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Find a and b so that the rational function f(x) = (ax^4 + bx^3 + 3) / (x^3 - 2) has an oblique asymptote given by y = 2x - 3

 Aug 25, 2018
 #1
avatar+94209 
+2

Performing polynomial divsion...we have....

 

                ax      +  b

 x^3 - 2  [ ax^4   + bx^3  +   0x     +   3  ]

                ax^4                   -2ax

              _______________________

                            bx^3   + 2ax    +  3

                            bx^3                 -2b

                          ________________

                                       2ax  + (3 + 2b)

 

We  need to  have ax + b  = 2x  - 3

So

 

ax  +  b  =  2x  - 3

a =2   b = -3

 

cool cool cool

 Aug 25, 2018

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