4.6 Lemma Let a be a curve in R' and let f be a differentiable function on R'. Then d(f(@)) a'(S] = dt

Q: In explicit method of hyperbolic PDES, the second initial condition, the one involving g, gives…

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Q: Find the orthogonal trajectories to the family of curves: x² = C-v'(ln y² –1).

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A: Here it is required to find a curve.

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A: Given there is a smooth (continuously differentiable) curve y = ƒ(x) whose length over the interval…

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Q: Consider f(x, y) =(ax² + by²). Based on the second derivative test, what are the conditions…

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Q: The maximum value of y = sin x, 0 &lt;= x &lt;= 2p, isand occurs at x =__________ .

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Q: 4. Write a script which uses finite difference approximations to compute the first derivative dy/dx…

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Q: Suppose you want to prove that ARST Theorem. If you know that ZR = LX, what else do you need to…

A: In ∆RST  &amp;  ∆XYZ, ∠R≅∠X.

Q: (6) Find the orthogonal trajectories of the 3C cos 0, where C family of curves r being parameter.

A: Answer

Q: Calculate the partial derivative using implicit differentiation for the given figure below

A: Given1w2+x2+1w2+y2=1To find ∂w∂y at (x,y,w)=(1,1,1)

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Q: (6) Find the orthogonal trajectories of the family of curves r = 3C sin 0, where C being parameter.

A: Orthogonal trajectory curve of a family of curve is defined as a curve which intersects every member…

Q: Use forward and backward difference approximations of O(h) and a centered difference approximation…

A: Step:-1 Note:-  1. Forward difference approximation for first derivative f'x ≈fx+h-fxh 2. Backward…

Q: Use Newton's method (2.12.4) to find the minimum value of the lunction f(x) = x + x,x, + (1 + x,)'…

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Q: Find the orthogonal trajectories of the one parameter family of curves ex+e-y=c

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Q: Let f(x, y,z) = z-sin(xy), x t, y Int, z et1. Find derivative of f directly and by using chain rule…

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Q: Find the orthogonal trajectories for the families of curves y+x^2 = w where w is a parameter

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Q: 2. Determine the directional derivative for u = log, x2lnz if it is defined by the direction at dx =…

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Q: 4. Find the differentiation dy. using definition with limit of the following: y = V2x + 1.

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Q: Compute the point of intersection of the curve sinx and x-1 with the help of Bisection method. Ans.…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: 4. Find the orthogonal trajectories of the family of curves: y = ke* %3D

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Q: 7,2 Find the critical noint(s) of al r) and use the Second Derivative Test to classify the

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Q: 7) Use a tangent line approximation with the function g(x)= Jx to estimate 9.2 . %3D

A: topic - tangent line approximation note :as per bartleby guidelines we are supposed to answer only…

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Q: 2. Prove that f(x) = |x + 1] 1| (−1,0) tangent line at has no

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Q: If f has a continuous second derivative on [a, b], then the error E in approximating f(x) dx by the…

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Q: 2. Show that the function psin(2r) e-*dt g(x) = is differentiable on R and compute its derivative.

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Q: a*+1 +1 t4 +1 dt with respect to x. Calculate the derivative ol Jsin(x)

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Q: If we discuss the derivative of the function f(z) = z. Imz by Cauchy- Riemann equations. we see fz)…

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Q: 27. Find the length of the curve Vcos 2t dt y = from x = 0 to x = "/4.

A: The given curve is We know that by Second Fundamental theorem of calculus ,if F(x) is continuous on…

Q: 7) Use a tangent line approximation with the function g(x)= Jx to estimate V9.2

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Q: 5. Compute the derivative, r'(t), of r(t) = (et-4, t, In(1 – t)).

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Q: Find the values of x on [0, 2 ) π where the tangent line of f x( ) be horizontal. y=e^-x (cosx)

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Q: (6) Find the orthogonal trajectories of the family of curves r= 2C sin 0, where C being parameter.

A: See the detailed solution below.