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

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7 Feb 202401:13

Summary

TLDRThe 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.

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CalculusLimitsFactorizationMathematicsEducationProblem SolvingEducational ContentMath TutorialCalculus LessonMath Solution
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