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Graph of Trigonometric Ratios

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$The function f (x) = sec x is continuous for all x \in R .$

A

False

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B

True

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Q. The function

f (x) = \frac{\sin (π [x - π])}{4 + {[x]}^{2}}

, where [⋅] denotes the greatest integer function, is
(a) continuous as well as differentiable for all x ∈ R
(b) continuous for all x but not differentiable at some x
(c) differentiable for all x but not continuous at some x.
(d) none of these

f (x) = |\log_{e} | x ||

, then
(a) f (x) is continuous and differentiable for all x in its domain
(b) f (x) is continuous for all for all × in its domain but not differentiable at x = ± 1
(c) f (x) is neither continuous nor differentiable at x = ± 1
(d) none of these

f (x + y) = f (x) + f (y)

for all x and y. If the function

f (x)

is continuous at

x = 0

f (x)

is continuous for all x.

The function f (x) = sec x is continuous for all x \in R .

f (x + y) = f (x) + f (y)

x

y

. If the function

f (x)

is continuous at

x = 0

f (x)

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Graph of Trigonometric Ratios

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