Use the definition of the hyperbolic functions to prove that 2cosh (x)-1=cosh(2x).

Q: find an equation of the tangent plane at the given point. f (x, y) = ln(4x2 − y2), (1, 1)

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Q: Find the tangent line to the function f (x) = x² – 4x + 5 at the point (3,2).

A: To find: The tangent line to function fx=x2-4x+5 at the point 3,2. Formula used: The slope of…

Q: Determine the equation of the tangent line and the quadratic approximation to the function z = e2"…

A: Given function is: z=e2x To find the equation of the tangent at a point x=x0 to curve y=fx,…

Q: Find the equation of the tangent line to the graph of f(x) = 2x² –In Vx at X = 1. %3D

A: First we differentiate to find the slope then use formula to find the equation

Q: Find an equation of the tangent plane to the graph of f(x, y) = 4x² – 7xy2 at the point (7, 8) z =

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Q: Find an equation of the tangent plane to the graph of f(x, y) = In(4x² – 2y2) at the point (1, 1). z…

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Q: Find an equation of the tangent line to f (x) = x² Vx4 – 12 at x = 2. - %3D

A: Explained below

Q: Find the slope and equation of the tangent line to f(z) = 5- 2z at a = 2 using the definition.

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Q: Does the graph of Sx²sin (1/x), x ± 0 f(x) = lo, x = 0 have a tangent line at the origin? Give…

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Q: Find the question of the that is tangent to the curve y=-3 cos2x at x= n/6. Express with exact…

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Q: Find the equation of the tangent line to the function f(x) = -3x2 – 2x at the point where x form y =…

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Q: If tanh x = 12/13  find the values of the other hyperbolic functions at x

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Q: Find the equation of the tangent line of f(x) = 8/x+3 at the point (4, 19) . Express your answer in…

A: Find the equation of the tangent line of fx=8x+3 at the pint (4,19).

Q: Define a function f : R² → R² by f 2.у 1. Show that f is differentiable on A = E R² |x > 0, y > 0}…

A: To show that the function f defined as below is differentiable on A and compute its derivative

Q: ) Find the equation of the tangent line ETL for f(x) = x³ - 2x +1 at x = −1

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Q: Find the equation of the tangent line of f(x) = x⁴ + 2x at x = 1 using the limits definition.

A: The function is fx=x4+2x and x=1.  Find the derivative of the function fx=x4+2x using the limit…

Q: is the equation af tangent line at X=/ y = mx+b. to the giaph of f c) =x² -x at x=/ m%= b.

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Q: Find the point where the CAUCHY- RIEMANN equation is satisied for the function f(2) =xy+Xyi

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Q: Find all values of x, xe[0,2n] where f(x) = secx has a horizontal tangent line

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Q: Let f(r, y) = - (5x² + 4xy+ y²). Then an implicit equation for the tangent plane to the graph of f…

A: Given function is, fx,y=−5x2+4xy+y2 To find the implicit equation of tangent plane to the graph of f…

Q: Find the derivative of the function at Po in the direction of A. 1- f(x, y) = 2xy - 3y² , Po ( 5,5),…

A: As per our guideline we are supposed to answer only one question you can repost other in next…

Q: Find the derivative. F(t) = In(sinh(2t)) %3D F'(t) %3D

A: Find the derivative of the function

Q: Find an equation of the tangent plane to z=ln(2x+3y) at the point (1, 1, ln5).

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Q: Find an equation of the tangent plane to the graph of f(x, y) = In(4x² – 2y2) at the point (1, 1).

A: To Determine: FInd the equation of tangent plane to the graph of…

Q: Find the derivative of the function at Po in the direction of u. f(x, y) = In( 6 x - 3 y), Po(-7, -4…

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Q: Verify the differentiation formula.

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Q: Find the equation of the tangent line to the curvef (x) = -x' + 2x at x = 1. о Тx) 3D 1 + (-1)(х —…

A: To find the equation of tangent line to the curve at x=1

Q: Assuming y cos (3xz) = 5 defines z as a function of x and y. Differentiate

A: we have to derivative

Q: use the fundamental theorem of calculus to find the derivative of y=intergral of cos(t)/t^10, from…

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Q: Find the equation of the tangent line to f(x) = 8x² – 5x – 40 at (3,17). %3D

A: Solution of the problem as follows

Q: The tangent line to the curve ³ + y³ = 9xy at the point (4,2) intersects the y-axis at y = -1. -2.…

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Q: Let z = x+iy and f(2)=√√|xy|. Show that ƒ(z) satisfies the Cauchy-Riemann equations at the origin,…

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Q: 1 Use the definition of the hyperbolic functions to prove the identity 1– - = tanh?(2x) cosh?(2x)

A: Explanation of the answer is as follows

Q: Find f(4) and f' (4), assuming that the tangent line to y = f(x) at a = 4 is y = -6x + 2. %3D

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Q: Find the equation of the fangent line to the graph of the function f (z) sin (3,/7) at the point…

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Q: - Find the derivative of each Funeton of this by definition. 3 atx= 3 2 ソ=Vメナ1 ② ソーシィナ at メーネ V2X-3…

A: Since you have posted multiple questions so we solve the first three for you, to get the remaining…

Q: Use the Intermediate Theorem show that there is a root of the given equation: sin a - x between…

A: Intermediate value Theorem states that if f is continuous on the interval (a ,b ) and L is a number…

Q: I* cos z lim 1³+2

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Q: tanh" (cose 3x

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Q: Use Secant method with p0 =1, p2 = 1.2 to find the root of f(x)= Inx - cosx that is accurate to…

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Q: Find the slope and equation of the tangent line to f(r) = 3+3x at a 3 using the definition. %3D

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Q: Find the absolute maximum of the function. fAx) = sin(6x) + cos(6x) on the interval 0. 18 %3D

A: Given: f(x)=sin(6x)+cos(6x) Differentiae the function.…

Q: 1 Use the definition of the hyperbolic functions to prove the identity 1- - tanh? (2x) cosh (2x)

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Q: Show that the function f(z)=sin x cosh y+i cosx sinh y is continious as well as analytic every…

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Q: Show that the derivative of f(x) = 2/x+3 is J (4) = VI ob no using the definition of the derivative.…

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Q: Q1) A) Find the tangent equation for the function: f(x) = Vx2 + 5 at =2 ? %3D B) Find the limits by…

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