Vault Of Euclid

Limit of an Integral Using the Definition of the Derivative

The definite integral core

Find \( \lim_{h \to 0} \frac{1}{h} \int_{2}^{2+h} \sqrt{t^{2}+2} \, dt \).
calculus-idefinite-integrallimitderivative-definitionfundamental-theorem-of-calculusevaluate-limitdifference-quotientintegration

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What this problem tests

Tests the ability to recognize the limit definition of a derivative in an unfamiliar context and to apply the First Fundamental Theorem of Calculus.

This type of problem frequently appears in Calculus I exams to test the understanding of the connection between limits, derivatives, and integrals.

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