Use the graph of \(f(x)\) to fill in the blanks. If a value does not exist, type DNE.   \(\displaystyle\lim_{x\to 4^-}f(x)=\) \(\displaystyle\lim_{x\to 4^+}f(x)=\) \(\displaystyle\lim_{x\to 4}f(x)=\) \(f(4)=\) Is \(f(x)\) continuous at \(x=4\)?

Numerically estimate \(\displaystyle\lim_{x\to 3^-}\left(1.25^x-0.1x\right),\) accurate to two decimal places. Fill in the table according to the conventions we have used in the textbook, practice problems, and homework.   \(x\to 3^-\) \(1.25^x-0.1x\) 2.9 We conclude that \(\displaystyle\lim_{x\to 3^-}\left(1.25^x-0.1x\right)=\)   Desmos (click to reveal)

Use the information below to answer the two (2) following questions:An inventor develops a stationary cycling device by which an individual, while pedaling, can convert all of the energy expended into heat for warming water. How much mechanical energy is required to increase the temperature of 300 g of water (enough for 1 cup of coffee) from 20°C to 95°C? (1 cal = 4.186 J, the specific heat of water is 4 186 J/kg⋅°C)

Use the information below to answer the four (4) following questions: A piston containing 1.0 mole of an ideal monatomic gas undergoes the following cycle: (i.) isochoric heating increasing pressure from 2 kPa to 5 kPa (ii.) isobaric expansion from 2 m3 to 8 m3(iii.) isochoric cooling decreasing pressure from 5 kPa to 2 kPa(iv.) isobaric contraction from 8 m3 to 2 m3Remember:  R = 8.314 J/mol K, cv mol = 12.47 J/mol K Calculate the temperature of the gas when it is at the point labeled a on the PV diagram.

Use the information below to answer the three (3) following questions: A cylindrical grindstone of mass m = 18 kg and radius R = 0.8 m is initially rotating freely at 26π radians/s.  An axe is brought into contact with the grindstone which brings it to a stop after 30 revolutions. What is the magnitude of the angular acceleration of the grindstone?

In the figure, R1 = R2 and cm represents the center of mass of the object.  The rotational inertia about an axis through point P1 is I1, the rotational inertia about an axis through point P2 is I2, and the rotational inertia about an axis through the cm is Icm.  The relationship among the moments is

Use the information below to answer the four (4) following questions: A piston containing 1.0 mole of an ideal monatomic gas undergoes the following cycle: (i.) isochoric heating increasing pressure from 2 kPa to 5 kPa (ii.) isobaric expansion from 2 m3 to 8 m3(iii.) isochoric cooling decreasing pressure from 5 kPa to 2 kPa(iv.) isobaric contraction from 8 m3 to 2 m3Remember:  R = 8.314 J/mol K, cv mol = 12.47 J/mol K How much heat flows into the system during step (i)?  

Use the information below to answer the two (2) following questions:A 50.0-gal steel container is filled completely with carbon tetrachloride when the temperature is 10.0°C.   The coefficient of volume expansion for carbon tetrachloride is β = 5.81 × 10-4 (°C)-1, and the coefficient of linear expansion for steel is α = 11 × 10-6 (°C)-1. How much of the carbon tetrachloride will spill over when the termpature rises to 30.0°C?

Use this information to answer the three (3) following questions: A mass m = 3 kg is placed on an ideal spring with spring constant k = 185 N/m and is free to oscillate on a horizontal surface with no friction.  The mass is pulled 16 cm to the left of equilibrium and released at t = 0 s. What is the maximum speed the mass attains as it oscillates on the spring?

A blimp is filled with 200 m3 of helium. How much mass can the balloon lift? The density of helium is 1/7 that of air, and the density of air is 1/800 that of water.  (ρwater = 1000 kg/m3)