Basic Calculus Culminating Performance Task Part 1 First Grading AY 2023-2024 This is a group activity (maximum of 5 members) and is worth 20 points. Be careful in solving each problem. Use short bond paper with 1" on all red margins and color. All answers should be handwritten in blue or black ink only. 1. Evaluate lim_{x o 2} (x^2 - 4) / (x - 2) algebraically. Show complete solution. 2. Find the value of the constant k that makes the function continuous. Show the complete solution. g(x) = { x^2 - k, if x < 2; kx + 4, if x ? 2 } 3. Explain in 2 to 3 sentences. A friend who is confused about limits asks you why we investigate the value of a function closer and closer to a point, instead of just finding the value of a function at the point. How would you explain this to your friend? 4. Determine whether the function f(x) is (a) continuous and (b) differentiable. Show complete proof. f(x) = { x^2 - 3, if x ? 2; 2x, if x > 2 } 5. Find the slope and the equation of the tangent line (in standard form) to the curve y = x^2 - 4x - 6 at the point (1, -9). Show complete solution and graph.
