X 1 (A) If g tan , find the derivative 1² +2 yz of g at point (1,2,-1) in the direction of the normal vector of the curve represented by 7 at t-1. √( ² + 1 ) + (1² + 2₁) j and F = In

Q: b) Consider the second-order truncation error (0 (Ax)2) with the step size (-Ax) and then, obtain a…

A: The truncation error is O∆x2 and the step size is -∆x

Q: Can you find the stationary points of V and classify each of them by using the 2nd derivative test?

A: Introduction: A real-valued function defined on a closed or bounded interval can have its absolute…

Q: 2 Suppose that A = 3xyz²7 + 2xy³j - x²yzk and p = 3x² - yz. Find, at the point (1,-1, 1), 2.1 Vo,…

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Q: 1) y%= (ans.: max.(1,0.5); min.(-1,-0.5)) 1+ x in (2 3-50,8))

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Q: d) Consider the fourth-order truncation error (0(Ax )4) with the step size Ax and also (-Ax) then,…

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Q: Q4: Find the derivative of the function at P, in the direction of A 2 1) f(x, y) = 2xy-3y², P.…

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: 6. Use a property of derivatives of vector valued functions to show that # [F(t) × F'(t)] = F(t) ×…

A: to show ddtrt→×rt→'=rt→×rt→'' we will use  ddtu→×v→=u→ddtv→+v→ddtu→

Q: cosh r – 1 · (xª4 + 2) +2). Compute the derivative of y = In | (2x + 1)

A: Given problem:-

Q: Find the derivative of the function f (, y, z) = 4ay z at the point (4, 64, 16) in the direction of…

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Q: Calculate the derivative of t2 -k 3 - t F(t) = cos(t) i + 3e2t+2j + |

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Q: 3. Let f(x) = 2x - x². (a) Find the secant line to the graph of f passing through the points (0,0)…

A: We can find equation of secant line and tangent line .

Q: Calculate the derivative of the function. Then find the value of the derivative as specified. 6. V12…

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Q: Use implicit differentiation to find az/ax and az/ay. x² + 4y² + 3z² = 5 ala ala дz ?х ду || ||

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Q: 2. What is the equation of the tangent line to the curve y = x? - 2x +1 at point (3,4)? а. у3 2x — 2…

A: The equation of line is y-y1=mx-x1, where m is the slope of the curve.

Q: c) Consider the third-order truncation error (0 (Ax )³) with the step size Ax and also (-Ax) then,…

A: The truncation error is of order O∆x3 The step length are ∆x, -∆x

Q: 3. Find the derivative of the function f(r, y, ) = xy + yz+ the direction A = 3i + 6j – 2k. zr at…

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Q: Calculate the derivative of the function. Then find the value of the derivative as specified. dr 6.…

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Q: The directional derivative of the function = x? - xyz + y at the point (1, 2, -1) in the direction…

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Q: Find the derivative of y with respect to x, t, or 0, as appropriate. 17) y =x*in x -x3 A) 4x3 - x2…

A: Given, Find derivative of y=x4lnx-13x3 with respect to x

Q: 5. (а) Find the directional derivative of f at P in the direction of ā if f(x,y) = y In(x) ; P(1,4);…

A: To find The directional derivative of f at p in the direction of a.

Q: Find the derivative of y with respect to x. 6x + 7 -1 6. y3-Cos %3D

A: dydx=?