The contrapositive of statement : "If f(x) is Continuous at x = a then f(x) 1s differentiable at x =a (1) It f(x) is continuous at x = a then f(x) is not continuous at x = a (2) If f(x) is not differentiable at x = a then f(x) is not continuous at x =a (3) If f(x) is differentiable at x = a then f(x) is continuous at x = a (4) If f(x) ts differentable at x = a then f(x) is not continuous
Answers
Let f(x)={
∫
0
x
{1+∣1−t∣}dt
5x−7
x>2
x≤2
}
Let y=∫
0
x
{1+∣1−t∣}dt as x>2
y=∫
0
1
(1+1−t)dt+∫
1
x
tdt
y=2−
2
1
+
2
(x
2
−1)
y=1+
2
x
2
f(x)={
1+
2
x
2
,
5x−7,
x>2
x≤2
}
f(2
+
)=1+
2
4
=3
f(2
−
)=10−7=3
Differentiating with respect to x we get
f
1
(x)={
x;
5;
x>2
x≤2
}
We can see that it is not differentiable at x=2 but continuous at x=2
Answer By.......
Answer:
✍Answer:–
"If f(x) is not differentiable at x=a then f(x) is not continuous at x=a.
✍Given:–
The statement is " if f(x) is continuous at x=a then f(x) is differentiable at x=a.
✍ Solution:–
The Statement is of the form
P→q
Here,
p=f(x) is continuous at x=a
q=f(x) is differentiable at x=a
Now, The contrapositive statement is of the form,
~q→~p
So,
The contrapositive statement is,
" if f(x) is not differentiable at x=a then f(x) is not continuous at x=a.