To determine if the given function f is continuously differentiable on R, we need to check if its derivative exists and is continuous on the entire real line. If the derivative of f exists and is continuous for all x in R, then f is continuously differentiable on R. If the derivative does not exist or is not continuous at any point in R, then f is not continuously differentiable on R. **

To show that g(x) is continuous at 0 if and only if f(r, r) is differentiable at 0, we can use the definition of continuity and differentiability. First, if g(x) is continuous at 0, then for any ε > 0, there exists a δ > 0 such that |x| < δ implies |g(x) - g(0)| < ε. Then, for f(r, r) to be differentiable at 0, we need to show that the limit as (x, y) approaches (0, 0) of (f(x, y) - f(0, 0) - L(x-0) - M(y-0))/(√(x^2 + y^2)) = 0, where L = ∂f/∂x and M = ∂f/∂y. This limit will be 0 if and only if g(x) is continuous at **

The Yamaha WR250R is better suited for off-road and long-distance riding, with a more powerful engine and better suspension. On the other hand, the Yamaha WR250F is designed for motocross and off-road racing, with a lighter weight and more aggressive power delivery. Ultimately, the choice between the two depends on the rider's specific needs and intended use for the bike. **

The maintenance costs for a Jaguar F-Type R can vary depending on factors such as the age of the vehicle, mileage, and any warranty coverage. On average, owners can expect to pay around $1,000 to $2,000 per year for routine maintenance, which includes oil changes, brake pad replacements, and other regular services. However, costs can increase significantly for more extensive repairs or if the vehicle is out of warranty. It is recommended to budget for these potential expenses when considering ownership of a Jaguar F-Type R. **

The Jaguar F-Pace R-Sport 25d comes with a 2.0-liter turbocharged diesel engine, while the 30d model is equipped with a 3.0-liter V6 diesel engine. The 25d offers a good balance of power and fuel efficiency, while the 30d provides more power and torque for a sportier driving experience. Both engines are known for their smooth performance and responsiveness, making them popular choices among Jaguar F-Pace buyers. **

The Jaguar F-Pace R-Sport is available with both the 25d and 30d engines. The 25d is a 2.0-liter turbocharged diesel engine, while the 30d is a 3.0-liter V6 turbocharged diesel engine. The 25d engine produces 178 horsepower, while the 30d engine produces 296 horsepower, providing a significant difference in performance between the two options. **

The answer to which motorcycle is better, the BMW F 900 R or the Yamaha MT-07, ultimately depends on individual preferences and needs. The BMW F 900 R offers a more powerful engine and advanced features like electronic aids and connectivity options, making it a great choice for riders looking for a high-performance and technologically advanced bike. On the other hand, the Yamaha MT-07 is known for its lightweight and agile handling, making it a popular option for riders who prioritize maneuverability and fun in their riding experience. Riders should consider factors such as riding style, preferences, and budget when choosing between these two motorcycles. **

The value of your Mega Bee in F R (Fossil Robo) can vary depending on its condition, rarity, and demand in the trading market. To determine its value, you can try researching recent trades or sales of similar Mega Bees in F R, or seek the assistance of experienced traders or collectors in the Fossil Robo community. Keep in mind that the value of virtual items in trading games can fluctuate, so it's important to stay updated on the current market trends. **