What is the value of k for which the function f(x) = { kx, x < 2; x^2, x >
Practice Questions
Q1
What is the value of k for which the function f(x) = { kx, x < 2; x^2, x >= 2 } is continuous at x = 2?
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4
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Questions & Step-by-Step Solutions
What is the value of k for which the function f(x) = { kx, x < 2; x^2, x >= 2 } is continuous at x = 2?
Step 1: Understand that we want the function f(x) to be continuous at x = 2.
Step 2: Recall that for a function to be continuous at a point, the left-hand limit and the right-hand limit at that point must be equal to the function's value at that point.
Step 3: Identify the two parts of the function: f(x) = kx for x < 2 and f(x) = x^2 for x >= 2.
Step 4: Calculate the value of the function as x approaches 2 from the left (using kx). This gives us f(2) = k(2) = 2k.
Step 5: Calculate the value of the function as x approaches 2 from the right (using x^2). This gives us f(2) = 2^2 = 4.
Step 6: Set the two values equal to each other: 2k = 4.
Step 7: Solve for k by dividing both sides of the equation by 2: k = 4 / 2.
