Consider and know that the function g defined by 1 g(x, y) = cos (Tx /g) + log3(x – y)* - Answer the following: b) Calculate/solve the instantaneous rate of change of g at the point (4, 1, 2) in the direction of the vector v = (1,2)

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A: This question can be solved by the concept of nature of graphs.

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A: integration

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A: I=∫12 t8-t4t6 dt=∫12 t2-t-2 dtformula: ∫ xn dx=xn+1n+1+C  =t33-t-1-112  =t33+1t12    =83-13+12-1…

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Q: Evaluate the following integrals. Show all the necessary solutions. 2. y In?(1 + 3*) dy 1 + y²

A: I=∫y ln7(1+y2)(1+y2) dyI=∫ y ln(1+y2)7(1+y2) dyln(1+y2)=t1(1+y2) (2y) dy =dty(1+y2) dy=dt2

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A: Here we have h(x,y)=x3-3x+3xy2 .............................................. (1)

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A: This question is related to Functions, we will solve it using given information.

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A: Given problem:-

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A: Use simple integration formula.

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A: topic - application of trigonometry

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A: We have to evaluate given laplace equation.

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A: Given :f'(x)=(x-1)e-x

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A: We can find the area as below.

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A: Here we have to use the Runge-Kutta 4th order method

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A: As per bartleby guidelines we only give first question answers.

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A: Rewrite

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A: Given, Aim: To Find AC

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A: This question is based on indefinite integral.

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Q: +)Use the Runge-Kutta Method SeVelue:.

A: Given y′=(1+1/x)⋅y,y(1)=2.7183,h=0.2,

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A: This is a problem related to calculus. Based on the available concept we will answer the question.…

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A: Vector

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A: A hot cup of tea has temperature T1=198°F, one minute after it has been sitting on the dining table.…