Podcast
Questions and Answers
What is the solution for the equations x+y-4=0 and x^2-y-8=0?
What is the solution for the equations x+y-4=0 and x^2-y-8=0?
As x approaches infinity, what is the limit of the expression x^2 + 1/x?
As x approaches infinity, what is the limit of the expression x^2 + 1/x?
What are the values of x that satisfy the equations y + 3x = 14 and x^2 - y = 14?
What are the values of x that satisfy the equations y + 3x = 14 and x^2 - y = 14?
What is the limit of the expression 5x + 1 / (10 + x) as x approaches infinity?
What is the limit of the expression 5x + 1 / (10 + x) as x approaches infinity?
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Which pair of values solves the equations 2x - y = 7 and x^2 + y - 8 = 0?
Which pair of values solves the equations 2x - y = 7 and x^2 + y - 8 = 0?
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Study Notes
Systems of Equations Solutions
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System 1: ( x + y - 4 = 0 ) and ( x^2 - y - 8 = 0 )
- Solutions: ( x = 3 ) and ( x = -4 )
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System 2: ( 2x - y = 7 ) and ( x^2 + y - 8 = 0 )
- Solutions: ( x = -5 ) and ( x = 3 )
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System 3: ( y + 3x = 14 ) and ( x^2 - y = 14 )
- Solutions: ( x = -7 ) and ( x = 4 )
Limits of Expressions as ( x ) Approaches Infinity
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Expression 1: ( x + \frac{1}{x^2} )
- Limit as ( x ) approaches infinity: ( 0 )
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Expression 2: ( x^2 + \frac{1}{x} )
- Limit as ( x ) approaches infinity: ( \infty )
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Expression 3: ( \frac{5x + 1}{10 + x} )
- Limit as ( x ) approaches infinity: ( 2.5 )
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Description
This quiz covers solving systems of equations and determining the limits of various expressions as x approaches infinity. Students will practice finding solutions for both linear and quadratic equations and learn to analyze the behavior of functions at infinity.
