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MATHEMATICS TEST-XII (Sub.)

TOPIC – Continuity

Max.Mark-30 Date-18/07/2015 Max.Time: 1Hrs.

1. If f(x) is continuous on [0,8] defined as f(x) =x2+ax+6, for 0≤x<2f(x) = 3x+2 for 2≤x≤4f(x) = 2ax+5b for 4<x≤8Find a and b.

2. If f(x) is continuous on [0,π] where f(x) =x+a√2sinx, for 0≤x<π4

f(x) =2x cot x+b, for π4 ≤x≤

π2

f(x) = a cos 2x-b sinx for π2 <x≤π

Find a and b.3. Find α and β, so that the function f(x) defined by

F(x) = -2.sinx, for -π≤x≤-π2

F(x) = α sin x+β, for -π2 <x<

π2

F(x) = cosx, for π2 ≤x≤π

Find the value of [-π,π].4. If f(x) is continuous on [0,3] where f(x) = 3x-4 for 0≤x≤2

F(x) = 2x+k, for 2<x≤3Find the value of k.

5. If f(x) = x3+3 x+5x3−3 x+2

. Discuss the continuity of f(x) on [0,5].

6. Discuss the continuity of the function log c x where c>0,x>0.7. If function f(x) is continuous in interval [-2,2] find the value of (a+b) where

F(x) = sin axx -2 for -2≤x<0

F(x) = 2x+1, for 0≤x≤1F(x) = 2b√ x2+3-1 for 1<x≤2

8. Test the continuity of function f(x) = x+1

( x−2 )(x−5) in the interval [0,1] and [4,6]

9. Discuss the continuity of the function f(x) in its domain if f(x) is defined by.

F(x) = x, for x≥0F(x) = x2, for x<0

10. Dicuss the continuity of the following functions in its domain, where.

F(x) = x2-4, for 0≤x≤2F(x) = 2x+3, for 2<x≤4F(x) = x2-5, for 4<x≤6