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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Question
![a) The function f: x1 a+b cos x, is defined for 0<x<2n. Given that
f(0) = 10 and that fn= 1, find
(i) the values of a and b,
(ii) the range of f,
iii) the exact value of f (n)
TC
b)
A geometric progression has 6 terms. The first term is 192 and the common
ratio is 1.5. An arithmetic progression has 21 terms and common difference 1.5.
Given that the sum of all the terms in the geometric progression is equal to the
sum of all the terms in the arithmetic progression, find the first term and the last
term of the arithmetic progression.
c) The equation of a curve is y = 5x + 4
%3D
i. Calculate the gradient of the curve at the point where x = 1
A point with coordinates (x,y) moves along the curve in such a way that
the rate of increase of x has the constant value 0.03 units per second. Find
the rate of increase of y ath the instant when x = 1.
ii.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F10f5f9ea-e586-4cd7-8691-30a08a7fcf05%2F4a748a03-4252-4b1a-8140-f85a44b26e9b%2Fppuzpjg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:a) The function f: x1 a+b cos x, is defined for 0<x<2n. Given that
f(0) = 10 and that fn= 1, find
(i) the values of a and b,
(ii) the range of f,
iii) the exact value of f (n)
TC
b)
A geometric progression has 6 terms. The first term is 192 and the common
ratio is 1.5. An arithmetic progression has 21 terms and common difference 1.5.
Given that the sum of all the terms in the geometric progression is equal to the
sum of all the terms in the arithmetic progression, find the first term and the last
term of the arithmetic progression.
c) The equation of a curve is y = 5x + 4
%3D
i. Calculate the gradient of the curve at the point where x = 1
A point with coordinates (x,y) moves along the curve in such a way that
the rate of increase of x has the constant value 0.03 units per second. Find
the rate of increase of y ath the instant when x = 1.
ii.
![iii. Find the area enclosed by the curve, the x- axis, the y- axis and the line
y 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F10f5f9ea-e586-4cd7-8691-30a08a7fcf05%2F4a748a03-4252-4b1a-8140-f85a44b26e9b%2Fgxlrnvm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:iii. Find the area enclosed by the curve, the x- axis, the y- axis and the line
y 1.
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