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In this lesson, we will learn how to determine the continuity of a function at a point on the number line by evaluating limits at that point.

Q1:

Find the value of π which makes the function π continuous at π₯ = 3 , given

Q2:

Find the set on which π ( π₯ ) = β π₯ + 1 4 + β 3 β π₯ is continuous.

Q3:

Which of the following holds for π ( π₯ ) = ( β 7 π₯ + 3 ) + 3 5 π₯ 7 s i n ?

Q4:

Given π ( π₯ ) = π₯ β 1 0 0 π₯ β 1 0 2 , if possible or necessary, define π ( 1 0 ) so that π is continuous at π₯ = 1 0 .

Q5:

Suppose What can be said of the continuity of π at π₯ = 0 ?

Q6:

Determine whether the function represented by the graph is continuous or discontinuous.

Q7:

Find the set on which π ( π₯ ) = π₯ β 2 2 π₯ β 2 π₯ β 6 3 2 is continuous.

Q8:

Find the set on which π ( π₯ ) = π₯ + 3 π₯ β 3 π₯ + 2 2 is continuous.

Q9:

Given π ( π₯ ) = β 9 π₯ + π₯ β 2 2 , what can be said of the continuity of π at π₯ = β 7 ?

Q10:

Use continuity to evaluate l i m l n π₯ β 5 2 οΎ 5 + 2 π₯ 6 β π₯ ο .

Q11:

Use continuity to evaluate l i m l n π₯ β 5 2 οΎ 3 + π₯ 3 + 5 π₯ ο .

Q12:

Determine the value of π that makes the function π continuous at π₯ = 9 , given

Q13:

Suppose Discuss whether it is possible to define π ( 6 ) to obtain a function that is continuous at this point.

Q14:

Given that π and π are continuous functions such that π ( 6 ) = 6 and l i m π₯ β 6 [ π ( π₯ ) β 9 π ( π₯ ) π ( π₯ ) ] = 5 , determine π ( 6 ) .

Q15:

Given that π and π are continuous functions such that π ( 1 ) = β 9 and l i m π₯ β 1 [ 8 π ( π₯ ) + 9 π ( π₯ ) π ( π₯ ) ] = 7 , determine π ( 1 ) .

Q16:

Given that π and π are continuous functions such that π ( 3 ) = 6 and l i m π₯ β 3 [ 2 π ( π₯ ) β π ( π₯ ) π ( π₯ ) ] = β 5 , determine π ( 3 ) .

Q17:

Use continuity to evaluate l i m π₯ β 1 β 3 π₯ + 2 π₯ β 1 5 2 .

Q18:

Use continuity to evaluate l i m π₯ β 6 β π₯ β 5 π₯ β 2 5 2 .

Q19:

Find the set on which π βΆ π ( π₯ ) = β 5 π₯ β 1 3 is continuous.

Q20:

Find the set on which π βΆ π ( π₯ ) = β 4 π₯ β 1 9 3 is continuous.

Q21:

Find the set on which π ( π₯ ) = π₯ + 9 π₯ + 1 c o s is continuous.

Q22:

Find the set on which π ( π₯ ) = 7 π₯ β 8 7 π₯ + 7 c o s is continuous.

Q23:

Use continuity to evaluate l i m s i n s i n π₯ β π 6 ( 2 π₯ β 7 6 π₯ ) .

Q24:

Use continuity to evaluate l i m s i n s i n π₯ β π 9 ( 3 π₯ + 9 π₯ ) .

Q25:

Use continuity to evaluate .

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