Explanation Given information : g ( x ) = cot x sin x − cos x Formula Used: Quotient identity cot x = cos x sin x & tan x = sin x cos x Concept Involved: Domain of a function means the values of the input that gives a defined output to the function. Whenever we are finding the domain, we need to look out for two mail restrictions: Negative inside an even square root if we have a radical function Zero in the denominator if we have a rational function Trigonometric function is period function; the graph of the given function will have vertical asymptotes for values of x which makes the denominator to zero. Calculation: Description Steps Rewriting the numerator of function g ( x ) = cot x sin x − cos x using the quotient identity g ( x ) = cos x sin x sin x − cos x Rewriting the denominator expression as a fraction g ( x ) = cos x sin x sin x − cos x 1 Description Steps Divide the fraction by flipping the bottom fraction and multiply with the top fraction. g ( x ) = cos x sin x ⋅ 1 sin x − cos x = cos x sin x ( sin x − cos x ) To find the vertical asymptotes or the point where the rational function discontinuous, we need to set the denominator expression to zero. sin x ( sin x − cos x ) = 0 Use the zero factor property which states that if a = b , then b = a to write the equation as compound equations

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 2.3, Problem 18PS

To determine

Toidentify:all suspicious points and points of discontinuity.

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Taylor Series Approximation Example- H.W More terms used implies better approximation f(x) 4 f(x) Zero order f(x + 1) = f(x;) First order f(x; + 1) = f(x;) + f'(x;)h 1.0 Second order 0.5 True f(x + 1) = f(x) + f'(x)h + ƒ"(x;) h2 2! f(x+1) 0 x; = 0 x+1 = 1 x h f(x)=0.1x4-0.15x³- 0.5x2 -0.25x + 1.2 51 Taylor Series Approximation H.w: Smaller step size implies smaller error Errors f(x) + f(x,) Zero order f(x,+ 1) = f(x) First order 1.0 0.5 Reduced step size Second order True f(x + 1) = f(x) + f'(x)h f(x; + 1) = f(x) + f'(x)h + "(xi) h2 f(x,+1) O x₁ = 0 x+1=1 Using Taylor Series Expansion estimate f(1.35) with x0 =0.75 with 5 iterations (or & s= 5%) for f(x)=0.1x 0.15x³-0.5x²- 0.25x + 1.2 52

Could you explain this using the formula I attached and polar coorindates

Could you explain this using the formula I attached and polar coordinates

Chapter 2 Solutions

Calculus

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Toidentify :all suspicious points and points of discontinuity.

Solution Summary: The author explains that the domain of a function is the values of the input that gives the defined output to the function.

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Chapter 2 Solutions