 = = (π,0,−2) and R' (t) = (2,…

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Q: Find an explicit formula for the general term  an  of the sequence. 1, −  1 3 ,   1 5 , −  1 7 ,…

A: We have to find the formula of general term.

Q: Consider the region R bounded by the functions f(x)=3x and g(x)=x²+2. The area of R is: Choices: sq.…

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Q: Graph the curve whose parametric equations are given and show its orientation. Find the rectangular…

A: To plot the graph of the curve with the given parametric equation, first  find the x and y values…

Q: dt 1²+8t+20

A: We can find the answer as below.

Q: Find the general solution dy

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Q: Find equations of all tangents to the curve f(x) = 4/x that have slope -1. Options attatched

A: f(x) = 4/x                    Slope of tangent = -1

Q: Find the absolute maximum value and the absolute minimum value, if any, of the function.…

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Q: The function whose derivative is given by f'(x)=(x-¹), x 2. What is the #+2 critical point of f?

A: Critical point of a function is a point where either the derivative of function is zero or not…