Go to page 125 for the analysis question. Determine whether the given improper integral converges or diverges, and calculate its value if it converges. Link: [https://drive.google.com/file/d/1RQ2OZK-LSxpRyejKEMg1t2q15dbpVLCS/view? usp=sharing] Include detailed reasoning.

A motorist starts braking for a stop sign. After t seconds, the distance, inmetres, from the front of the car to the sign is s(t) = 62 - 16t + t^2.a. How far was the front of the car from the sign when the driver startedbraking?b. Does the car go beyond the stop sign before stopping?c. Explain why it is unlikely that the car would hit another vehicle that istravelling perpendicular to the motorist's road when the car first comes toa stop at the intersection.

Find the area of the shaded region.

An inflatable pumpkin and a ghost are connected with an airpump. As the pumpkin deflates, the ghost inflates, then the process reverses. Assume that no air is leaking out, only moving between the pumpkin and the ghost. In addition, assume that the approximate shape of the pumpkin is a sphere, and the approximate shape of the ghost is a cone. The pumpkin’s radius is decreasing by 0.5 inches per second. Assume that the ghost’s height is always 10 times the radius of its base. Find the rate at which the ghost’s height is increasing at the moment when the diameter of the pumpkin is 40 inches, and the radius of the ghost’s base is 10 inches.

y = In( sech2x)

Differentiate y = 3e2x/(1 + x2.)

The figure gives the time it takes a Mitsubishi Eclipse GSX to reach speeds from 0 mph to 100 mph, in increments of 10 mph, with a curve connecting them. оо Speed (mph) Yes 100 No 80 60 40 This car will travel 20 The area under this curve from t = 0 seconds to t = 21.1 seconds represents the total amount of distance traveled over the 21.1-second period. Count the squares under the curve to estimate this distance (in miles). (Be careful with time units. Round your answer to two decimal places.) miles 4 8 12 16 20 Elapsed Time (seconds) X 1 4 1 mile in 15.4 seconds, to a speed of 89.0 mph, so your estimate should be more than mile. Is it? 4

Find the area of the region bounded by f(x)=-x^2+6x-5, the x axis, and the lines x=2 and x=5. Graph and shade the bounded area for the function fx

You are constructing a box out of cardboard with the dimensions 2 m by 3 m. You then cut equal-size squares from each corner so you may fold the edges. Find a that maximizes the volume of the box. Answer exactly. Preview TIP Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4) Enter DNE for Does Not Exist, oo for Infinity

A car drives with velocity v(t)=2.8+t meters per second. How far does the car drive in 8 seconds? Please report yoL