SIC] foreign minus sine t j plus e raised to 3 d k. Okay, find d r by d d, and d square r formula D by dt of e raised to 80 n1 e raised to 80 into 80 foreign.04:41Um, if r of t is equal to t, square I plus e raised to t, j minus 2, cos pi t k. Find dash of t. If r of t is equal to tan inverse t plus t into cos t j minus 2 root t k, tan inverse t I plus t into cos t j minus 2 root t k.07:24Okay, helpful D by d x of tan inverse x, and then d by dx of tan inverse x is equal to 1 by 1 plus x square at the t into cosine product r. dash of t is equal to equal to tan inverse theta derivative formula. Okay, but again, sine phi by 2 one nano cos pi, [applause] is minus 2 into Uh, sine pi by four, sine pi by four, then one by root two into k n minus e two root two cancel number root two i minus root two k negative Either Promising Three markers at the point is equal to pi.13:48Okay, is equal to my factor r of t Is equal to c t i plus time t j. Uh time dj T letter written enough c t panty into i. Okay, time t derivative d by d x of tan x Is equal to c square x.14:58Um, uh, tiny is equal to c 0, tan 0. i plus c square 0 j 0 cosine square known by square [music] e raised to minus t j plus t raised to 4 k. Find find r dash of t at t is equal to 2..16:18differentiate minus 1 into j plus t raised to 484 t cube into k. I'm going to find the entire r dash of t at t is equal to two. Final t two would come either one by two i minus e raise to minus two j plus 4 into 2, cube 4 into 2, cube 1, and the 4 into 8, 4 into 8, 1 and 3 and 32 k. Calculus of Vector Functions |MAT102 | Module 1| S2 |KTU Part 1 Last-Minute Limits Study Sheet Essential Standard Limits These fundamental limits are crucial for evaluating indeterminate forms, especially , and are frequently tested in calculus. Sine Limit: This is a foundational limit often used to simplify and solve more complex trigonometric limit problems. Tangent Limit: This limit is analogous to the sine limit and can be derived from it. Cosine Limit (Type 1): This limit is useful in various contexts, including the definition of derivatives. Cosine Limit (Type 2): This specific limit is very important, with its result of often appearing in problems. Hints from the content point towards a calculation resulting in from . General Limit Concepts While specific "tricks" are not explicitly detailed, the concept of applying limits to problems is highlighted. Understanding basic limit properties (e.g., limits of sums, products, quotients) is essential for solving problems efficiently.