Jika lim x->-3 (x^2+4x+3)/(x+3)=a-1,nilai a adalah...

Summary

The script discusses a mathematical problem-solving approach involving limits. It explains the process of factoring the numerator and then canceling out common factors with the denominator to simplify the expression. The example given involves a limit as x approaches -3, where the function simplifies to x + 1. Substituting x with -3, the limit is calculated, leading to the conclusion that the value of 'a' is -1. The explanation is aimed at helping viewers understand the concept of limits in calculus.

Takeaways

• 🔢 The problem involves finding the limit of a function as x approaches -3.
• 📐 The first step is to factorize the numerator of the given expression.
• 🔄 The expression simplifies by canceling out the common factor (x + 3) from the numerator and the denominator.
• ✅ The limit is then calculated by substituting x with -3 in the simplified expression.
• 📘 The simplified expression after factorization and cancellation is 'x + 1'.
• 👉 The substitution of x = -3 into the simplified expression yields -3 + 1.
• 💡 The result of the substitution is equated to a variable 'a', which is part of the problem setup.
• 📌 The equation formed is -2 = a - 1, which is derived from the substitution.
• 🔑 Solving the equation for 'a' gives the value of 'a' as -1.
• 📝 The final answer to the problem is that the value of 'a' is -1.

Q & A

What is the first step in solving the problem presented in the script?

The first step is to factor the numerator of the given expression.

What does the script suggest to do with the denominator of the expression?

The script suggests canceling out the common factor in the numerator and the denominator, which is (x + 3).

What is the value that x approaches in the limit discussed in the script?

The value that x approaches in the limit is -3.

What is the simplified form of the function after canceling out the common factor?

After canceling out the common factor (x + 3), the simplified form of the function is x + 1.

What is the significance of substituting x with -3 in the simplified function?

Substituting x with -3 allows us to evaluate the limit as x approaches -3.

What is the result of substituting x = -3 into the simplified function x + 1?

The result of substituting x = -3 into the simplified function x + 1 is -3 + 1, which equals -2.

How does the script relate the result of the limit to the variable 'a'?

The script sets the limit equal to 'a' minus 1, so -2 = a - 1.

What is the value of 'a' calculated in the script?

The value of 'a' is calculated to be -1, as -2 + 1 equals a.

What is the final answer to the problem according to the script?

The final answer to the problem is that the value of 'a' is -1.

What does the script imply about the relationship between the limit and the variable 'a'?

The script implies that the limit as x approaches -3 is equal to the value of 'a' minus 1.