To solve the problem, we need to:
1. Evaluate [tex]\( f(1) \)[/tex]
2. Evaluate [tex]\( g(1) \)[/tex]
3. Compute [tex]\( f(1) \div g(1) \)[/tex]
Let's go through each step in detail.
### Step 1: Evaluate [tex]\( f(1) \)[/tex]
The function [tex]\( f(n) \)[/tex] is given by:
[tex]\[ f(n) = 2n^3 + 5n \][/tex]
Substituting [tex]\( n = 1 \)[/tex] into the function:
[tex]\[ f(1) = 2(1)^3 + 5(1) \][/tex]
[tex]\[ f(1) = 2 \cdot 1 + 5 \cdot 1 \][/tex]
[tex]\[ f(1) = 2 + 5 \][/tex]
[tex]\[ f(1) = 7 \][/tex]
So, [tex]\( f(1) = 7 \)[/tex].
### Step 2: Evaluate [tex]\( g(1) \)[/tex]
The function [tex]\( g(n) \)[/tex] is given by:
[tex]\[ g(n) = n + 3 \][/tex]
Substituting [tex]\( n = 1 \)[/tex] into the function:
[tex]\[ g(1) = 1 + 3 \][/tex]
[tex]\[ g(1) = 4 \][/tex]
So, [tex]\( g(1) = 4 \)[/tex].
### Step 3: Compute [tex]\( f(1) \div g(1) \)[/tex]
We have:
[tex]\[ f(1) = 7 \][/tex]
[tex]\[ g(1) = 4 \][/tex]
Now, compute the division:
[tex]\[ \frac{f(1)}{g(1)} = \frac{7}{4} \][/tex]
Evaluating the fraction:
[tex]\[ \frac{7}{4} = 1.75 \][/tex]
### Final Answer
Thus, the value of [tex]\( f(1) \div g(1) \)[/tex] is [tex]\( 1.75 \)[/tex].
To summarize, we found:
- [tex]\( f(1) = 7 \)[/tex]
- [tex]\( g(1) = 4 \)[/tex]
- [tex]\( f(1) \div g(1) = 1.75 \)[/tex]
