RD Sharma - Mathematics (Volume 1)

Book: RD Sharma - Mathematics (Volume 1)

Chapter: 9. Continuity

Subject: Maths - Class 12th

Q. No. 42 of Exercise 9.1

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42

For what value of is the function continuous at x = 0? What about continuity at x = ± 1?

we have to find the value of '' such that f(x) is continuous at x = 0


If f(x) is be continuous at x = 0,then, f(0)=f(0) + =f(0)


LHL = f(0)=





(02 + 2×0)


0 ...(1)


RHL = f(0) + =




4(0) + 1


1 ...(2)


From (1) & (2),we get f(0)=f(0) + ,


Hence f(x) is not continuous at x = 0


we also have to find out the continuity at point


For f(x) is be continuous at x = 1,


then ,f(0)=f(0) + =f(0)


LHL = f(1) + =





(02–1)


...(1)


RHL = f(1) + =




(5 + 4×0)


5 ...(2)


From (1) & (2),we get f(0) = f(0) + ,


i.e, – = 5


= –5


Hence f(x) is continuous at x = 1,when = –5


Similarly, For f(x) is be continuous at x = –1,


then ,f(–1)=f(–1) + =f(–1)


LHL = f(–1)=






(02 + 4×0 + 3)


–3 ...(3)


RHL = f(–1) + =




(–3 + 4×0)


–3 ...(2)


From (1) & (2),we get, f(–1)=f(–1) +


i.e, –3 = –3


= 1


Hence f(x) is continuous at x = 1,when = 1


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