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what do you meant by continuity of a function in open interval and closed interval ?
Sinx is continuous function in interval between _ infinity to plus infinity
explain.

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a:0:{}

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Q. If h(x) = g(x) + f(x) is a continuous function in a given interval then g(x) and f(x) individually will also be continuous in the same interval.

Q. If h(x) = g(x) + f(x) is a continuous function in a given interval then g(x) and f(x) individually will also be continuous in the same interval.

Q. Consider the function

y = | x - 1 | + | x - 2 |

in the interval

[0, 3]

and discuss the continuity and differentiability of the function in this interval.

Sketch the function

y = | x - 2 |

in the interval

(- 1, 3)

. Is this function continuous.

f

be a differentiable function on the open interval

(a, b)

. Which of the following statements must be true?

(i) f

is continuous on the closed interval

(a, b)

(i i) f

is bounded on the open interval

(a, b)

(i i i)

a < a_{1} < b_{1} < b

f (a_{1}) < 0 < f (b_{1})

, then there is a number

c

a_{1} < c < b_{1}

f (c) = 0

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