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Evaluating a limit using the definition of a derivative #apcalculus #calculus #apcalcab #derivatives #mathteacher

Math With Yosh

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39,900 次观看 • 2 个月前 •via TikTok

教育 #apcalculus #calculus #apcalcab #derivatives #mathteacher

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An MIT professor explained the one idea funds pay $500K for, and he does it in the first hour of freshman calculus. MIT put the whole lecture online. it has been free for twenty years. almost nobody finishes it. his point: calculus is not a hundred formulas to memorize. it is one idea. take two points on a curve, slide them together until the gap vanishes, and the slope you are left with is the derivative. everything else is just consequences. he is David Jerison, and his 18.01 lectures have taught more people calculus than any room on earth. skip to the board, where the power rule, the product rule, the chain rule, the fifty things you were forced to memorize, all fall out of that one limit. no formula sheet. no tricks. one definition, reused. that same slope is velocity. it is marginal cost. it is the gradient that trains a neural network. one operation, hiding everywhere something moves. the math is free. what nobody can sell you is the patience to understand the one limit instead of cramming the fifty formulas that fall out of it. that hour is the foundation, and it is the only part that ever pays.

An MIT professor explained the one idea funds pay $500K for, and he does it in the first hour of freshman calculus. MIT put the whole lecture online. it has been free for twenty years. almost nobody finishes it. his point: calculus is not a hundred formulas to memorize. it is one idea. take two points on a curve, slide them together until the gap vanishes, and the slope you are left with is the derivative. everything else is just consequences. he is David Jerison, and his 18.01 lectures have taught more people calculus than any room on earth. skip to the board, where the power rule, the product rule, the chain rule, the fifty things you were forced to memorize, all fall out of that one limit. no formula sheet. no tricks. one definition, reused. that same slope is velocity. it is marginal cost. it is the gradient that trains a neural network. one operation, hiding everywhere something moves. the math is free. what nobody can sell you is the patience to understand the one limit instead of cramming the fifty formulas that fall out of it. that hour is the foundation, and it is the only part that ever pays.

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