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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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