Question

find all number at
which f is continuous

f (x) =
cot +1/3 x​

Answer 1

Step-by-step explanation:

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12th

Maths

Continuity and Differentiability

Continuity

Let f(x) = √(sgn(alphax^2 +...

MATHS

Let f(x)=

cot

−1

(x

2

−α)

sgn(αx

2

+αx+1)

. If f(x) is continuous for all x∈R, then number of integer in the range of α, is

[Note : sgn k denotes signum function of k.]

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ANSWER

Given: f(x)=

cot

−1

(x

2

−α)

sgn(αx

2

+αx+1)

andf(x)iscontinousforallxεR

To find: Number of integer in the range of α

Sol: αx

2

+αx+1→isaquadratic

Whose discriminant=x

2

−4α

Now, for f(x) to be a valid function

sgn(αx

2

+αx+1)≥0forallxεR

⟹αx

2

+αx+1≥0⟹Discriminant≤0

⟹α(α−4)≤0

⟹α∈[0,4]

∴α∈[0,4]

⟹5 integers are in the range of α

Hence, the correct answer is 5