Find the equation of the tangent line to the graph of F(r)= 2z²+2r+1 evi dy at r 0. sech z

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A: The equation of the  tangent line for the function f(x) at the point x=a is, y-fa=f'ax-a. The…

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Q: What is the equation of the tangent line to the function y = e-* – arcsin( 2 at x= 0 ? A) y - (1+) =…

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Q: Determine the anti-derivative of Y = 2e3x +5 and use the fact that y(0) = 7 to %3D dx determine c,…

A: We first separate the variables and then integrate  c= integrating constant Formula used:

Q: Find the equation of the line tangent to the graph of y = arctan (sinh(r)) at z = 0. %3!

A: Given: y=arctan(sinh(x)) Since, ddxtan-1fx = 11+fx2f'x Therefore, dydx=11+sinh2xcoshx

Q: I. Find an equation of the tangent line to the graph of t cosh (f² – 1) dt tan-l † | f(x)%3D /1+ln…

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Q: Determine the equation of the tangent line to the graph of g(x) = mz [1 – sin(ne')]dt at the point…

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Q: The linear approximation at x = 0 to sin(3x) is A + Bx where A is: Preview and where B is: Preview

A: Given function:

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Q: nd the points at which f(x) = cos² x has a horizontal tangent line. %3D

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Q: Find an equation of the tangent line of y = e" cos T, at z= 0.

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Q: Find all the critical points of f(2z, v) = - . 1 + 4x – xy? and classify them using the second…

A: The given function is;  f(x)=-x3/3 +4x -xy2.

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Q: Find the equation of the line tangent to the cardioid r = 1+ sin(0) at Ô0 =

A: Given that,, Here, differentiate w.r.t. ,we get, We know that, To find: equation of the line…

Q: What is the equation of the tangent line to the function y = e-* - arcsin) x+1 2. at x= 0 ? A) y-…

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Q: Compute the differential dy  for  y=(6x+sinx)^3

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Q: Find the length of the curve f(x) = ln(sin x), 0 ≤x ≤π/6.

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Q: Find the fourth derivative of f (z) = 2z¬3 Vā lal * sin (a) f(4) (z) =

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Q: 11. Find the length of the curve x = on the interval (2, 4] (integrate with respect to y) 12y3 un

A: Given that the function x =y55+112y3 Find the arc length of the graph of the given curve on the…

Q: I. Find an equation of the tangent line to the graph of 1 t cosh (t² – 1) dt - f (x) = 1 tan-t 1+ln…

A: The given function is fx=∫1+lnx1tcosht2-1tan-1t dt.

Q: What is the derivative of y = sin1 (x² + 2)? dy dr /1-(z²+2)² dy O dr 2x V1-(2²+2)² O dz V1+(x²+2)²…

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Q: Compute the derivative: 4 te* dt d 3z2 L tet dz -1

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Q: Find an equation of the line tangent to graph of y =x2 + sin (Ex) at x=-1. A. 2x - y+2 = 0 B. 2x +…

A: To find the equation of tangent line of the given graph.

Q: Compute the indicated derivative using the chain rule. dy x = 1 - t/3, y = 8t – 1;- dx dy dx

A: x=1-t3 differentiating with respective t dxdt=-13 y=8t-1 differentiating with respective t dydt=8

Q: Find an equation of the tangent line to the graph of f(x) = | t cosh (t² – 1) dt tan-lt 1+In (x) at…

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Q: Determine the equation of the tangent line to the graph of g(x) = | [1- sin(re')] dt at the /In x…

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Q: Use implicit differentiation to find dz/ yz = 5 In(x + z) az dz dy II

A: The given equation is yz=5lnx+z Differentiate the given equation partially with respect to x.…

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Q: Find the point of intersection of the tangent line to v=sin(2r) at y=0 and the line %3D x+2y=5.

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Q: Find the derivative dy dx || dy dx of the function y = sec (₁ +√4+ sin ¹(4 + ²))

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Q: Find the slope of the tangent line to the graph of f(x) = x· 2e*cos-1t dt at x = 1 Jln x

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Q: Find the equation of the tangent plane to z = ln(2x + y) at −1,3

A: Find the equation of the tangent plane to z = ln(2x + y) at −1,3

Q: Determine the equation of the tangent line to the graph of g(x) = Sm, [1 – sin(ne')]dt at %3D In x…

A: We have to find the equation of the tangent line to the graph of gx=∫lnx01-sinπetdt at the point…

Q: +Inz 1. Determine the equation of the tangent line to the graph of f(r) = | V3 + 5t5 dt at x = 1.…

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Q: Find the slope of the tangent line to the graph of f(x) 2e'cos-1t dt at x = 1. In x = X'

A: Find the slope with the help of derivative of f(x) at x=1 .

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Q: Repeat Exercise 60, except with these derivative boundary conditions: y'(0) = 0, y'(π) = 1. In part…

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Q: Find the derivative dy/dx of the Archimedean spiral.

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Q: The second derivative d^2y/dx^2 of y^3 = xy + 1 at the point (0,1) is

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