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During a psychology class, students learn about different types of learning processes. A student named Sarah suddenly figures out how to solve a complex math problem after thinking about it for a while, which illustrates the concept of __________. Meanwhile, John has been watching his older sister play the piano for months and, without explicit instruction, is now able to play a simple song by mimicking her actions; this demonstrates __________. Finally, another student, Alex, remembers how to navigate a maze he practiced earlier, even though he didn’t show any signs of learning during the initial trials, showcasing __________. Which of the following best fills in the blanks?  

Use Lagrange multipliers to minimize the function subject to the following constraint.​

Use Lagrange multipliers to find the maximum and the minimum value of  subject to the constraint

Use Lagrange multipliers to find the maximum value of where and subject to the constraint .​

Find the limit. ​ ​

The radius r and height h of a right circular cylinder are measured with possible errors of 6% and 2%, respectively. Approximate the maximum possible percent error in measuring the volume.  

Find symmetric equations of the normal line to the surface  at the point .​

Use the Chain Rule to find .

31) How can Jupiter generate so much internal heat?

8) The age of our solar system is approximately