HW_1 (1).pdf - CEE 3040 Homework 1 MATH REVIEW 1 Solve the...

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CEE 3040 Homework 1 ( MATH REVIEW ) 1) Solve the following definite integrals ( ) ( ) ( ) ? ) sin( 2 exp ) cos( ? ) sin( 2 exp ) cos( , ? 3 exp 5 1 1 2 2 1 1 0 3 2 = = = dx x x x dx x x dx x x 2) Solve the following indefinite integrals ? cos 2 cos 1 sin , ? 4 9 3 2 2 = + + = dx x x x dx x 3) Solve the following double integrals ? cos ) 3 sin( , ? ) 1 ( 1 0 2 1 0 1 0 2 3 1 0 = = + dxdy x y dxdy y x 4) For which values of the parameter β the following system admits a unique solution Υ Υ Υ Φ Τ ΢ ΢ ΢ Σ Ρ = Υ Υ Υ Φ Τ ΢ ΢ ΢ Σ Ρ Υ Υ Υ Φ Τ ΢ ΢ ΢ Σ Ρ 0 2 1 0 4 2 2 0 2 2 1 1 z y x β β β 5) Solve the limits ? 1 2 1 lim ? 1 2 1 lim ? 4 16 lim ? 4 16 lim 2 1 2 2 2 4 2 2 =
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