1. Consider the piecewise function S(1+ x)* – 1, x < 0 g(x) = sin (4x), x > 0 Discover whether g(x) is differentiable at r = 0 using the differentiability test. Without carrying out any further calculation, what can you conclude about the continuity at point x = 0? 2. The second derivative of a parametric function can be calculated using the formula:

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. Consider the piecewise function
S(1 + x)* – 1, x < 0
g(x) =
sin (4x),
x > 0
Discover whether g(x) is differentiable at x = 0 using the differentiability test.
Without carrying out any further calculation, what can you conclude about
the continuity at point x = 0?
2. The second derivative of a parametric function can be calculated using the
formula:
dy
dx
dx?
Find an expression for the derivative of the parametric function and use it
to calculate the second derivative.
x(t) = In (t*) and y(t) = tet
Simplify your answer.
Transcribed Image Text:1. Consider the piecewise function S(1 + x)* – 1, x < 0 g(x) = sin (4x), x > 0 Discover whether g(x) is differentiable at x = 0 using the differentiability test. Without carrying out any further calculation, what can you conclude about the continuity at point x = 0? 2. The second derivative of a parametric function can be calculated using the formula: dy dx dx? Find an expression for the derivative of the parametric function and use it to calculate the second derivative. x(t) = In (t*) and y(t) = tet Simplify your answer.
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