Explanation Given: A function: f ( x ) = x + 4 x − 8 Calculation: We know that a rational function is discontinuous, when the denominator is equal to zero. Let us find zeros of denominator as shown below: x − 8 = 0 x − 8 + 8 = 0 + 8 x = 8 Since denominator of give

7th Edition

ISBN: 9781524916817

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

Publisher: Kendall Hunt Publishing

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Chapter 2, Problem 61SP

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Whether the given function is continuous on the interval [0,10] . If not define or redefine the function at one point to make it continuous everywhere on the given interval, or else explain why that cannot be done.

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Chapter 2, Problem 60SP

Chapter 2, Problem 62SP

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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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Whether the given function is continuous on the interval [ 0 , 10 ] . If not define or redefine the function at one point to make it continuous everywhere on the given interval, or else explain why that cannot be done.

Solution Summary: The author explains that a rational function is discontinuous when the denominator is equal to zero. Since 8 lies inside the interval [0,10], the given is not continuous.

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Whether the given function is continuous on the interval [0,10] . If not define or redefine the function at one point to make it continuous everywhere on the given interval, or else explain why that cannot be done.

Want to see the full answer?

Chapter 2 Solutions