Find the average value of f(x) = 4-x2 on the interval [2,3] Find the area enclosed by f(x) = -x2+4x and g(x) = 2x-3

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A: Direct variation:The quantities are said to be in direct proportion if:  An increase in the quantity…

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Q: 5. St? V1- t dt (2x+3) dx 6. S (x2+3x-6)

A: Please see the answer below.

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Q: diverges: 3n/22n-4=27/4+81/16+243/64+729/156

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A: Let A be the coefficient matrix of the system.So,A=11134-12-1-1AX=BX=A-1Bwhere X=xyz, B=113

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Q: 2r Find the absolute maximum and absolute minimum of the function f(x) = 2x 3 over the interval [0,…

A: Absolute Maximum and Absolute Minimum in a closed interval: step 1 : Find the critical point of the…

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Q: Suppose that f has zeros at 1 and 3. Show that there are two distinct real numbers x1 and x2 such…

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Q: TOPIC 1: Illustration of an Antiderivative of a function. (p.225) Written Works Determine the…

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Q: Find the area represented by the definite int 8. x-2 dx

A: ∫08x-2dx=∫01-(x-2)dx+∫18x-2dx

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Q: 5. DETAILS LARCALC11 11.3.007 Find u · v, u · u, ||v||?, (u · v)v, and u u = (2, -2, 5), v = (0, 7,…

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Q: III. Derive the following HOCAT USA dx 1. The unity rule: =1983 99 dx du dv a(=) dx dx 2. The…

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Q: Question dx If z? = x +y. dt dy = -3, and z > 0, find dt dz -2, at (x, y) = (4, 0). dt %3D %3D…

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Q: Find r'(t), r"(t), and r'(t) · r"(t). r(t) = (t2 + 6t)i - 9t2j (a) r'(t) (b) r"(t) (c) r'(t) r"(t)

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Q: Find the area under the graph of f over the interval [-1,4]. x²+2 xs2 = ()4 x> 2 3x The area is…

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Q: Directions: Complete the table by determining the derivatives of the outer and inner functions of…

A: (8.) f(x) = (6x2 + 7x)4 Derivative of Outer Function : 4(6x2 + 7x)3 Derivative of Inner Function :…

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Q: Write the following expression as a single definite integral of the form f(x) dx. f(x) dx -6 dx +…

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Q: d -e'(t² + 5) at t = 0. dt Find

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Q: In how many different ways can 7 potted plants be arranged in a row with 5 spaces? O 720 O 2 520 5…

A: There are total 7 potted plantsThere are 5 spaces in a rowNumber of ways  to arrange 7 potted plants…

Q: Evaluate I = Se(sin z + 4y) dz + (5x + y) dy for the nonclosed path ABCD in the figure. %3! A =…

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Q: x 6. Copy each graph of (x) and g(x). Then, apply the superposition principle to graph f(x) + g(x).…

A: Graph of the functions f(x) and g(x) are given, we have to graph f(x)+g(x)

Q: Consider the power series P (x) = ∞ ∑ (2n/5n+1)xn=1/2+x/3+2x2/13+43/64+... n=0 (a) Find its radius…

A: We have to find radius and interval of convergence.

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Q: Find the limit algebraically by factoring the expression first. lim X-6 -8x2-56x-48 x + 6

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Q: Consider the series (-1)n*(3n2+n+5)/(4n3+2) = 5/2 - 3/2 + 19/32 - 7/22

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Q: Calculate -3 + li. Give your answer in a + bi form. In polar form, use the angle 0 < 0 < 27. a = b =

A: This question is based on conversion of rectangular form to exponential to polar form of complex…