Please help me with questions 3 and 4 of this homework. Thanks Descriptionf(x) == What is1 a) Consider the functionits domain? b) Now consider the functiong(x, y) =What is its domain? c) What isthe domain of the function h (x, y) = √√x+y? d) What is the domain of the functionk (x, y) =√2+8?2 Suppose that I (r, y, z) represents thetemperature at the point (x, y, z), measured in8TKelvin. What are the units of ax, if "x" ismeasured in miles? What about the units of²T82² ?3) Suppose f(",) is a differentiable function.a) If (a, b) is a critical point of f(x, y) (in theafsense that(a,b)-0,(a,b) - 0Will(a, b) be a critical point ofg(x, y) = (f (r. y))²? b) if (a, b) is a criticalpoint of 9 (x, y) = (f (x, y))², in the sense(a, b) = 0,(a, b) = 089that dewill (a, b)be a critical point of f(x,y)? hint: how are thepartial derivatives of f(x,y) and g(x, y)related?94) Suppose that the level curves of a functionz = f(x, y) consists of straight lines. Must thegraph of be a plane?5) In thermodynamics, the ideal gas law statesthatPVNKTHereN,k are constants• P is the pressure of the gas. V is the volume of the container. T is the temperature.Notice that you can play with this equation inseveral ways. For example:• You can think of P as a function of V and TP =NKTvia the equationV. So you canOP OPfind the partial derivatives T¹ V. You can think of T as a function of P and VT -PV=via the equationNk. So you can find8TOT Tthe partial derivativesP¹ av• You can think of V as a function of P and TV =NKTvia the equationP. So you canavavfind the partial derivatives OP Ta) What do you thinkOP OT BVST OV DPwill be equal to, based on a "naive" manipulationof the symbols? Similar to how "naively onedydy dadzd in the case of the chainwrites drule?b) What do you actually find if you do theproduct of these partial derivatives? [hint: thereis a video on our Canvas sites:Thermodynamics and Partial Derivatives, aCautionary Tale, where I go over this.]

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Please help me with questions 3 and 4 of this homework. Thanks Descriptionf(x) == What is1 a) Consider the functionits domain? b) Now consider the functiong(x, y) =What is its domain? c) What isthe domain of the function h (x, y) = √√x+y? d) What is the domain of the functionk (x, y) =√2+8?2 Suppose that I (r, y, z) represents thetemperature at the point (x, y, z), measured in8TKelvin. What are the units of ax, if &#34;x&#34; ismeasured in miles? What about the units of²T82² ?3) Suppose f(&#34;,) is a differentiable function.a) If (a, b) is a critical point of f(x, y) (in theafsense that(a,b)-0,(a,b) - 0Will(a, b) be a critical point ofg(x, y) = (f (r. y))²? b) if (a, b) is a criticalpoint of 9 (x, y) = (f (x, y))², in the sense(a, b) = 0,(a, b) = 089that dewill (a, b)be a critical point of f(x,y)? hint: how are thepartial derivatives of f(x,y) and g(x, y)related?94) Suppose that the level curves of a functionz = f(x, y) consists of straight lines. Must thegraph of be a plane?5) In thermodynamics, the ideal gas law statesthatPVNKTHereN,k are constants• P is the pressure of the gas. V is the volume of the container. T is the temperature.Notice that you can play with this equation inseveral ways. For example:• You can think of P as a function of V and TP =NKTvia the equationV. So you canOP OPfind the partial derivatives T¹ V. You can think of T as a function of P and VT -PV=via the equationNk. So you can find8TOT Tthe partial derivativesP¹ av• You can think of V as a function of P and TV =NKTvia the equationP. So you canavavfind the partial derivatives OP Ta) What do you thinkOP OT BVST OV DPwill be equal to, based on a &#34;naive&#34; manipulationof the symbols? Similar to how &#34;naively onedydy dadzd in the case of the chainwrites drule?b) What do you actually find if you do theproduct of these partial derivatives? [hint: thereis a video on our Canvas sites:Thermodynamics and Partial Derivatives, aCautionary Tale, where I go over this.]

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