NORMAL TANGENT AND STRAIGHT PLAN   Determine the equations of the tangent plane and parametric equations for the normal line graph of the functions at the specified point

Q: 4. x= 3+4 sine, y = 3cos0-4

A: Note:- I am solving here first 2 parts of this question. Second derivative and draw the figure . But…

Q: 2. x- t2 -1, y = t + t

A: x=t2-1, y=t2+t

Q: 7. x=3+ 4 sine, y 3cose-4

A: From the given problem:   x=3+4sinθ ;y=3cosθ-4   We can write as:   dydx=dydθ×dθdx=dydθdxdθ....(1)…

Q: Equations of tangent linesa. Find an equation of the line tangent to the given curve at a.b. Use a…

A: For x=a=0 we find y So the point is (0,1)

Q: Density distribution A right circular cylinder with height 8 cm and radius 2 cm is filled with…

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Q: Tangent lines Find an equation of the line tangent to the curve at the point corresponding to the…

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Q: Slopes of tangent lines Find the slope of the line tangent to the following polar curves at the…

A: Given:   To find: The slope of the line tangent to the given polar curve at the given point.

Q: Surface area Find the area of the surface generated when the curve ƒ(x) = tan x on [0, π/4] is…

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Q: 51

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Q: Surface area Find the area of the surface generated when the curve ƒ(x) = sin x on [0, π/2] is…

A: Given function and interval are fx=sinx and 0,π2. Compute the derivative. f'x=cosx.

Q: Slopes of tangent lines Find all points at which the following curves have the given slope. x = 2…

A: Given that x=2cost   and  y=8sint. Slope = -1. x=2cost y=8sint dxdt=-2sint dydt=8cost…

Q: 11-18 · Equation of a Tangent Line Find an equation of the tangent line to the curve at the given…

A: Authoring guidelines*****…

Q: Tangent line given Determine the constants b and c such that the line tangent to f(x) = x² + bx + c…

A: Here we have to determine the constant a and b. The given function is f(x)=x2+bx+c…

Q: Distance from a point to a line Find the distance between the given point Q and the given line. Q(5,…

A: Given that: The point Q(5, 6, 1) ; The line defined by the parametric equation x = 1+ 3t , y = 3 -…

Q: Tangent Lines Find equations of all tangent lines to thegraph of f (x) = arctan x that have slope…

A: To find: The equation of all tangent to fx=tan-1x having slope 14. Concept used: The equation of…

Q: Tangent Line Find an equation of the line tangent to thecircle x2 + y2 = 169 at the point (5, 12).

A: To find the equation of the line tangent to the circle

Q: Tangent lines Assume f and g are differentiable on their domains with h(x) = Ag(x)). Suppose the…

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Q: 4. x = VI - i , y = t³ – 3t

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Q: 5. x-1-1 ,y-6-2+름

A: Given: x = 1-1t,  y = 6 -7t +2t2 To find: The second derivative of y with respect to x from the…

Q: 4. x = V1 - t, y = t3 - 3t

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Q: Equations of tangent lines a. Find an equation of the line tangent to the given curve at a. b. Use a…

A: y=exx,  a=1 Differentiating with respect to x, we get dydx=dexdx·x-dxdx·exx2=ex·x-1·exx2=exx-1x2 a).…

Q: Can i get help with this problem step by step please?

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Q: (c) x²y – 4z² = -7 in point P(-3,1,–2)

A: Given x2y-4z2=-7,and the point P-3,1,-2. The tangent plane equation of a function fx,y,z at the…

Q: Find the slope and equation of the tangent line 1. f(x)= -2-x2             (2,-6) 2. f(x)= x-x2…

A: The slope m  of the function fx at a point x1,y1 is the derivative of the function at x1,y1. Then,…

Q: PARAMETRIC EQUATIONS. Find the second derivative of y with respect to x from the parametric…

A: The given parametric equations are: x=1t2, y=t2-4t+1 To find the second derivative of y with respect…

Q: PARAMETRIC EQUATIONS. Find the second derivative of y with respect to x from the parametric…

A: Given: x=t2-3t+4y=t2+4t-5 We know that the derivative of the parametric form is: dydx=dydtdxdt…

Q: Find the equation of the tangent line and normal line to the curve y = (4 + 6x)² at the point (4,…

A: Given equation of curve is We know that slope of tangent line to curve y=f(x) at x=a is f'(a).…

Q: Parametric curvesa. Eliminate the parameter to obtain an equation in x and y.b. Describe the curve,…

A: x=3cos-t, y=3sin-t-1 a). x=3cos-t, y=3sin-t-1⇒cos-t=x3, 3sin-t=y+1 ⇒cost=x3, -sint=y+13…

Q: Hyperbolic relationship in regression equations between variables used in practice and convert…

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Q: 5. x=1-.y= 6-+

A: See the attachment

Q: Plane Area in Rectangular Coordinates Find the area bounded by the given curves. Sketch the curves,…

A: This is a problem of Application of Integral Calculus.

Q: Tangent lines Assume ƒ and g are differentiable on their domainswith h(x) = ƒ(g(x)). Suppose the…

A: Given: f and g are differentiable on their domains with hx=fgxThe equation of the line tangent to…

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Q: PARAMETRIC EQUATIONS. Find the second derivative of y with respect to x from the parametric…

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Q: Equations of tangent linesa. Find an equation of the line tangent to the given curve at a.b. Use a…

A: Given: y=x3-4x2+2x-1; x=2 for finding equation of tangent at given point, we need to find slopem of…

Q: Equations of tangent linesa. Find an equation of the line tangent to the given curve at a.b. Use a…

A:

Q: Two circles of radius 6 are tangent to the graph of y = 4x at the point (1, 2). Find y' at the point…

A: Given : Radius of two circle is 6. And the circles tangent to the graph of  y2 = 4x. At the point…

Q: Part I: PARAMETRIC EQUATIONS. Find the second derivative of y the curve and draw the tangent line…

A: First derivate with respect to t then derivate with respect to x to get desired result

Q: Necessary Conditions What conditions do you think are necessary for there to be a tangent line…

A: the given figure is: we have to determine what condition is necessary for there to be a tangent…

Q: Tangent lines Find an equation of the line tangent to thefollowing curves at the given point.

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Two highways intersect at a right angle. An  car A, moves along one of the highways, approaching the…

A: given that                                         car A approaching intersection at 80kmph,…

Q: Equations of tangent linesa. Find an equation of the line tangent to the given curve at a.b. Use a…

A: Given: The curve y=ex and the point a=ln3 To find: The equation of the line tangent to the given…

Q: CQustion) sketch the curve of the fellowing cuNe Using first derivative and second derivative.show…

A: The given function is, fx=x2-8x+3,     .............(1)             x≠-3 Here the domain of f(x) is…

Q: Slopes of tangent lines Find the slope of the line tangent to the following polar curves at the…

A: Consider the given equation r=4+sinθ and 3,3π2 The polar coordinate is of the form x=rcosθ, y=…

Q: Parametric Equations. Show complete solutions. 1. Find the equation of the tangent line (s) to the…

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Q: Slopes of tangent lines Find the slope of the line tangent to the following polar curves at the…

A: Consider the given polar equation as r=fθ=4cosθ Now differentiate  f'θ=-4sinθ

Q: tangent. is a normal line of the circle. Complete the table with the missing information. POINT OF…

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Q: 3. x =. y = t- 4t +1

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Q: Finding slope Find the slope of the curve

A: Given: 5x-10y= sin x

Q: Equations of tangent linesa. Find an equation of the line tangent to the following curves at…

A: Given the curve y=1+2sinx. We need to find the equation of the tangent line to the following curve…