Calculate lim dt.

Q: Calculate the length of the tangent line, normal line, sub-tangent and subnormal from: a. xy² = 18…

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Q: Compute the derivative of g(x)=arctan(x^3+1)

A: From the given data:

Q: Use the Cauchy Integral Formula for Derivatives to compute

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Q: What is the geometric interpretgtron of the derivative f'(a)?

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Q: Use the limit definition of partial derivatives

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Q: Give a vector valued function whose graph is same as y=ln (x)

A: We know that a function with the representation r→t=ft i∧+gt j∧ is called a vector valued function…

Q: Prove that moments are independent of change of origin but not of scale.

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Q: Differentiate the function. y = etan(θ)

A: Given y=etanθ Use chain rule of differentiation to differentiate the given function.

Q: compute the derivative

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Q: Use a linear approximation to estimate V65.

A: 653

Q: Use the Power Rule to compute the derivative: %3D lx=7

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Q: y = In

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Q: Find the derivative dydx of the Archimedean spiral.

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Q: Find the derivative dydx of Galileo’s spiral.

A: To find: Derivative of Galileo's spiral

Q: Vz²+1 ev° dy In a

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Q: find the derivative of arctan 4x/5

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Q: Compute the derivative of f() = arcsin(x² e3x). %3D

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Find the derivative us ing the defini tion O fx). %3D

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Q: 3. y= 1 at point (0, -) X-3

A: To find, equation of tangent line at the given point.

Q: so  by an = 0 ,   does the divergence test apply ?

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Q: To compute fxyz, we first take the partial derivative with respect to which variable?

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Q: Use differentials to give an informal justification for the chain rules for derivatives.

A: Consider the given statement. The chain rule of derivatives is defined as. dydx=dydududx Let's take…

Q: Use the Power Rule to compute the derivative.

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Q: Find the partial derivative. revIlzy

A: We can find the partial derivative as below.

Q: state the limit definition of the derivative

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Q: 1. у %3D 4x2 — 3х — 2.

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Q: Find the equation of the tangent line of funclion y= ²+1 23 -2 at (40,- 73)

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Q: Acrsin a2_v2

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Q: State the limit definition of the derivative.

A: derivative can be defined as below:-

Q: Locate the point where the slope of tangent line to y=In 2x² IS –1- O (-1, In 2) O (-2, In 8) 9. In…

A: Given  y=log(2x2)Slope =dydxdydx=4x2x2=12x

Q: Find the derivative using Implicit differen tiation 3 %3D 3xy? 2

A: Given: x3+y3=3xy2 We have to differentiate above equation using implicit differentiation. In…

Q: Use derivative to show that fx)= In(x²1) %3D is one-to-one.

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Q: Find the slope of the tangent line to the graph of x4 + 5xy - 12x + 11 = dt at the point (1 , 0) on…

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Q: Find where the tangent line to y= (5x-1)2 (4x+7)3 is horizontel.

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Q: Use the limit definition of the derivative to [cos a] = - sin . %3D da

A: Given function, f(x)=cos x

Q: Use a linearization to approximate tan(π/100).

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Q: Find the equation of the tangent line on 3xe™v² - ez 2ye at (1,1)

A: Given  3xexy2-ex3=2yex2first we find dydx at point (1,1)

Q: Use the Fundamental Theorem of Calculus to find the derivative. dt

A: We have to find the derivative by fundamental theorem of calculus.

Q: Find the indicabee.partial. derivative.s

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Q: Find the derivative. (Hint: do chain rule. ) * 12° dt 6x 8x6 12x/2

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Q: Find by implicit dlitferentiathin; That the tangent to the eclipse x =1 at point (torY%) is LoX + Yo…

A: The slope of the curve at any point (x0, y0) is : m = f'(x0, y0)     The equation of a line in slope…

Q: Find the velocity of th

A: We have given a displacement function of a particle : s=1t2 We have to find the velocity  of the…

Q: Find the derivative..thefallowing.vecten. Fumctens. a.. -1 ..... ...

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Q: Compute derivative for the of the

A: Given: hx=log2x232x3

Q: 3. х %3D у* — 2у3 2y3

A: We can find the answer as below using delta method

Q: Find the first and Secord derivatives of fanction

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Q: Calculate the length of the tangent line, normal line, sub-tangent and subnormal from: a. x²+ y²-4x…

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Q: s(w) = In( w - %3D

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Q: In x g(x) = 2

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