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Calculus – Linear Equations Practice Set · 2

Calculus · Calculus

Course: Calculus Book: Calculus

Question

Question:
Find the slope of the tangent line to g of x equals the square root of x, at x equals 9.

Calculus – Linear Equations Practice Set · 2

This lesson finds the slope of the tangent line to g(x) = √x at x = 9 using the limit definition of the derivative. The key technique is rationalizing the numerator with a conjugate to resolve the indeterminate form, then verifying the result with the Power Rule.

In this lesson, you will learn to:
• Apply the limit definition of the derivative to evaluate g′(a) for a given function and point
• Rationalize a difference-of-square-roots expression in a difference quotient to eliminate an indeterminate form
• Cancel common factors in the simplified difference quotient and evaluate the resulting limit by direct substitution
• Verify a limit-definition result using the Power Rule

Course: Calculus
Level: Grade 12

Pause before each step, try the nex

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