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In this lesson, we will learn how to find the instantaneous rate of change for a function using limits.

Q1:

Evaluate the rate of change of π ( π₯ ) = 2 π₯ + 9 2 at π₯ = β 3 .

Q2:

Evaluate the rate of change of π ( π₯ ) = π₯ β 3 π₯ + 2 2 at π₯ = 5 .

Q3:

Find the rate of change of 5 π₯ β 1 8 3 with respect to π₯ when π₯ = 2 .

Q4:

Evaluate the rate of change of π ( π₯ ) = β 9 4 π₯ β 7 at π₯ = 4 .

Q5:

Find the rate of change of π ( π₯ ) = 4 π₯ β π₯ β 3 2 when π₯ = 1 and determine, to the nearest minute, the positive angle between the tangent at ( 1 , 0 ) and the positive π₯ -axis.

Q6:

Evaluate the rate of change of π ( π₯ ) = β 6 π₯ + 7 at π₯ = 3 .

Q7:

Determine the rate of change of the function π ( π₯ ) = 5 9 π₯ at π₯ = β 2 .

Q8:

If the function π ( π₯ ) = 5 π₯ + 7 4 π₯ + 2 , determine its rate of change when π₯ = 2 .

Q9:

A length π is initially 9 cm and increases at a rate of 3 cm/s. Write the length as a function of time, π‘ .

Q10:

Evaluate the rate of change of π ( π₯ ) = 9 π₯ β 4 7 π₯ at π₯ = 3 .

Q11:

What is the rate of change for the function π¦ = 4 π₯ + 7 ?

Q12:

A circular disc preserves its shape as it shrinks. What is the rate of change of its area with respect to radius when the radius is 59 cm?

Q13:

Evaluate the rate of change of π ( π₯ ) = 7 π₯ + 9 2 at π₯ = π₯ 1 .

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