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In the triangle pictured, let A, B, C be the angles at the three vertices, and let a,b,c be the sides opposite those angles. C a A B C According to the law of sines," you always have: b_sinB a sinA Suppose that a and b are pieces of metal which are hinged at C. At first the angle A is 1/4 radians=45° and the angle B is 7/3 radians = 60°. You then widen A to 46°, without changing the sides a and b. Our goal in this problem is to use the tangent line approximation to estimate the angle B. (a) Notice that the angle B is a function of the angle A; i.e. B=f(A). Consequently, it makes sense to calculate the implicit derivative: (b) Calculate when A=1/4 and B=x/3; leave your answer in EXACT FORM: dB dA (c) Write the linear approximation of fat A= x/4: (A - 1/4)+ (d) Using (c), when A= 46°, B is approximately degrees; either answer exactly or to three decimal places. Suppose that the only information we have about a function f is that f(1) = 3 and the graph of its derivative is as shown. x 2 3 4 (a) Use a linear approximation to estimate f(0.99) and f(1.01).

In the triangle pictured, let A, B, C be the angles at the three vertices, and let a,b,c be the sides opposite those angles. C a A B C According to the law of sines," you always have: b_sinB a sinA Suppose that a and b are pieces of metal which are hinged at C. At first the angle A is 1/4 radians=45° and the angle B is 7/3 radians = 60°. You then widen A to 46°, without changing the sides a and b. Our goal in this problem is to use the tangent line approximation to estimate the angle B. (a) Notice that the angle B is a function of the angle A; i.e. B=f(A). Consequently, it makes sense to calculate the implicit derivative: (b) Calculate when A=1/4 and B=x/3; leave your answer in EXACT FORM: dB dA (c) Write the linear approximation of fat A= x/4: (A - 1/4)+ (d) Using (c), when A= 46°, B is approximately degrees; either answer exactly or to three decimal places. Suppose that the only information we have about a function f is that f(1) = 3 and the graph of its derivative is as shown. x 2 3 4 (a) Use a linear approximation to estimate f(0.99) and f(1.01).

Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter74: Introduction To Compound Angles
Section: Chapter Questions
Problem 1A
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In the triangle pictured, let A, B, C be the angles at the three vertices, and let a,b,c be the sides opposite those angles. C a A B C According to the law of sines," you always have: b_sinB a sinA Suppose that a and b are pieces of metal which are hinged at C. At first the angle A is 1/4 radians=45° and the angle B is 7/3 radians = 60°. You then widen A to 46°, without changing the sides a and b. Our goal in this problem is to use the tangent line approximation to estimate the angle B. (a) Notice that the angle B is a function of the angle A; i.e. B=f(A). Consequently, it makes sense to calculate the implicit derivative: (b) Calculate when A=1/4 and B=x/3; leave your answer in EXACT FORM: dB dA (c) Write the linear approximation of fat A= x/4: (A - 1/4)+ (d) Using (c), when A= 46°, B is approximately degrees; either answer exactly or to three decimal places.
Transcribed Image Text:In the triangle pictured, let A, B, C be the angles at the three vertices, and let a,b,c be the sides opposite those angles. C a A B C According to the law of sines," you always have: b_sinB a sinA Suppose that a and b are pieces of metal which are hinged at C. At first the angle A is 1/4 radians=45° and the angle B is 7/3 radians = 60°. You then widen A to 46°, without changing the sides a and b. Our goal in this problem is to use the tangent line approximation to estimate the angle B. (a) Notice that the angle B is a function of the angle A; i.e. B=f(A). Consequently, it makes sense to calculate the implicit derivative: (b) Calculate when A=1/4 and B=x/3; leave your answer in EXACT FORM: dB dA (c) Write the linear approximation of fat A= x/4: (A - 1/4)+ (d) Using (c), when A= 46°, B is approximately degrees; either answer exactly or to three decimal places.
Suppose that the only information we have about a function f is that f(1) = 3 and the graph of its derivative is as shown. x 2 3 4 (a) Use a linear approximation to estimate f(0.99) and f(1.01).
Transcribed Image Text:Suppose that the only information we have about a function f is that f(1) = 3 and the graph of its derivative is as shown. x 2 3 4 (a) Use a linear approximation to estimate f(0.99) and f(1.01).
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