The regions bounded by the graphs of y = 6x and y = 5x²regions?AB[² (6z — (52²³ - 2³)) dzSo-[² (6 x − (5x² − x³)) dr +-3Sy((5x² – x³) – 6x) dx15+10+5+O+23Xx³ are shaded in the figure above. The graphs intersect at x = 0, x = 2, and x = 3. Which of the following gives the sum of the areas of the shaded ASoD(6(6x — (5x² – x³)) dx-6 (62-(52²-2³)) dx + ((5x² – 2³) - 6z) dz[² drSoB2©©33[(52²-2³)dz + f Grdz3dx5x²6zdz + (52²-2³) d=[² d²6xdx

Answered: (В y (62 - (52²-2³)) dz [² (62 − (52² −…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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1. Differentiate. All the asnwer must be brought to their simplest factored form possible AND in terms of x only. a) y = −²ln(−8x³+5) y = 5x².e5x c) f(x)= = cos 2x 65x b)
(16) A triangle is inscribed in the unit circle in such a way as its base is the line segment along the x-axis from (-1,0) to (1,0), and its third point sits on the top half of the circle, somewhere in the first or second quadrant. Find the largest area this triangle could have.
#21
5. Find the x- and y- intercepts of the rational function : f(x) = (a) (6, 0),(0,2) (b) (6,0) ,(0,-2) (c) (3, 0) ,(0,-2) (d) (-2, 0), (6,0)
Use the five rectangles in Figure, to find two approximations of the area of the region lying between the graph of f(x) = −x2 + 5 and the x-axis between x = 0 and x = 2.
On a dark night, two ships, Saga and Hero, sail parallel to a straight coastline on which there are two lights of equal brightness, 16 kilometres apart. P(x, b) (-8, 0) (8, 0) x Suppose the coastline is represented by the x axis where the origin O is chosen to be the midpoint of the light sources. It is known that the (total) brightness from the lights on a ship at point P(x, b) is 1 I = b² +(x+8)² 'b² +(x-8)² + dI (i) Show that dx 2P where P= (x+8)(3² +(x – 8)*)* +(x -8)(s² +(x + 8)*)* | and Q = (3° +(x +8)*)} (s? +(x-87)'. To answer parts (ii) and (iii), you may assume the following factorisation, given by a computer package, that P= 2x(x² + 64 + b? +16/64 + b² (x² + 64 + b² –16/64 + b²). (ii) Saga sails parallel to the coast at a distance 15 km from the coast. dI show that, as Saga sails from left to right, the brightness By considering on Saga increases to a maximum when x= 0 and then decreases. dx (iii) Hero sails parallel to the coast at a distance 6 km from the coast. Describe…

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