lab1_f11 (1)

lab1_f11 (1) - , ) nd a formula for f-1 . g) If f ( t ) = e...

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Math 116 - Lab 1 - Fall 2011. Functions: exponential, trig, inverses, log, unit-step, hyperbolic (Sections 1.4-1.8 of L-G). You are to provide full solutions to the following problems. You are allowed to collaborate with your classmates, use your notes and textbook and ask the TA for guidance. Direct copying of solutions is not encouraged, nor is it allowed or ethical. Last name: First name: Student number: 1
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Math 116 - Lab 1 - Fall 2011. Student number: Functions: exponential, trig, inverses, log, unit-step, hyperbolic (Sections 1.4-1.8 of L-G) 1. General questions on functions. Justify your answers carefully. a) Given that y ( t ) = t +3 t +4 , g ( t ) = t + 2 and y ( t ) = ( f g )( t ) ±nd f . b) Suppose f is an odd function, and g is an even function. Is the function h ( t ) = f ( t ) /g ( t ) even, odd, or neither? Why? c) If f ( t ) = e 7 t cos8 t ±nd f ( t + 2). d) Solve the equation 3 6 x = 5(9 2 x ). e) Write the expression sec(tan - 1 ( x )) in an equivalent form containing no trigono- metric functions. f) If f ( t ) = log 5 (3 t - 9), over (3
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Unformatted text preview: , ) nd a formula for f-1 . g) If f ( t ) = e 18 t 3-12 , nd f-1 (1). h) For what values of k does the equation log 5 (6 x 2 + 3) = k have no solution. i) Expand the expression log 4 x 6 y 5 ( x + y ) 8 into one that contains several simpler loga-rithms. 2. Questions on unit-step functions (Heaviside functions). a) Express the piecewise dened functions in terms of unit-step functions and draw the graph of each function. i) f ( x ) = 1 , x < 2-x, < x < 2 2 , x > 2 ii) f ( x ) = b sin x, x < 2 + 2 cos x, x > iii) f ( x ) = , x <-1 x-2 ,-1 < x < 3 x-4 , 3 < x < 5 , x > 5 b) Draw the graph of the given functions i) f ( x ) = h ( x 2-1) ii) f ( x ) = 5 h (4-x 2 ) 3. Questions on hyperbolic functions . a) Evalutate 3 cosh1 b) Show that sinh-1 ( x ) = ln p x + r x 2 + 1 P 2...
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lab1_f11 (1) - , ) nd a formula for f-1 . g) If f ( t ) = e...

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