3. A triangle has vertices A(2,4,1), B(-1,2,2), C(7,0-4) a) Determine the measure of the angle at B. b) Determine the area of the triangle.

Q: Calculate the iterated integral. 1 '1 15 15(u - v)5 du dv

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A: Given.

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A: I am attaching image so that you understand each and every step.

Q: Q3. Find the cross product of the vectors and .

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Q: Solve for x: |x+5| < |X-71

A: Follow the procedure given below.

Q: 14. The Integral:√4-3x² a. cos²0.de dx, can be transformed into : b. 2f cose.de c. 2 f tano.de d. 4…

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Q: Find the volume of the solid of revolution below. (1,1) 0.5 y = x³ 1 -0.5 X = X 0.5 1.5 2

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Q: Q1. Find the distance between the points A (-1, 3, 7) and B (2, -1, 6).

A: The given points A(-1,3,7) and B(2,-1,6).

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Q: e) y=sin(tanx) f) y = sin³ 7x

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Q: (-3², what values should "a" take to ge c. a> 3 d. a 0

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Q: Evaluate the following integrals using FTC. Show solution

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Q: (x³-4x) dx

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A: We know, Average velocity =Total DisplacementTotal time

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Q: Find the open intervals where the function f(x) = − 2x³ + 6x² +172x-3 is concave upward or concave…

A: The given function f(x)=-2x3+6x2+172x-3

Q: Evaluate the following integral by using Odd and Even Powers Method: y = [ cos³ (;x) dx

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Q: Find the derivative of the function. y=-5e-4x+1 dx 11

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Q: Within y = 4x², x = 0, y = 16; about y axis

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Q: )) 5 = لا 5 1 2X e - ل6 لاو لا -

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Q: Q6) Find the Area bounded by the curves y = √x and x = 2y-y² ,with sketch.

A: First we find the limits of integration.

Q: Use the Table of Integrals to evaluate the integral. Show ALL work. S 11x³√4x²x¹ dx

A: Follow the procedure given below.

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Q: (d) f(x)=√√x-8 (e) h(x)=√x+2

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Q: 1. For the vectors v = and u = a. Find v-u b. Find ||v|| and ||u|| c. Find the angle between v and…

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Q: Taylor Series Approximation Formula f" f"" (a) ² f(x) = f(a) + f'(a)(x − a) + ¹¹¹(a) (x − a)² +…

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Q: (x² - 12x + 9) dx (x²-3x + 2)²

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Q: Graph the parabola y=(x^2-100x)/50

A: Graph the parabola y=(x^2-100x)/50

Q: 2. Find y' if y = 7* (log4 x)⁹.

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Q: Use the table of integrals to evaluate the integral. 6² 3saxav 53x³√4x² - x4 dx

A: To evaluate the integral.

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Q: Use the ratio test for absolute convergence to determine whether the series converges or diverges.…

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Q: Q4) Find dy /dx for the following functions : a) y².cotx = [sin(x.y)]-¹ b) y = (In x + x) tan x

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Q: Using the polya's four step problem, how many square are in the figure?

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Q: 3 tabler W y = JUN 13 MacBook Pro (A)

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Q: c) e³x 2x+1 d) y=cos² (x³ + ²)

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Q: find the area of the region bounded by the curves 4x - y2 = 0 and y = 2x - 4

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Q: 4. With the fact of 1² +2²+...+ n² = n(n+1)(2n + 1)/6, prove that n n n(n −1) ΣΣ(i-j)² 6 i=1 j=1…

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Q: 4. Evaluate √x² - 2x + 1dx

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Q: 1. For the curve given by R(t) = (cost + tsin t)i + (sin t − t cost)j + (t^2)k, find a. the length…

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Q: Find a point on y = x closest to (18,0) For what x is the slope of the tangent line at x to the…

A: Given

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Q: Q6. Find the volume of parallelopiped formed by the vectors , and .

A: Given :a=&lt;2,-4, 5&gt;b=&lt;-1, 0,-3&gt;c=&lt;3,-5,-3&gt;