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Anyone can solve these questions? (4) Let if (z, y)メ(0,0) if (x, y) (0,0) f(z, y)... Anyone can solve these questions?

(4) Let if (z, y)メ(0,0) if (x, y) (0,0) f(z, y) / 0 a) Show that f is a continuous function b) Show that f has partial derivatives at (0,0) and find (0,0) as well as c) Is f differentiable at (0, 0)? d) Are the partial derivatives r tinuous at (0,0)? (0,0) (5) Let A E M(mx n,R) and f : RnRm be the linear map f(x)-Ax. Show that f is a differentiable function and find the derivative of f. (6) The pressure P (in kilopascals), volume V (in liters), and temperature T (in kelvins) of a mol of an ideal gas are related by the equation P. V-8.31 . T. a) Find the rate at which the pressure is changing when the temperature is 300K and increasing at a rate of 0.1K/s and the volume is 100L and increasing at a rate of 0.2L/s b) Find the rate at which the volume is changing when the temperature is 320K and increasing at a rate of 0.15K/s and the pressure is 20kPa and increasing at a rate of 0.05kPa/s (7) Let g(t) = (at, bt) for a,be R and if(x, y) if (x, y) (0,0) (0,0) f(x, y) 0 a) Show that f has partial derivatives at (0,0) and find 쓿(0,0) as well as (0,0) Use these to show that ▽f(0,0) . g'(0) b) Show that f og is differentiable and 0 c) Explain why the results of a) and b) do not contradict the Chain Rule    Earn Coins

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