Software-Engineering
October 14, 2023GATE 2017 [Set-1]
October 14, 2023GATE 2007
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Question 1
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Consider the following two statements about the function f(x)=|x|
P. f(x) is continuous for all real values of x Q. f(x) is differentiable for all real values of x
Which of the following is TRUE?
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P is true and Q is false.
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P is false and Q is true.
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Both P and Q are true.
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Both P and Q are false.
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Question 1 Explanation:
f(x) = |x|
→ f(x) is continuous for all real values of x
For every value of x, there is corresponding value of f(x).
For x is positive, f(x) is also positive
x is negative, f(x) is positive.
So, f(x) is continuous for all real values of x.
→ f(x) is not differentiable for all real values of x.
For x<0, derivative is negative
x>0, derivative is positive.
Here, left derivative and right derivatives are not equal.
→ f(x) is continuous for all real values of x
For every value of x, there is corresponding value of f(x).
For x is positive, f(x) is also positive
x is negative, f(x) is positive.
So, f(x) is continuous for all real values of x.
→ f(x) is not differentiable for all real values of x.
For x<0, derivative is negative
x>0, derivative is positive.
Here, left derivative and right derivatives are not equal.
Correct Answer: A
Question 1 Explanation:
f(x) = |x|
→ f(x) is continuous for all real values of x
For every value of x, there is corresponding value of f(x).
For x is positive, f(x) is also positive
x is negative, f(x) is positive.
So, f(x) is continuous for all real values of x.
→ f(x) is not differentiable for all real values of x.
For x<0, derivative is negative
x>0, derivative is positive.
Here, left derivative and right derivatives are not equal.
→ f(x) is continuous for all real values of x
For every value of x, there is corresponding value of f(x).
For x is positive, f(x) is also positive
x is negative, f(x) is positive.
So, f(x) is continuous for all real values of x.
→ f(x) is not differentiable for all real values of x.
For x<0, derivative is negative
x>0, derivative is positive.
Here, left derivative and right derivatives are not equal.
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