Math Problem Statement
Solution
Let's break this down and solve each part step by step. The function given is:
1.
We need to substitute into the function :
2.
Substitute into the function :
Now expand each term:
3.
We now calculate :
Simplify the expression inside the numerator:
Now factor out in the numerator:
Since , cancel out :
Final answers:
Let me know if you'd like more details or have any other questions!
Here are some related questions for practice:
- What is (the derivative of )?
- What happens to as ?
- How would you interpret the expression geometrically?
- How would change if the coefficient of were different?
- Can you compute for the general function ?
Tip: Always expand and simplify carefully to avoid mistakes when calculating limits or differences in functions!
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Math Problem Analysis
Mathematical Concepts
Algebra
Functions
Limits
Difference Quotient
Formulas
f(x) = 6x^2 + 5x
Difference Quotient = (f(a + h) - f(a)) / h
Theorems
Basic function evaluation
Expansion of binomials
Suitable Grade Level
Grades 10-12
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