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midterm1 - Q8 Student ID Row No Last Name First Name Q7(10...

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October 30, 2009 IS ¸IK UNIVERSITY, MATH 101 MIDTERM EXAM I Q1 Q2 Student ID: Row No: Last Name: First Name: Q1. Find the domain of the functions: ( a )(6 pt) f ( x ) = ln( x 2 - 4) ( b )(5 pt) f ( x ) = q 3 - | x + 1 | Q2. (9 pt) Determine the interval on which the function f ( x ) = x + 1 ( x 2 - 9) x is continuous.
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October 30, 2009 IS ¸IK UNIVERSITY, MATH 101 MIDTERM EXAM I Q3 Q4 Student ID: Row No: Last Name: First Name: Q3. (12 pt) Find the inverse of the function f ( x ) = cos(3 x - 1)+2. Verify ( f f - 1 )( x ) = x . Q4. Determine whether f ( x ) is even, odd, or neither: ( a )(4 pt) f ( x ) = x 3 + sin x ( b )(4 pt) f ( x ) = e - x + x
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October 30, 2009 IS ¸IK UNIVERSITY, MATH 101 MIDTERM EXAM I Q5 Q6 Student ID: Row No: Last Name: First Name: Q5. (12 pt) Find the asymptotes of the function f ( x ) = x 2 + 3 x + 3 x + 2 . Q6. (8 pt) For what value(s) of c is the function f ( x ) = 1 - 2 x , x ≤ - 1 cx - x 2 2 , x > - 1 continuous at x = - 1?
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October 30, 2009 IS ¸IK UNIVERSITY, MATH 101 MIDTERM EXAM I
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Unformatted text preview: Q8 Student ID: Row No: Last Name: First Name: Q7. (10 pt) By using the shifting graph techniques, graph the functions: ( a )(5 pt) f ( x ) = e x-1 + 2 ( b )(5 pt) f ( x ) = ln( x + 2)-2 Q8. (8 pt) The inequalities 1-x 2 6 < x sin x 2-2 cos x < 1 hold for all values of x close to zero. Find the limit lim x → x sin x 2-2 cos x . Give reasons to your answers. October 30, 2009 IS ¸IK UNIVERSITY, MATH 101 MIDTERM EXAM I Q9 Student ID: Row No: Last Name: First Name: Q9. Evaluate the limits (DO NOT USE the L’hopital’s Rule): ( a )(6 pt) lim x → sin x-x tan x ( b )(7 pt) lim x → 2 x 2-4 x 3 / 2-√ 2 x ( c )(5 pt) lim x → 1 ln( ex ) + e x-1 sin-1 ± x 2 ² ( d )(4 pt) lim x → 9 + x 2 ( x-9) | x-9 |...
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