10) Consider the following two functions p(t) = and 7e-2)-7 t-2 P: R R if 0 < t < 2, 7 t=2 tre. (7(t²-4) (-2) ift > 2 q: R→R q(t) = \t(t-7)(t-2) and the following statements (a function is said to be continuous (respectively differentiable) if it is continuous (respectively differentiable) at all the points in the domain of the function).

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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10) Consider the following two functions
p(t) =
and
7e(t-2)-7
t-2
P: R → R
if 0 < t < 2,
t=2
7
7 (t²-4) (-2) ift > 2
q: R→R
q(t)=t(t-7) (t2) and the following statements
(a function is said to be continuous (respectively
differentiable) if it is continuous (respectively
differentiable) at all the points in the domain of the
function).
Statement P: Both the functions p(t) and g(t) are
continuous.
Statement Q: Both the functions p(t) and g(t) are
not differentiable.
Statement R: p(t) is continuous, q(t) is
differentiable.
Statement S: g(t) is continuous, p(t) is not
differentiable.
Statement T: Neither p(t) nor q(t) is continuous
Find the number of correct statements.
Transcribed Image Text:10) Consider the following two functions p(t) = and 7e(t-2)-7 t-2 P: R → R if 0 < t < 2, t=2 7 7 (t²-4) (-2) ift > 2 q: R→R q(t)=t(t-7) (t2) and the following statements (a function is said to be continuous (respectively differentiable) if it is continuous (respectively differentiable) at all the points in the domain of the function). Statement P: Both the functions p(t) and g(t) are continuous. Statement Q: Both the functions p(t) and g(t) are not differentiable. Statement R: p(t) is continuous, q(t) is differentiable. Statement S: g(t) is continuous, p(t) is not differentiable. Statement T: Neither p(t) nor q(t) is continuous Find the number of correct statements.
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