Show that UV=12 given, UX = 8, and XY = 10 using the intersecting %3D Secant-Tangent Theorem. * U

Q: Plot along with its tangent r = -6ecos0 + 8 cos 40 in %3D 4

A: We knowx = rcosθy = rsinθGiven: r = -6ecosθ+8cos4θ                     Where θ∈0,2π     Hence, x =…

Q: Find Equatien of the tavgnt lin tu th cuve at tk giver pointe y= sec X ,

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Q: use implicit differentiation to find dy/dxin terms of x and y .

A: We have to find implicit derivative (dy/dx) of the curve .Information is given below:

Q: Evaluate and determine its particular antiderivative whose x-intercept is 3. y = arcsin () y =…

A: We have to find the particular antiderivative .

Q: Find the points on the cardioid r = 1−cosθ at which there is a horizontal tangent line, a vertical…

A: Consider the given: r=1−cosθWrite the cartesian…

Q: Prove the formula for the derivative of a) (Inverse of cotangent) b) (Hyperbolic cosecant) y = csch…

A: formula for derivative of both function is following:-

Q: Exercise (c) Show that y = Vx has a vertical tangent line at (0, 0). ...

A: first we will find derivative of function. So, derivative will be slope of tangent. for vertical…

Q: 2. Find the coordinate of the points on the cardioid r=1- cose at which there is a horizontal…

A: We are given the polar curve: r = 1- cosθ use formula:         x=r cosθy=r sinθ then,  dxdθ=-sinθ+2…

Q: Let f(x,y)=x^3-cosy. Find the tangent plan for f(x,y) based at (1,pi).

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Q: Get the partial derivatives δω θω дх’ ду δω given that Əz w = Arc sin (x² + y) — tan 2z + 1 and

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Q: Use first principle rule and prove that dy if y= secl tann = secx

A: To Prove: That the derivative of y=sec x is dydx=sec x·tan x. Concept used: First principle: The…

Q: Let fex) = %3D a) Find Xo tangent lir (Xo , f(Xo) b) Find the in a).

A: f(x)=kx2+C Tangent lines to the graph at (x0,f(x0)) and (-x0,f(-x0)) we know that when the tangent…

Q: Compute dx using the -1 (a) Trapezoidal rule (b) Trapezoidal rule with end corrections using the…

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Q: The angle between tangent and the radius vector of the curve r 5(1- sin@) at 0= is %3D

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Q: Find the equation of the tangent line to the parametric curve at (1, 3). z =1+ Int y = t +2

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Q: Let fcxry)= 2X sinly)+3X Cos CY ). Find the tangent Plane at the point 2,0).Use the tangent Plane to…

A: In this question, concept of tangent plane at any point is applied. Tangent Plane Naturally, it…

Q: Use first principle rule and proue that dy = if y= secn tand %3D secxo

A: Proving using first principle rule.

Q: find the to the the tang horizontal. X-volves at which the _9x+2 Y = ex curve ent

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Q: Find the tangent plane to the equation 3y cos(4x – 2y) at the point (2,4,12) Z =

A: Z=3ycos(4x-2y)  Point= (2,4,12)

Q: Sketch the regions enclosed by the given curves. y=6 cos(4x), y= 6 sin(8x), x - 0, x = T/B y…

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Q: Find the tangent plane to the equation 5y cos(2x – 4y) at the point (4, 2, 10). - = Z z =

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Q: A-Estimate J, 2e-3* dx using trapezoidal rule with four subinterval round your answer to one decimal…

A: Given is the integral  ∫-11 2e-3xdx The aim is evaluate the integral using trapezoidal rule.

Q: Find the tangent plane to the equation z = 6y cos(4x – 2y) at the point (2,4,24) Z =

A: It is given that z=6ycos4x-2y and the point is 2,4,24. Recall the fact that if the equation of the…

Q: Use the Trapezium Rule with four strips to estimate the value of: dz. (In z)² Give your answer…

A: Use the formula of the Trapezium Rule to solve the integral. This rule is used to solve the integral…

Q: Eliminate the parameter to express the curve in the form y = ƒ(x) . x = cos t, y = tan t

A: Given that, x=cost, y=tant We have to eliminate the t and express curve in the form y=f(x). As we…

Q: Use implicit differentiation to find y' for 5a'y + In (ry') = 5. %3D y' Preview

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Q: Compute . dx using the (a) Trapezoidal rule (b) Trapezoidal rule with end corrections using the…

A: The given integral is

Q: Use an appropriate local linear approximation to estimate the value of the given quantity. tan…

A: Here is the solution

Q: Find the equation of the tangent line to the parametric curve at the indicated point. Show all work.…

A: Equation of tangent line : y - y0 = m ( x - x0 ) m is the slope of tangent line .

Q: Sketch the regions enclosed by the given curves. y = 2 cos(5x), y 2 sin(10x), x = 0, x = 1/10 2.0…

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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…

Q: Find in terms of x and y if arctan(r + x²y) = ry

A: Given that         arctan(x+x2y) = xy We have to find dy/dx in terms of x and y.

Q: Use Implici+ Differentiation to fing dy X Siny + cos2y = cos y

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Q: 5, find dt when r = 3. dt Let A be the area of a circle with radius r. If %3D %3D

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Q: Find arc length of vactor  valued function r(t)=ti+4tj+3tk over(0,1)

A: r(t)=ti+4tj+3tk over(0,1)

Q: Find the curvature of y = sin(-lx) at x = .

A: Solution:-

Q: a) Find the equation of tangent line of curve that is given by parametric equations x = 3cost + sint…

A: The slope of the tangent at a point on the curve, y=f(x) is equal to the first derivative of the…

Q: Find the exact length of the cur curve. y = Vx- x2 + - sin (V)

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Q: Use an appropriate local linear approximation to estimate the value of the given quantity. tan…

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Q: x = 1+ vt, y = et X =1+1 Y. %3D

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Q: Find the area inside the larger loop and outside the smaller loop of the curve + sin(0) 2

A: To find the area inside the larger loop and outside the smaller loop of the below curve. r=12+sinθ

Q: what  is the arc length of the parametric curve x=cos2 θ y=cosθ and  θ  is bounded between 0 and π/2

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Q: Sketch the cardioid r = 3 cos 0 and find the coordinates of the points on the cardioid where the…

A: Given polar equation is r=3cosθ

Q: Find the derivative dydx of the polar function r=sec(2θ) at θ=π4

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Q: \ Compute dx using the (a) Trapezoidal rule

A: 6.(a)  Given function is ∫-11e-x2dx Trapezoidal rule ∫abfxdx≈∆x2fx0+2fx1+2fx2+2fx3+........+fxn…

Q: Find all the points where r = 4 + 2sin(theta) has verticle and horizontal tangent lines.

A: Find the points on the vertical and horizontal tangent lines.

Q: Show that the function f(z)=sin x coshy+I cosx sinh y  is continuous as well as analytic every where

A: