1. Consider the piecewise function S(1 + x)* – 1, x< 0 g(x) sin (4x), x >0 0 using the differentiability test. Discover whether g(x) is differentiable at x = Without carrying out any further calculation, what can you conclude about the continuity at point a = 0? 2. The second derivative of a parametric function can be calculated using the formula: dy _ #) d (dy dx? dx dt 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.
1. Consider the piecewise function S(1 + x)* – 1, x< 0 g(x) sin (4x), x >0 0 using the differentiability test. Discover whether g(x) is differentiable at x = Without carrying out any further calculation, what can you conclude about the continuity at point a = 0? 2. The second derivative of a parametric function can be calculated using the formula: dy _ #) d (dy dx? dx dt 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.
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
![1. Consider the piecewise function
S(1 + x)* – 1, x< 0
g(x) =
sin (4x),
x >0
0 using the differentiability test.
Discover whether g(x) is differentiable at x =
Without carrying out any further calculation, what can you conclude about
the continuity at point a = 0?
2. The second derivative of a parametric function can be calculated using the
formula:
d (dy
dt
dx?
dx
dt
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd39b4fe7-8955-486a-b188-9496ca1530b8%2Fa263c14d-da37-4210-a318-402e228fdd42%2Fm3umh3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Consider the piecewise function
S(1 + x)* – 1, x< 0
g(x) =
sin (4x),
x >0
0 using the differentiability test.
Discover whether g(x) is differentiable at x =
Without carrying out any further calculation, what can you conclude about
the continuity at point a = 0?
2. The second derivative of a parametric function can be calculated using the
formula:
d (dy
dt
dx?
dx
dt
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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