Answer:
[tex]k=\frac{22}{3}[/tex]
Step-by-step explanation:
The oblique asymptote of
[tex]f(x)=\frac{9x^2+37x+41}{3x+5}[/tex],
We perform the long division as shown in the attachment.
The quotient is;
[tex]3x+\frac{22}{3}[/tex]
Comparing to 3x+k
Hence the value of k is [tex]\frac{22}{3}[/tex]
Answer:
[tex]\frac{22}{3}[/tex]
Step-by-step explanation:
To find out oblique asymptote we divide the polynomials using long division
To find quotient divide the first term. then multiply the answer with 3x+5 and write it down. Subtract it from the top. Repeat the process till we get remainder.
[tex]3x+\frac{22}{3}[/tex]
------------------------------
[tex]3x+5[/tex] [tex]9x^2+37x+41[/tex]
[tex]9x^2+15x[/tex]
-------------------------------------(Subtract)
[tex]22x+41[/tex]
[tex]22x+\frac{110}{3}[/tex]
------------------------------------(subtract)
[tex]\frac{13}{3}[/tex]
Quotient is [tex]3x+\frac{22}{3}[/tex] that is our oblique asympotote
the value of k is 22/3
