The speed of a runner increased steadily during the first three seconds of a race. Her speed at half-second intervals is given in the table. Find lower and upper estimates for the distance that she traveled during these three seconds. t (s) 0 0.5 1.0 1.5 2.0 2.5 3.0 v (ft/s) 06.2 10.8 14.9 18.1 19.4 20.2 Step 1 We will use either L6 or R6 for the upper and lower estimates. Since the runner's speed is an increasing function, then 0 X will give the lower estimate, and 45.1 X will give the upper estimate.

Q: The total stopping distance T of a vehicle is shown below, where T is in feet and x is the speed in…

A:

Q: Sylvia works in a gardening store. She graphed the growth of a tomato plant. a) What is the rate of…

A: We have to find a)Rate of change in height of tomato plant in centimeter per day b)Rate of change in…

Q: The following formula gives the relationship between the thoracic mass of the butterfly and its mean…

A:

Q: If a person learns y items in æ hours, as given by y = 19V2?, find the rate of learning for a person…

A: We need to find the rate of learning.

Q: Garrett planted some parsley seeds in his garden and has been measuring their weeks. Week 12 Height…

A: (a) Calculate the increase in growth of plants from week 1-2, week 2-3 and week 3-4. week 1-2…

Q: A tire swing moving back and forth in the wind can be modelled by the equation d(t) = 5sin (t),…

A: To find the rate of change of Therefore, the rate of change,

Q: A balloon is rising at a constant speed of 3 ft/s. An insect is flying in a straight line at 10…

A: Let, D=distance between the balloon and insect at time t. h=height x=distance travelled by insect.

Q: The acceleration of a particular sports car is proportional to the difference between 300 km/h and…

A: We will find the time.

Q: X 0-2 2 y Y = Ln(y) X² XY 0.4 0.2 0.60.4 0.80.6 10.8

A:

Q: The table gives distance d versus time t for a downhill skier.   Estimate the speed of the skier at…

A: Given,         The table gives distance d versus time t for a downhill skier.

Q: Given the information below, estimate the total distance travelled during these 6 seconds using…

A: Given query is to find the total distance traveled.

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.