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Astronomers discover a fascinating atmosphere on exoplanet LTT 9779 b a scorching Neptune-sized planet. Learn about the findings from the James Webb Space Telescope. READ MORE...

Learn how projectors create black. Discover the physics behind the absence of light and how it’s perceived as black on a screen. READ MORE...

Learn about static electricity from everyday sparks to lightning. Discover causes examples like shocks from metal and how to prevent it. READ MORE...

Struggling with functional equations for your math midterm? This post provides tips and tricks including substituting values using mathematical induction and finding fixed points to help you solve these challenging problems. READ MORE...

Conquer the CBSE Board Exams 2025 with our guide! Learn effective study strategies, time management tips, and overcome exam anxiety for success. READ MORE...

Find \( \lim_{x \to 3} (2x + 5) \) Solution:To solve this limit, we substitute the value of \( x \) directly because the function is continuous at \( x = 3 \).\( \lim_{x \to 3} (2x + 5) = 2(3) + 5 = 6 + 5 = 11 \) READ MORE...

5 Basic Problems on Limits just to refresh your mind. Problem 1 Find the limit: \( \lim_{x \to 2} (3x - 4) \) Solution: To solve this limit, we substitute the value of \(x\) directly because the function is continuous at \(x = 2\). \[ \lim_{x \to 2} (3x - 4) = 3(2) - 4 = 6 - 4 = 2 \] Problem 2 Find the limit: \( \lim_{x \to 0} \frac{\sin x}{x} \) Solution: This is a standard limit. The result is known and is based on the squeeze theorem: \[ \lim_{x \to 0} \frac{\sin x}{x} = 1 \] Problem 3 Find the limit: \( \lim_{x \to 3} \frac{x^2 - 9}{x - 3} \) Solution: This function is not […] READ MORE...