ws_2 - | x |(iv f x =-3-x ix f x = 2-log(2-x(v f x = ln x 2...

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Mathematics for Engineers I (Math103). .. student-intranet/faculties/math/ 2009 - Fall/math103 Class Work Sheet 2. 1. Simplify: (i) e ln(7 . 2) ( vi ) 2 ln( e ). (ii) e - ln( x 2 ) ( vii ) ln ± ln( e e ) ² . (iii) e [ln( x ) - ln( y )] ( viii ) ln ± e ( e x ) ² . (iv) e ln( x 2 + y 2 ) ( ix ) ln ± e (2 ln x ) ² . (v) e x - ln( x ) . 2. Use properties of logarithmic function to simplify: (i) ln 4 q x 2 +1 x 2 - 1 ( v ) ln(3 x 2 - 9 x ) + ln[ 1 3 x ]. (ii) ln sin 2 x tan 4 x ( x 2 +1) 2 ( vi ) ln(sec θ ) + ln(cos θ ). (iii) ln ( x 3 +1) 4 sin 2 x 3 x ( vii ) 3 ln 3 t 2 - 1 - ln( t + 1). (iv) ln(sin θ ) - ln[ sin θ 5 ]. 3. Solve for y in terms of x : (i) ln y = 2 x + 4. (ii) ln y = - x + 5. (iii) ln( y - 1) - ln 2 = x + ln x . (iv) ln( y 2 - 1) - ln( y + 1) = ln(sin x ). 4. Solve the following equations: (i) 2 ln x = 1 ( v ) ln(5 - 2 x ) = - 3. (ii) e (2 x +3) - 7 = 0 ( vi ) ln(2 x + 1) = 2 - ln x . (iii) ln(ln x ) = 1 ( vii ) 7 e x - e (2 x ) = 12. (iv) e ( e x ) = 10. 1
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5. Graph each of the following functions: (i) f ( x ) = - (3 x + 2) ( vi ) f ( x ) = ln x + 2. (ii) f ( x ) = 2 x + 1 ( vii ) f ( x ) = 1 + ln( - x ). (iii) f ( x ) = e ( x +1) ( viii ) f ( x ) = ln
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Unformatted text preview: | x | . (iv) f ( x ) =-3 (-x ) ( ix ) f ( x ) = 2-log(2-x ). (v) f ( x ) = ln( x + 2). 6. Find the numerical value of: (i) sinh 0 ( v ) sinh(ln 2). (ii) cosh 0 ( vi ) cosh(ln 3). (iii) tanh 0 ( vii ) cosh-1 (1). (iv) tanh 1 ( viii ) sinh-1 (1). 7. Starting from the definition, prove that: (i) sinh(-x ) =-sinh x . (ii) cosh(-x ) = cosh x . (iii) cosh x + sinh x = e x . (iv) cosh x-sinh x = e-x . (v) cosh( x + y ) = cosh x cosh y + sinh x sinh y . (vi) tanh(ln x ) = x 2-1 x 2 +1 . (vii) 1+tanh x 1-tanh x = e 2 x . 8. If sinh( x ) = 3 4 , find the values of the other hyperbolic functions at x . 2...
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This note was uploaded on 01/08/2010 for the course MATH Math103 taught by Professor Dr.prof.mostafaamer during the Winter '09 term at German University in Cairo.

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ws_2 - | x |(iv f x =-3-x ix f x = 2-log(2-x(v f x = ln x 2...

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